Problems related to technologies for protecting spacecraft from extreme
temperatures during re-entry, along with their answers: Mathematical
Problems on Spacecraft Thermal Protection Systems for Re-entry
1. If a spacecraft's heat shield can withstand 2000°C for 10 minutes, how long can it withstand
1000°C assuming linear temperature-time relationship?
A) 5 minutes B) 20 minutes C) 15 minutes D) 25 minutes
Answer: B) 20 minutes
2. A thermal protection tile weighs 2.5 kg and covers an area of 0.5 m². How many tiles are needed to
cover a spacecraft with a surface area of 15 m²?
A) 25 B) 30 C) 35 D) 40
Answer: B) 30
3. If the heat flux during re-entry peaks at 1.5 MW/m², what is the total heat input on a 10 m² heat
shield over 5 minutes?
A) 4500 MJ B) 2250 MJ C) 3750 MJ D) 5000 MJ
Answer: A) 4500 MJ
4. A spacecraft's velocity decreases from 7.8 km/s to 3 km/s during re-entry. What percentage of its
initial kinetic energy is converted to heat?
A) 61.5% B) 85.2% C) 76.8% D) 92.3%
Answer: C) 76.8%
5. If a heat shield's thermal conductivity is 0.1 W/(m·K) and its thickness is 5 cm, what is the
temperature difference across the shield when the heat flux is 500 kW/m²?
A) 2500°C B) 1500°C C) 3000°C D) 2000°C
Answer: A) 2500°C
6. A spacecraft with a mass of 5000 kg experiences a deceleration of 50 m/s² during re-entry. What is
the force acting on the spacecraft?
A) 200 kN B) 250 kN C) 300 kN D) 350 kN
Answer: B) 250 kN
7. If the specific heat capacity of a heat shield material is 1000 J/(kg·K) and its mass is 100 kg, how
much energy is required to raise its temperature by 500°C?
A) 25 MJ B) 50 MJ C) 75 MJ D) 100 MJ
Answer: B) 50 MJ
8. A spacecraft's heat shield ablates at a rate of 0.1 mm/s. If the initial thickness is 20 mm, how long
will it last before being completely consumed?
A) 100 s B) 150 s C) 200 s D) 250 s
Answer: C) 200 s
9. If the emissivity of a thermal protection system is 0.8 and it radiates 1 MW/m² at temperature T,
what is T according to Stefan-Boltzmann law? (σ = 5.67 × 10⁻⁸ W/(m²·K⁴))
A) 1639 K B) 1823 K C) 2011 K D) 2205 K
Answer: B) 1823 K
10. A spacecraft's heat shield has a thermal diffusivity of 5 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 2 cm thick layer?
A) 400 s B) 600 s C) 800 s D) 1000 s
Answer: C) 800 s
11. If a heat shield tile expands by 0.1% when heated to 1000°C, what is its coefficient of thermal
expansion?
A) 1 × 10⁻⁶ /°C B) 5 × 10⁻⁶ /°C C) 1 × 10⁻⁵ /°C D) 5 × 10⁻⁵ /°C
Answer: C) 1 × 10⁻⁵ /°C
12. A spacecraft experiences a heat load of 100 MJ/m² during re-entry. If its heat shield has a heat
capacity of 2 MJ/(m²·K), what is the temperature rise assuming no heat loss?
A) 25°C B) 50°C C) 75°C D) 100°C
Answer: B) 50°C
13. If the drag coefficient of a spacecraft during re-entry is 1.2 and its frontal area is 10 m², what is
the drag force at an altitude where the air density is 1 × 10⁻⁴ kg/m³ and velocity is 5 km/s?
A) 10 kN B) 15 kN C) 20 kN D) 25 kN
Answer: B) 15 kN
14. A thermal protection system can withstand a maximum stress of 100 MPa. If it experiences a
thermal gradient of 1000°C/cm and has a thermal expansion coefficient of 5 × 10⁻⁶ /°C, what is the
maximum allowable Young's modulus?
A) 100 GPa B) 150 GPa C) 200 GPa D) 250 GPa
Answer: C) 200 GPa
15. If a spacecraft's kinetic energy is reduced by 90% during re-entry and 80% of this energy goes into
heating the thermal protection system, how much energy (as a percentage of initial kinetic energy) is
available for other processes?
A) 10% B) 18% C) 28% D) 38%
Answer: B) 18%
16. A heat shield tile has a thermal conductivity that varies with temperature according to k = 0.1 +
0.0002T W/(m·K), where T is in °C. What is the average thermal conductivity between 20°C and
1020°C?
A) 0.15 W/(m·K) B) 0.20 W/(m·K) C) 0.25 W/(m·K) D) 0.30 W/(m·K)
Answer: B) 0.20 W/(m·K)
17. If a spacecraft's heat shield mass is 15% of the total spacecraft mass, and the total mass is 6000
kg, what is the heat shield mass?
A) 600 kg B) 750 kg C) 900 kg D) 1050 kg
Answer: C) 900 kg
18. A spacecraft experiences a deceleration of 40 m/s² for 3 minutes during re-entry. What is its
change in velocity?
A) 5.2 km/s B) 6.2 km/s C) 7.2 km/s D) 8.2 km/s
Answer: C) 7.2 km/s
19. If the heat of ablation for a thermal protection material is 20 MJ/kg and the heat flux during re-
entry is 10 MW/m², what is the ablation rate in mm/s for a material with density 1600 kg/m³?
A) 0.25 mm/s B) 0.3125 mm/s C) 0.375 mm/s D) 0.4375 mm/s
Answer: B) 0.3125 mm/s
20. A spacecraft's heat shield has a mass of 500 kg and specific heat capacity of 1200 J/(kg·K). If it
absorbs 300 MJ of heat during re-entry, what is its temperature increase?
A) 400°C B) 450°C C) 500°C D) 550°C
Answer: C) 500°C
21. If a thermal protection system has an emissivity of 0.9 and radiates 2 MW/m² at a temperature of
2000 K, what is the Stefan-Boltzmann constant to two significant figures?
A) 5.6 × 10⁻⁸ W/(m²·K⁴) B) 5.8 × 10⁻⁸ W/(m²·K⁴) C) 6.0 × 10⁻⁸ W/(m²·K⁴) D) 6.2 × 10⁻⁸ W/(m²·K⁴)
Answer: A) 5.6 × 10⁻⁸ W/(m²·K⁴)
22. A spacecraft's heat shield loses 2 kg of mass during re-entry. If the heat of ablation is 15 MJ/kg,
how much energy was absorbed by the ablation process?
A) 20 MJ B) 25 MJ C) 30 MJ D) 35 MJ
Answer: C) 30 MJ
23. If a thermal protection tile has a thermal expansion coefficient of 3 × 10⁻⁶ /°C and expands by 0.3
mm when heated, what was its original length if the temperature change was 500°C?
A) 150 mm B) 175 mm C) 200 mm D) 225 mm
Answer: C) 200 mm
24. A spacecraft's heat shield has a thermal conductivity of 0.2 W/(m·K) and thickness of 10 cm. If
the outer surface is at 1500°C and the inner surface at 50°C, what is the heat flux through the shield?
A) 290 kW/m² B) 310 kW/m² C) 330 kW/m² D) 350 kW/m²
Answer: A) 290 kW/m²
25. If a heat shield tile has a density of 200 kg/m³ and a specific heat capacity of 1000 J/(kg·K), what
is its volumetric heat capacity?
A) 100 kJ/(m³·K) B) 150 kJ/(m³·K) C) 200 kJ/(m³·K) D) 250 kJ/(m³·K)
Answer: C) 200 kJ/(m³·K)
26. A spacecraft enters the atmosphere at 11 km/s and experiences a constant deceleration until it
reaches 300 m/s. If the deceleration takes 5 minutes, what is the average deceleration?
A) 35.8 m/s² B) 35.8 g C) 3.58 g D) 3.58 m/s²
Answer: A) 35.8 m/s²
27. If a heat shield's emissivity increases from 0.7 to 0.9 due to surface changes during re-entry, by
what factor does its radiative heat dissipation capability increase at a given temperature?
A) 1.14 B) 1.22 C) 1.29 D) 1.36
Answer: C) 1.29
28. A thermal protection system uses phase change material that absorbs 400 kJ/kg during melting. If
the total heat input during re-entry is 80 MJ and the heat shield mass is 500 kg, what percentage of
the material undergoes phase change?
A) 30% B) 35% C) 40% D) 45%
Answer: C) 40%
29. If a spacecraft's kinetic energy decreases from 50 GJ to 10 GJ during re-entry, and 75% of the
energy difference goes into heating the thermal protection system, how much heat does the system
absorb?
A) 20 GJ B) 25 GJ C) 30 GJ D) 35 GJ
Answer: C) 30 GJ
30. A heat shield tile has a thermal diffusivity of 4 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 5 cm thick layer?
A) 1562.5 s B) 2500 s C) 3125 s D) 3750 s
Answer: C) 3125 s
31. If a spacecraft's heat shield can withstand a maximum heat flux of 1.2 MW/m² and the actual
heat flux during re-entry peaks at 900 kW/m², what is the safety factor?
A) 1.2 B) 1.33 C) 1.5 D) 1.67
Answer: B) 1.33
32. A thermal protection system uses a material with a density of 300 kg/m³. If the heat shield has a
surface area of 20 m² and a thickness of 5 cm, what is its mass?
A) 250 kg B) 275 kg C) 300 kg D) 325 kg
Answer: C) 300 kg
33. If the temperature of a heat shield increases from 20°C to 1520°C in 2 minutes, what is the
average rate of temperature increase?
A) 10°C/s B) 12.5°C/s C) 15°C/s D) 17.5°C/s
Answer: B) 12.5°C/s
34. A spacecraft with a mass of 4000 kg experiences a drag force of 200 kN during re-entry. What is
its deceleration?
A) 40 m/s² B) 45 m/s² C) 50 m/s² D) 55 m/s²
Answer: C) 50 m/s²
35. If a heat shield's thermal conductivity increases by 5% for every 100°C rise in temperature, what
is its thermal conductivity at 1000°C if it was 0.2 W/(m·K) at 0°C?
A) 0.28 W/(m·K) B) 0.30 W/(m·K) C) 0.32 W/(m·K) D) 0.34 W/(m·K)
Answer: C) 0.32 W/(m·K)
36. A spacecraft's heat shield has a mass of 600 kg and absorbs 90 MJ of heat during re-entry. If its
temperature rises by 250°C, what is its specific heat capacity?
A) 500 J/(kg·K) B) 550 J/(kg·K) C) 600 J/(kg·K) D) 650 J/(kg·K)
Answer: C) 600 J/(kg·K)
37. If a thermal protection tile expands by 0.15% when heated from 20°C to 1020°C, what is its
coefficient of thermal expansion?
A) 1.5 × 10⁻⁶ /°C B) 2.0 × 10⁻⁶ /°C C) 2.5 × 10⁻⁶ /°C D) 3.0 × 10⁻⁶ /°C
Answer: A) 1.5 × 10⁻⁶ /°C
38. A spacecraft's velocity decreases from 10 km/s to 2 km/s during re-entry. What percentage of its
initial kinetic energy is converted to heat?
A) 80% B) 84% C) 88% D) 96%
Answer: D) 96%
39. If a heat shield material has a thermal diffusivity of 3 × 10⁻⁷ m²/s and a thermal conductivity of
0.3 W/(m·K), what is its volumetric heat capacity?
A) 0.5 MJ/(m³·K) B) 1.0 MJ/(m³·K) C) 1.5 MJ/(m³·K) D) 2.0 MJ/(m³·K)
Answer: B) 1.0 MJ/(m³·K)
40. A spacecraft experiences a constant deceleration of 30 m/s² during re-entry. How long does it
take to reduce its velocity from 7.5 km/s to 0.5 km/s?
A) 200 s B) 233 s C) 266 s D) 300 s
Answer: B) 233 s
. A spacecraft with a mass of 5000 kg experiences a deceleration of 50 m/s² during re-entry. What is
the force acting on the spacecraft?
A) 200 kN B) 250 kN C) 300 kN D) 350 kN
Answer: B) 250 kN
7. If the specific heat capacity of a heat shield material is 1000 J/(kg·K) and its mass is 100 kg, how
much energy is required to raise its temperature by 500°C?
A) 25 MJ B) 50 MJ C) 75 MJ D) 100 MJ
Answer: B) 50 MJ
8. A spacecraft's heat shield ablates at a rate of 0.1 mm/s. If the initial thickness is 20 mm, how long
will it last before being completely consumed?
A) 100 s B) 150 s C) 200 s D) 250 s
Answer: C) 200 s
9. If the emissivity of a thermal protection system is 0.8 and it radiates 1 MW/m² at temperature T,
what is T according to Stefan-Boltzmann law? (σ = 5.67 × 10⁻⁸ W/(m²·K⁴))
A) 1639 K B) 1823 K C) 2011 K D) 2205 K
Answer: B) 1823 K
10. A spacecraft's heat shield has a thermal diffusivity of 5 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 2 cm thick layer?
A) 400 s B) 600 s C) 800 s D) 1000 s
Answer: C) 800 s
11. If a heat shield tile expands by 0.1% when heated to 1000°C, what is its coefficient of thermal
expansion?
A) 1 × 10⁻⁶ /°C B) 5 × 10⁻⁶ /°C C) 1 × 10⁻⁵ /°C D) 5 × 10⁻⁵ /°C
Answer: C) 1 × 10⁻⁵ /°C
12. A spacecraft experiences a heat load of 100 MJ/m² during re-entry. If its heat shield has a heat
capacity of 2 MJ/(m²·K), what is the temperature rise assuming no heat loss?
A) 25°C B) 50°C C) 75°C D) 100°C
Answer: B) 50°C
13. If the drag coefficient of a spacecraft during re-entry is 1.2 and its frontal area is 10 m², what is
the drag force at an altitude where the air density is 1 × 10⁻⁴ kg/m³ and velocity is 5 km/s?
A) 10 kN B) 15 kN C) 20 kN D) 25 kN
Answer: B) 15 kN
14. A thermal protection system can withstand a maximum stress of 100 MPa. If it experiences a
thermal gradient of 1000°C/cm and has a thermal expansion coefficient of 5 × 10⁻⁶ /°C, what is the
maximum allowable Young's modulus?
A) 100 GPa B) 150 GPa C) 200 GPa D) 250 GPa
Answer: C) 200 GPa
15. If a spacecraft's kinetic energy is reduced by 90% during re-entry and 80% of this energy goes into
heating the thermal protection system, how much energy (as a percentage of initial kinetic energy) is
available for other processes?
A) 10% B) 18% C) 28% D) 38%
Answer: B) 18%
16. A heat shield tile has a thermal conductivity that varies with temperature according to k = 0.1 +
0.0002T W/(m·K), where T is in °C. What is the average thermal conductivity between 20°C and
1020°C?
A) 0.15 W/(m·K) B) 0.20 W/(m·K) C) 0.25 W/(m·K) D) 0.30 W/(m·K)
Answer: B) 0.20 W/(m·K)
17. If a spacecraft's heat shield mass is 15% of the total spacecraft mass, and the total mass is 6000
kg, what is the heat shield mass?
A) 600 kg B) 750 kg C) 900 kg D) 1050 kg
Answer: C) 900 kg
18. A spacecraft experiences a deceleration of 40 m/s² for 3 minutes during re-entry. What is its
change in velocity?
A) 5.2 km/s B) 6.2 km/s C) 7.2 km/s D) 8.2 km/s
Answer: C) 7.2 km/s
19. If the heat of ablation for a thermal protection material is 20 MJ/kg and the heat flux during re-
entry is 10 MW/m², what is the ablation rate in mm/s for a material with density 1600 kg/m³?
A) 0.25 mm/s B) 0.3125 mm/s C) 0.375 mm/s D) 0.4375 mm/s
Answer: B) 0.3125 mm/s
20. A spacecraft's heat shield has a mass of 500 kg and specific heat capacity of 1200 J/(kg·K). If it
absorbs 300 MJ of heat during re-entry, what is its temperature increase?
A) 400°C B) 450°C C) 500°C D) 550°C
Answer: C) 500°C
21. If a thermal protection system has an emissivity of 0.9 and radiates 2 MW/m² at a temperature of
2000 K, what is the Stefan-Boltzmann constant to two significant figures?
A) 5.6 × 10⁻⁸ W/(m²·K⁴) B) 5.8 × 10⁻⁸ W/(m²·K⁴) C) 6.0 × 10⁻⁸ W/(m²·K⁴) D) 6.2 × 10⁻⁸ W/(m²·K⁴)
Answer: A) 5.6 × 10⁻⁸ W/(m²·K⁴)
22. A spacecraft's heat shield loses 2 kg of mass during re-entry. If the heat of ablation is 15 MJ/kg,
how much energy was absorbed by the ablation process?
A) 20 MJ B) 25 MJ C) 30 MJ D) 35 MJ
Answer: C) 30 MJ
23. If a thermal protection tile has a thermal expansion coefficient of 3 × 10⁻⁶ /°C and expands by 0.3
mm when heated, what was its original length if the temperature change was 500°C?
A) 150 mm B) 175 mm C) 200 mm D) 225 mm
Answer: C) 200 mm
24. A spacecraft's heat shield has a thermal conductivity of 0.2 W/(m·K) and thickness of 10 cm. If
the outer surface is at 1500°C and the inner surface at 50°C, what is the heat flux through the shield?
A) 290 kW/m² B) 310 kW/m² C) 330 kW/m² D) 350 kW/m²
Answer: A) 290 kW/m²
25. If a heat shield tile has a density of 200 kg/m³ and a specific heat capacity of 1000 J/(kg·K), what
is its volumetric heat capacity?
A) 100 kJ/(m³·K) B) 150 kJ/(m³·K) C) 200 kJ/(m³·K) D) 250 kJ/(m³·K)
Answer: C) 200 kJ/(m³·K)
26. A spacecraft enters the atmosphere at 11 km/s and experiences a constant deceleration until it
reaches 300 m/s. If the deceleration takes 5 minutes, what is the average deceleration?
A) 35.8 m/s² B) 35.8 g C) 3.58 g D) 3.58 m/s²
Answer: A) 35.8 m/s²
27. If a heat shield's emissivity increases from 0.7 to 0.9 due to surface changes during re-entry, by
what factor does its radiative heat dissipation capability increase at a given temperature?
A) 1.14 B) 1.22 C) 1.29 D) 1.36
Answer: C) 1.29
28. A thermal protection system uses phase change material that absorbs 400 kJ/kg during melting. If
the total heat input during re-entry is 80 MJ and the heat shield mass is 500 kg, what percentage of
the material undergoes phase change?
A) 30% B) 35% C) 40% D) 45%
Answer: C) 40%
29. If a spacecraft's kinetic energy decreases from 50 GJ to 10 GJ during re-entry, and 75% of the
energy difference goes into heating the thermal protection system, how much heat does the system
absorb?
A) 20 GJ B) 25 GJ C) 30 GJ D) 35 GJ
Answer: C) 30 GJ
30. A heat shield tile has a thermal diffusivity of 4 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 5 cm thick layer?
A) 1562.5 s B) 2500 s C) 3125 s D) 3750 s
Answer: C) 3125 s
31. If a spacecraft's heat shield can withstand a maximum heat flux of 1.2 MW/m² and the actual
heat flux during re-entry peaks at 900 kW/m², what is the safety factor?
A) 1.2 B) 1.33 C) 1.5 D) 1.67
Answer: B) 1.33
32. A thermal protection system uses a material with a density of 300 kg/m³. If the heat shield has a
surface area of 20 m² and a thickness of 5 cm, what is its mass?
A) 250 kg B) 275 kg C) 300 kg D) 325 kg
Answer: C) 300 kg
33. If the temperature of a heat shield increases from 20°C to 1520°C in 2 minutes, what is the
average rate of temperature increase?
A) 10°C/s B) 12.5°C/s C) 15°C/s D) 17.5°C/s
Answer: B) 12.5°C/s
34. A spacecraft with a mass of 4000 kg experiences a drag force of 200 kN during re-entry. What is
its deceleration?
A) 40 m/s² B) 45 m/s² C) 50 m/s² D) 55 m/s²
Answer: C) 50 m/s²
35. If a heat shield's thermal conductivity increases by 5% for every 100°C rise in temperature, what
is its thermal conductivity at 1000°C if it was 0.2 W/(m·K) at 0°C?
A) 0.28 W/(m·K) B) 0.30 W/(m·K) C) 0.32 W/(m·K) D) 0.34 W/(m·K)
Answer: C) 0.32 W/(m·K)
36. A spacecraft's heat shield has a mass of 600 kg and absorbs 90 MJ of heat during re-entry. If its
temperature rises by 250°C, what is its specific heat capacity?
A) 500 J/(kg·K) B) 550 J/(kg·K) C) 600 J/(kg·K) D) 650 J/(kg·K)
Answer: C) 600 J/(kg·K)
37. If a thermal protection tile expands by 0.15% when heated from 20°C to 1020°C, what is its
coefficient of thermal expansion?
A) 1.5 × 10⁻⁶ /°C B) 2.0 × 10⁻⁶ /°C C) 2.5 × 10⁻⁶ /°C D) 3.0 × 10⁻⁶ /°C
Answer: A) 1.5 × 10⁻⁶ /°C
38. A spacecraft's velocity decreases from 10 km/s to 2 km/s during re-entry. What percentage of its
initial kinetic energy is converted to heat?
A) 80% B) 84% C) 88% D) 96%
Answer: D) 96%
39. If a heat shield material has a thermal diffusivity of 3 × 10⁻⁷ m²/s and a thermal conductivity of
0.3 W/(m·K), what is its volumetric heat capacity?
A) 0.5 MJ/(m³·K) B) 1.0 MJ/(m³·K) C) 1.5 MJ/(m³·K) D) 2.0 MJ/(m³·K)
Answer: B) 1.0 MJ/(m³·K)
40. A spacecraft experiences a constant deceleration of 30 m/s² during re-entry. How long does it
take to reduce its velocity from 7.5 km/s to 0.5 km/s?
A) 200 s B) 233 s C) 266 s D) 300 s
Answer: B) 233 s
. A spacecraft with a mass of 5000 kg experiences a deceleration of 50 m/s² during re-entry. What is
the force acting on the spacecraft?
A) 200 kN B) 250 kN C) 300 kN D) 350 kN
Answer: B) 250 kN
7. If the specific heat capacity of a heat shield material is 1000 J/(kg·K) and its mass is 100 kg, how
much energy is required to raise its temperature by 500°C?
A) 25 MJ B) 50 MJ C) 75 MJ D) 100 MJ
Answer: B) 50 MJ
8. A spacecraft's heat shield ablates at a rate of 0.1 mm/s. If the initial thickness is 20 mm, how long
will it last before being completely consumed?
A) 100 s B) 150 s C) 200 s D) 250 s
Answer: C) 200 s
9. If the emissivity of a thermal protection system is 0.8 and it radiates 1 MW/m² at temperature T,
what is T according to Stefan-Boltzmann law? (σ = 5.67 × 10⁻⁸ W/(m²·K⁴))
A) 1639 K B) 1823 K C) 2011 K D) 2205 K
Answer: B) 1823 K
10. A spacecraft's heat shield has a thermal diffusivity of 5 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 2 cm thick layer?
A) 400 s B) 600 s C) 800 s D) 1000 s
Answer: C) 800 s
11. If a heat shield tile expands by 0.1% when heated to 1000°C, what is its coefficient of thermal
expansion?
A) 1 × 10⁻⁶ /°C B) 5 × 10⁻⁶ /°C C) 1 × 10⁻⁵ /°C D) 5 × 10⁻⁵ /°C
Answer: C) 1 × 10⁻⁵ /°C
12. A spacecraft experiences a heat load of 100 MJ/m² during re-entry. If its heat shield has a heat
capacity of 2 MJ/(m²·K), what is the temperature rise assuming no heat loss?
A) 25°C B) 50°C C) 75°C D) 100°C
Answer: B) 50°C
13. If the drag coefficient of a spacecraft during re-entry is 1.2 and its frontal area is 10 m², what is
the drag force at an altitude where the air density is 1 × 10⁻⁴ kg/m³ and velocity is 5 km/s?
A) 10 kN B) 15 kN C) 20 kN D) 25 kN
Answer: B) 15 kN
14. A thermal protection system can withstand a maximum stress of 100 MPa. If it experiences a
thermal gradient of 1000°C/cm and has a thermal expansion coefficient of 5 × 10⁻⁶ /°C, what is the
maximum allowable Young's modulus?
A) 100 GPa B) 150 GPa C) 200 GPa D) 250 GPa
Answer: C) 200 GPa
15. If a spacecraft's kinetic energy is reduced by 90% during re-entry and 80% of this energy goes into
heating the thermal protection system, how much energy (as a percentage of initial kinetic energy) is
available for other processes?
A) 10% B) 18% C) 28% D) 38%
Answer: B) 18%
16. A heat shield tile has a thermal conductivity that varies with temperature according to k = 0.1 +
0.0002T W/(m·K), where T is in °C. What is the average thermal conductivity between 20°C and
1020°C?
A) 0.15 W/(m·K) B) 0.20 W/(m·K) C) 0.25 W/(m·K) D) 0.30 W/(m·K)
Answer: B) 0.20 W/(m·K)
17. If a spacecraft's heat shield mass is 15% of the total spacecraft mass, and the total mass is 6000
kg, what is the heat shield mass?
A) 600 kg B) 750 kg C) 900 kg D) 1050 kg
Answer: C) 900 kg
18. A spacecraft experiences a deceleration of 40 m/s² for 3 minutes during re-entry. What is its
change in velocity?
A) 5.2 km/s B) 6.2 km/s C) 7.2 km/s D) 8.2 km/s
Answer: C) 7.2 km/s
19. If the heat of ablation for a thermal protection material is 20 MJ/kg and the heat flux during re-
entry is 10 MW/m², what is the ablation rate in mm/s for a material with density 1600 kg/m³?
A) 0.25 mm/s B) 0.3125 mm/s C) 0.375 mm/s D) 0.4375 mm/s
Answer: B) 0.3125 mm/s
20. A spacecraft's heat shield has a mass of 500 kg and specific heat capacity of 1200 J/(kg·K). If it
absorbs 300 MJ of heat during re-entry, what is its temperature increase?
A) 400°C B) 450°C C) 500°C D) 550°C
Answer: C) 500°C
21. If a thermal protection system has an emissivity of 0.9 and radiates 2 MW/m² at a temperature of
2000 K, what is the Stefan-Boltzmann constant to two significant figures?
A) 5.6 × 10⁻⁸ W/(m²·K⁴) B) 5.8 × 10⁻⁸ W/(m²·K⁴) C) 6.0 × 10⁻⁸ W/(m²·K⁴) D) 6.2 × 10⁻⁸ W/(m²·K⁴)
Answer: A) 5.6 × 10⁻⁸ W/(m²·K⁴)
22. A spacecraft's heat shield loses 2 kg of mass during re-entry. If the heat of ablation is 15 MJ/kg,
how much energy was absorbed by the ablation process?
A) 20 MJ B) 25 MJ C) 30 MJ D) 35 MJ
Answer: C) 30 MJ
23. If a thermal protection tile has a thermal expansion coefficient of 3 × 10⁻⁶ /°C and expands by 0.3
mm when heated, what was its original length if the temperature change was 500°C?
A) 150 mm B) 175 mm C) 200 mm D) 225 mm
Answer: C) 200 mm
24. A spacecraft's heat shield has a thermal conductivity of 0.2 W/(m·K) and thickness of 10 cm. If
the outer surface is at 1500°C and the inner surface at 50°C, what is the heat flux through the shield?
A) 290 kW/m² B) 310 kW/m² C) 330 kW/m² D) 350 kW/m²
Answer: A) 290 kW/m²
25. If a heat shield tile has a density of 200 kg/m³ and a specific heat capacity of 1000 J/(kg·K), what
is its volumetric heat capacity?
A) 100 kJ/(m³·K) B) 150 kJ/(m³·K) C) 200 kJ/(m³·K) D) 250 kJ/(m³·K)
Answer: C) 200 kJ/(m³·K)
26. A spacecraft enters the atmosphere at 11 km/s and experiences a constant deceleration until it
reaches 300 m/s. If the deceleration takes 5 minutes, what is the average deceleration?
A) 35.8 m/s² B) 35.8 g C) 3.58 g D) 3.58 m/s²
Answer: A) 35.8 m/s²
27. If a heat shield's emissivity increases from 0.7 to 0.9 due to surface changes during re-entry, by
what factor does its radiative heat dissipation capability increase at a given temperature?
A) 1.14 B) 1.22 C) 1.29 D) 1.36
Answer: C) 1.29
28. A thermal protection system uses phase change material that absorbs 400 kJ/kg during melting. If
the total heat input during re-entry is 80 MJ and the heat shield mass is 500 kg, what percentage of
the material undergoes phase change?
A) 30% B) 35% C) 40% D) 45%
Answer: C) 40%
29. If a spacecraft's kinetic energy decreases from 50 GJ to 10 GJ during re-entry, and 75% of the
energy difference goes into heating the thermal protection system, how much heat does the system
absorb?
A) 20 GJ B) 25 GJ C) 30 GJ D) 35 GJ
Answer: C) 30 GJ
30. A heat shield tile has a thermal diffusivity of 4 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 5 cm thick layer?
A) 1562.5 s B) 2500 s C) 3125 s D) 3750 s
Answer: C) 3125 s
31. If a spacecraft's heat shield can withstand a maximum heat flux of 1.2 MW/m² and the actual
heat flux during re-entry peaks at 900 kW/m², what is the safety factor?
A) 1.2 B) 1.33 C) 1.5 D) 1.67
Answer: B) 1.33
32. A thermal protection system uses a material with a density of 300 kg/m³. If the heat shield has a
surface area of 20 m² and a thickness of 5 cm, what is its mass?
A) 250 kg B) 275 kg C) 300 kg D) 325 kg
Answer: C) 300 kg
33. If the temperature of a heat shield increases from 20°C to 1520°C in 2 minutes, what is the
average rate of temperature increase?
A) 10°C/s B) 12.5°C/s C) 15°C/s D) 17.5°C/s
Answer: B) 12.5°C/s
34. A spacecraft with a mass of 4000 kg experiences a drag force of 200 kN during re-entry. What is
its deceleration?
A) 40 m/s² B) 45 m/s² C) 50 m/s² D) 55 m/s²
Answer: C) 50 m/s²
35. If a heat shield's thermal conductivity increases by 5% for every 100°C rise in temperature, what
is its thermal conductivity at 1000°C if it was 0.2 W/(m·K) at 0°C?
A) 0.28 W/(m·K) B) 0.30 W/(m·K) C) 0.32 W/(m·K) D) 0.34 W/(m·K)
Answer: C) 0.32 W/(m·K)
36. A spacecraft's heat shield has a mass of 600 kg and absorbs 90 MJ of heat during re-entry. If its
temperature rises by 250°C, what is its specific heat capacity?
A) 500 J/(kg·K) B) 550 J/(kg·K) C) 600 J/(kg·K) D) 650 J/(kg·K)
Answer: C) 600 J/(kg·K)
37. If a thermal protection tile expands by 0.15% when heated from 20°C to 1020°C, what is its
coefficient of thermal expansion?
A) 1.5 × 10⁻⁶ /°C B) 2.0 × 10⁻⁶ /°C C) 2.5 × 10⁻⁶ /°C D) 3.0 × 10⁻⁶ /°C
Answer: A) 1.5 × 10⁻⁶ /°C
38. A spacecraft's velocity decreases from 10 km/s to 2 km/s during re-entry. What percentage of its
initial kinetic energy is converted to heat?
A) 80% B) 84% C) 88% D) 96%
Answer: D) 96%
39. If a heat shield material has a thermal diffusivity of 3 × 10⁻⁷ m²/s and a thermal conductivity of
0.3 W/(m·K), what is its volumetric heat capacity?
A) 0.5 MJ/(m³·K) B) 1.0 MJ/(m³·K) C) 1.5 MJ/(m³·K) D) 2.0 MJ/(m³·K)
Answer: B) 1.0 MJ/(m³·K)
40. A spacecraft experiences a constant deceleration of 30 m/s² during re-entry. How long does it
take to reduce its velocity from 7.5 km/s to 0.5 km/s?
A) 200 s B) 233 s C) 266 s D) 300 s
Answer: B) 233 s
. A spacecraft with a mass of 5000 kg experiences a deceleration of 50 m/s² during re-entry. What is
the force acting on the spacecraft?
A) 200 kN B) 250 kN C) 300 kN D) 350 kN
Answer: B) 250 kN
7. If the specific heat capacity of a heat shield material is 1000 J/(kg·K) and its mass is 100 kg, how
much energy is required to raise its temperature by 500°C?
A) 25 MJ B) 50 MJ C) 75 MJ D) 100 MJ
Answer: B) 50 MJ
8. A spacecraft's heat shield ablates at a rate of 0.1 mm/s. If the initial thickness is 20 mm, how long
will it last before being completely consumed?
A) 100 s B) 150 s C) 200 s D) 250 s
Answer: C) 200 s
9. If the emissivity of a thermal protection system is 0.8 and it radiates 1 MW/m² at temperature T,
what is T according to Stefan-Boltzmann law? (σ = 5.67 × 10⁻⁸ W/(m²·K⁴))
A) 1639 K B) 1823 K C) 2011 K D) 2205 K
Answer: B) 1823 K
10. A spacecraft's heat shield has a thermal diffusivity of 5 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 2 cm thick layer?
A) 400 s B) 600 s C) 800 s D) 1000 s
Answer: C) 800 s
11. If a heat shield tile expands by 0.1% when heated to 1000°C, what is its coefficient of thermal
expansion?
A) 1 × 10⁻⁶ /°C B) 5 × 10⁻⁶ /°C C) 1 × 10⁻⁵ /°C D) 5 × 10⁻⁵ /°C
Answer: C) 1 × 10⁻⁵ /°C
12. A spacecraft experiences a heat load of 100 MJ/m² during re-entry. If its heat shield has a heat
capacity of 2 MJ/(m²·K), what is the temperature rise assuming no heat loss?
A) 25°C B) 50°C C) 75°C D) 100°C
Answer: B) 50°C
13. If the drag coefficient of a spacecraft during re-entry is 1.2 and its frontal area is 10 m², what is
the drag force at an altitude where the air density is 1 × 10⁻⁴ kg/m³ and velocity is 5 km/s?
A) 10 kN B) 15 kN C) 20 kN D) 25 kN
Answer: B) 15 kN
14. A thermal protection system can withstand a maximum stress of 100 MPa. If it experiences a
thermal gradient of 1000°C/cm and has a thermal expansion coefficient of 5 × 10⁻⁶ /°C, what is the
maximum allowable Young's modulus?
A) 100 GPa B) 150 GPa C) 200 GPa D) 250 GPa
Answer: C) 200 GPa
15. If a spacecraft's kinetic energy is reduced by 90% during re-entry and 80% of this energy goes into
heating the thermal protection system, how much energy (as a percentage of initial kinetic energy) is
available for other processes?
A) 10% B) 18% C) 28% D) 38%
Answer: B) 18%
16. A heat shield tile has a thermal conductivity that varies with temperature according to k = 0.1 +
0.0002T W/(m·K), where T is in °C. What is the average thermal conductivity between 20°C and
1020°C?
A) 0.15 W/(m·K) B) 0.20 W/(m·K) C) 0.25 W/(m·K) D) 0.30 W/(m·K)
Answer: B) 0.20 W/(m·K)
17. If a spacecraft's heat shield mass is 15% of the total spacecraft mass, and the total mass is 6000
kg, what is the heat shield mass?
A) 600 kg B) 750 kg C) 900 kg D) 1050 kg
Answer: C) 900 kg
18. A spacecraft experiences a deceleration of 40 m/s² for 3 minutes during re-entry. What is its
change in velocity?
A) 5.2 km/s B) 6.2 km/s C) 7.2 km/s D) 8.2 km/s
Answer: C) 7.2 km/s
19. If the heat of ablation for a thermal protection material is 20 MJ/kg and the heat flux during re-
entry is 10 MW/m², what is the ablation rate in mm/s for a material with density 1600 kg/m³?
A) 0.25 mm/s B) 0.3125 mm/s C) 0.375 mm/s D) 0.4375 mm/s
Answer: B) 0.3125 mm/s
20. A spacecraft's heat shield has a mass of 500 kg and specific heat capacity of 1200 J/(kg·K). If it
absorbs 300 MJ of heat during re-entry, what is its temperature increase?
A) 400°C B) 450°C C) 500°C D) 550°C
Answer: C) 500°C
21. If a thermal protection system has an emissivity of 0.9 and radiates 2 MW/m² at a temperature of
2000 K, what is the Stefan-Boltzmann constant to two significant figures?
A) 5.6 × 10⁻⁸ W/(m²·K⁴) B) 5.8 × 10⁻⁸ W/(m²·K⁴) C) 6.0 × 10⁻⁸ W/(m²·K⁴) D) 6.2 × 10⁻⁸ W/(m²·K⁴)
Answer: A) 5.6 × 10⁻⁸ W/(m²·K⁴)
22. A spacecraft's heat shield loses 2 kg of mass during re-entry. If the heat of ablation is 15 MJ/kg,
how much energy was absorbed by the ablation process?
A) 20 MJ B) 25 MJ C) 30 MJ D) 35 MJ
Answer: C) 30 MJ
23. If a thermal protection tile has a thermal expansion coefficient of 3 × 10⁻⁶ /°C and expands by 0.3
mm when heated, what was its original length if the temperature change was 500°C?
A) 150 mm B) 175 mm C) 200 mm D) 225 mm
Answer: C) 200 mm
24. A spacecraft's heat shield has a thermal conductivity of 0.2 W/(m·K) and thickness of 10 cm. If
the outer surface is at 1500°C and the inner surface at 50°C, what is the heat flux through the shield?
A) 290 kW/m² B) 310 kW/m² C) 330 kW/m² D) 350 kW/m²
Answer: A) 290 kW/m²
25. If a heat shield tile has a density of 200 kg/m³ and a specific heat capacity of 1000 J/(kg·K), what
is its volumetric heat capacity?
A) 100 kJ/(m³·K) B) 150 kJ/(m³·K) C) 200 kJ/(m³·K) D) 250 kJ/(m³·K)
Answer: C) 200 kJ/(m³·K)
26. A spacecraft enters the atmosphere at 11 km/s and experiences a constant deceleration until it
reaches 300 m/s. If the deceleration takes 5 minutes, what is the average deceleration?
A) 35.8 m/s² B) 35.8 g C) 3.58 g D) 3.58 m/s²
Answer: A) 35.8 m/s²
27. If a heat shield's emissivity increases from 0.7 to 0.9 due to surface changes during re-entry, by
what factor does its radiative heat dissipation capability increase at a given temperature?
A) 1.14 B) 1.22 C) 1.29 D) 1.36
Answer: C) 1.29
28. A thermal protection system uses phase change material that absorbs 400 kJ/kg during melting. If
the total heat input during re-entry is 80 MJ and the heat shield mass is 500 kg, what percentage of
the material undergoes phase change?
A) 30% B) 35% C) 40% D) 45%
Answer: C) 40%
29. If a spacecraft's kinetic energy decreases from 50 GJ to 10 GJ during re-entry, and 75% of the
energy difference goes into heating the thermal protection system, how much heat does the system
absorb?
A) 20 GJ B) 25 GJ C) 30 GJ D) 35 GJ
Answer: C) 30 GJ
30. A heat shield tile has a thermal diffusivity of 4 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 5 cm thick layer?
A) 1562.5 s B) 2500 s C) 3125 s D) 3750 s
Answer: C) 3125 s
31. If a spacecraft's heat shield can withstand a maximum heat flux of 1.2 MW/m² and the actual
heat flux during re-entry peaks at 900 kW/m², what is the safety factor?
A) 1.2 B) 1.33 C) 1.5 D) 1.67
Answer: B) 1.33
32. A thermal protection system uses a material with a density of 300 kg/m³. If the heat shield has a
surface area of 20 m² and a thickness of 5 cm, what is its mass?
A) 250 kg B) 275 kg C) 300 kg D) 325 kg
Answer: C) 300 kg
33. If the temperature of a heat shield increases from 20°C to 1520°C in 2 minutes, what is the
average rate of temperature increase?
A) 10°C/s B) 12.5°C/s C) 15°C/s D) 17.5°C/s
Answer: B) 12.5°C/s
34. A spacecraft with a mass of 4000 kg experiences a drag force of 200 kN during re-entry. What is
its deceleration?
A) 40 m/s² B) 45 m/s² C) 50 m/s² D) 55 m/s²
Answer: C) 50 m/s²
35. If a heat shield's thermal conductivity increases by 5% for every 100°C rise in temperature, what
is its thermal conductivity at 1000°C if it was 0.2 W/(m·K) at 0°C?
A) 0.28 W/(m·K) B) 0.30 W/(m·K) C) 0.32 W/(m·K) D) 0.34 W/(m·K)
Answer: C) 0.32 W/(m·K)
36. A spacecraft's heat shield has a mass of 600 kg and absorbs 90 MJ of heat during re-entry. If its
temperature rises by 250°C, what is its specific heat capacity?
A) 500 J/(kg·K) B) 550 J/(kg·K) C) 600 J/(kg·K) D) 650 J/(kg·K)
Answer: C) 600 J/(kg·K)
37. If a thermal protection tile expands by 0.15% when heated from 20°C to 1020°C, what is its
coefficient of thermal expansion?
A) 1.5 × 10⁻⁶ /°C B) 2.0 × 10⁻⁶ /°C C) 2.5 × 10⁻⁶ /°C D) 3.0 × 10⁻⁶ /°C
Answer: A) 1.5 × 10⁻⁶ /°C
38. A spacecraft's velocity decreases from 10 km/s to 2 km/s during re-entry. What percentage of its
initial kinetic energy is converted to heat?
A) 80% B) 84% C) 88% D) 96%
Answer: D) 96%
39. If a heat shield material has a thermal diffusivity of 3 × 10⁻⁷ m²/s and a thermal conductivity of
0.3 W/(m·K), what is its volumetric heat capacity?
A) 0.5 MJ/(m³·K) B) 1.0 MJ/(m³·K) C) 1.5 MJ/(m³·K) D) 2.0 MJ/(m³·K)
Answer: B) 1.0 MJ/(m³·K)
40. A spacecraft experiences a constant deceleration of 30 m/s² during re-entry. How long does it
take to reduce its velocity from 7.5 km/s to 0.5 km/s?
A) 200 s B) 233 s C) 266 s D) 300 s
Answer: B) 233 s
. A spacecraft with a mass of 5000 kg experiences a deceleration of 50 m/s² during re-entry. What is
the force acting on the spacecraft?
A) 200 kN B) 250 kN C) 300 kN D) 350 kN
Answer: B) 250 kN
7. If the specific heat capacity of a heat shield material is 1000 J/(kg·K) and its mass is 100 kg, how
much energy is required to raise its temperature by 500°C?
A) 25 MJ B) 50 MJ C) 75 MJ D) 100 MJ
Answer: B) 50 MJ
8. A spacecraft's heat shield ablates at a rate of 0.1 mm/s. If the initial thickness is 20 mm, how long
will it last before being completely consumed?
A) 100 s B) 150 s C) 200 s D) 250 s
Answer: C) 200 s
9. If the emissivity of a thermal protection system is 0.8 and it radiates 1 MW/m² at temperature T,
what is T according to Stefan-Boltzmann law? (σ = 5.67 × 10⁻⁸ W/(m²·K⁴))
A) 1639 K B) 1823 K C) 2011 K D) 2205 K
Answer: B) 1823 K
10. A spacecraft's heat shield has a thermal diffusivity of 5 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 2 cm thick layer?
A) 400 s B) 600 s C) 800 s D) 1000 s
Answer: C) 800 s
11. If a heat shield tile expands by 0.1% when heated to 1000°C, what is its coefficient of thermal
expansion?
A) 1 × 10⁻⁶ /°C B) 5 × 10⁻⁶ /°C C) 1 × 10⁻⁵ /°C D) 5 × 10⁻⁵ /°C
Answer: C) 1 × 10⁻⁵ /°C
12. A spacecraft experiences a heat load of 100 MJ/m² during re-entry. If its heat shield has a heat
capacity of 2 MJ/(m²·K), what is the temperature rise assuming no heat loss?
A) 25°C B) 50°C C) 75°C D) 100°C
Answer: B) 50°C
13. If the drag coefficient of a spacecraft during re-entry is 1.2 and its frontal area is 10 m², what is
the drag force at an altitude where the air density is 1 × 10⁻⁴ kg/m³ and velocity is 5 km/s?
A) 10 kN B) 15 kN C) 20 kN D) 25 kN
Answer: B) 15 kN
14. A thermal protection system can withstand a maximum stress of 100 MPa. If it experiences a
thermal gradient of 1000°C/cm and has a thermal expansion coefficient of 5 × 10⁻⁶ /°C, what is the
maximum allowable Young's modulus?
A) 100 GPa B) 150 GPa C) 200 GPa D) 250 GPa
Answer: C) 200 GPa
15. If a spacecraft's kinetic energy is reduced by 90% during re-entry and 80% of this energy goes into
heating the thermal protection system, how much energy (as a percentage of initial kinetic energy) is
available for other processes?
A) 10% B) 18% C) 28% D) 38%
Answer: B) 18%
16. A heat shield tile has a thermal conductivity that varies with temperature according to k = 0.1 +
0.0002T W/(m·K), where T is in °C. What is the average thermal conductivity between 20°C and
1020°C?
A) 0.15 W/(m·K) B) 0.20 W/(m·K) C) 0.25 W/(m·K) D) 0.30 W/(m·K)
Answer: B) 0.20 W/(m·K)
17. If a spacecraft's heat shield mass is 15% of the total spacecraft mass, and the total mass is 6000
kg, what is the heat shield mass?
A) 600 kg B) 750 kg C) 900 kg D) 1050 kg
Answer: C) 900 kg
18. A spacecraft experiences a deceleration of 40 m/s² for 3 minutes during re-entry. What is its
change in velocity?
A) 5.2 km/s B) 6.2 km/s C) 7.2 km/s D) 8.2 km/s
Answer: C) 7.2 km/s
19. If the heat of ablation for a thermal protection material is 20 MJ/kg and the heat flux during re-
entry is 10 MW/m², what is the ablation rate in mm/s for a material with density 1600 kg/m³?
A) 0.25 mm/s B) 0.3125 mm/s C) 0.375 mm/s D) 0.4375 mm/s
Answer: B) 0.3125 mm/s
20. A spacecraft's heat shield has a mass of 500 kg and specific heat capacity of 1200 J/(kg·K). If it
absorbs 300 MJ of heat during re-entry, what is its temperature increase?
A) 400°C B) 450°C C) 500°C D) 550°C
Answer: C) 500°C
21. If a thermal protection system has an emissivity of 0.9 and radiates 2 MW/m² at a temperature of
2000 K, what is the Stefan-Boltzmann constant to two significant figures?
A) 5.6 × 10⁻⁸ W/(m²·K⁴) B) 5.8 × 10⁻⁸ W/(m²·K⁴) C) 6.0 × 10⁻⁸ W/(m²·K⁴) D) 6.2 × 10⁻⁸ W/(m²·K⁴)
Answer: A) 5.6 × 10⁻⁸ W/(m²·K⁴)
22. A spacecraft's heat shield loses 2 kg of mass during re-entry. If the heat of ablation is 15 MJ/kg,
how much energy was absorbed by the ablation process?
A) 20 MJ B) 25 MJ C) 30 MJ D) 35 MJ
Answer: C) 30 MJ
23. If a thermal protection tile has a thermal expansion coefficient of 3 × 10⁻⁶ /°C and expands by 0.3
mm when heated, what was its original length if the temperature change was 500°C?
A) 150 mm B) 175 mm C) 200 mm D) 225 mm
Answer: C) 200 mm
24. A spacecraft's heat shield has a thermal conductivity of 0.2 W/(m·K) and thickness of 10 cm. If
the outer surface is at 1500°C and the inner surface at 50°C, what is the heat flux through the shield?
A) 290 kW/m² B) 310 kW/m² C) 330 kW/m² D) 350 kW/m²
Answer: A) 290 kW/m²
25. If a heat shield tile has a density of 200 kg/m³ and a specific heat capacity of 1000 J/(kg·K), what
is its volumetric heat capacity?
A) 100 kJ/(m³·K) B) 150 kJ/(m³·K) C) 200 kJ/(m³·K) D) 250 kJ/(m³·K)
Answer: C) 200 kJ/(m³·K)
26. A spacecraft enters the atmosphere at 11 km/s and experiences a constant deceleration until it
reaches 300 m/s. If the deceleration takes 5 minutes, what is the average deceleration?
A) 35.8 m/s² B) 35.8 g C) 3.58 g D) 3.58 m/s²
Answer: A) 35.8 m/s²
27. If a heat shield's emissivity increases from 0.7 to 0.9 due to surface changes during re-entry, by
what factor does its radiative heat dissipation capability increase at a given temperature?
A) 1.14 B) 1.22 C) 1.29 D) 1.36
Answer: C) 1.29
28. A thermal protection system uses phase change material that absorbs 400 kJ/kg during melting. If
the total heat input during re-entry is 80 MJ and the heat shield mass is 500 kg, what percentage of
the material undergoes phase change?
A) 30% B) 35% C) 40% D) 45%
Answer: C) 40%
29. If a spacecraft's kinetic energy decreases from 50 GJ to 10 GJ during re-entry, and 75% of the
energy difference goes into heating the thermal protection system, how much heat does the system
absorb?
A) 20 GJ B) 25 GJ C) 30 GJ D) 35 GJ
Answer: C) 30 GJ
30. A heat shield tile has a thermal diffusivity of 4 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 5 cm thick layer?
A) 1562.5 s B) 2500 s C) 3125 s D) 3750 s
Answer: C) 3125 s
31. If a spacecraft's heat shield can withstand a maximum heat flux of 1.2 MW/m² and the actual
heat flux during re-entry peaks at 900 kW/m², what is the safety factor?
A) 1.2 B) 1.33 C) 1.5 D) 1.67
Answer: B) 1.33
32. A thermal protection system uses a material with a density of 300 kg/m³. If the heat shield has a
surface area of 20 m² and a thickness of 5 cm, what is its mass?
A) 250 kg B) 275 kg C) 300 kg D) 325 kg
Answer: C) 300 kg
33. If the temperature of a heat shield increases from 20°C to 1520°C in 2 minutes, what is the
average rate of temperature increase?
A) 10°C/s B) 12.5°C/s C) 15°C/s D) 17.5°C/s
Answer: B) 12.5°C/s
34. A spacecraft with a mass of 4000 kg experiences a drag force of 200 kN during re-entry. What is
its deceleration?
A) 40 m/s² B) 45 m/s² C) 50 m/s² D) 55 m/s²
Answer: C) 50 m/s²
35. If a heat shield's thermal conductivity increases by 5% for every 100°C rise in temperature, what
is its thermal conductivity at 1000°C if it was 0.2 W/(m·K) at 0°C?
A) 0.28 W/(m·K) B) 0.30 W/(m·K) C) 0.32 W/(m·K) D) 0.34 W/(m·K)
Answer: C) 0.32 W/(m·K)
36. A spacecraft's heat shield has a mass of 600 kg and absorbs 90 MJ of heat during re-entry. If its
temperature rises by 250°C, what is its specific heat capacity?
A) 500 J/(kg·K) B) 550 J/(kg·K) C) 600 J/(kg·K) D) 650 J/(kg·K)
Answer: C) 600 J/(kg·K)
37. If a thermal protection tile expands by 0.15% when heated from 20°C to 1020°C, what is its
coefficient of thermal expansion?
A) 1.5 × 10⁻⁶ /°C B) 2.0 × 10⁻⁶ /°C C) 2.5 × 10⁻⁶ /°C D) 3.0 × 10⁻⁶ /°C
Answer: A) 1.5 × 10⁻⁶ /°C
38. A spacecraft's velocity decreases from 10 km/s to 2 km/s during re-entry. What percentage of its
initial kinetic energy is converted to heat?
A) 80% B) 84% C) 88% D) 96%
Answer: D) 96%
39. If a heat shield material has a thermal diffusivity of 3 × 10⁻⁷ m²/s and a thermal conductivity of
0.3 W/(m·K), what is its volumetric heat capacity?
A) 0.5 MJ/(m³·K) B) 1.0 MJ/(m³·K) C) 1.5 MJ/(m³·K) D) 2.0 MJ/(m³·K)
Answer: B) 1.0 MJ/(m³·K)
40. A spacecraft experiences a constant deceleration of 30 m/s² during re-entry. How long does it
take to reduce its velocity from 7.5 km/s to 0.5 km/s?
A) 200 s B) 233 s C) 266 s D) 300 s
Answer: B) 233 s
. A spacecraft with a mass of 5000 kg experiences a deceleration of 50 m/s² during re-entry. What is
the force acting on the spacecraft?
A) 200 kN B) 250 kN C) 300 kN D) 350 kN
Answer: B) 250 kN
7. If the specific heat capacity of a heat shield material is 1000 J/(kg·K) and its mass is 100 kg, how
much energy is required to raise its temperature by 500°C?
A) 25 MJ B) 50 MJ C) 75 MJ D) 100 MJ
Answer: B) 50 MJ
8. A spacecraft's heat shield ablates at a rate of 0.1 mm/s. If the initial thickness is 20 mm, how long
will it last before being completely consumed?
A) 100 s B) 150 s C) 200 s D) 250 s
Answer: C) 200 s
9. If the emissivity of a thermal protection system is 0.8 and it radiates 1 MW/m² at temperature T,
what is T according to Stefan-Boltzmann law? (σ = 5.67 × 10⁻⁸ W/(m²·K⁴))
A) 1639 K B) 1823 K C) 2011 K D) 2205 K
Answer: B) 1823 K
10. A spacecraft's heat shield has a thermal diffusivity of 5 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 2 cm thick layer?
A) 400 s B) 600 s C) 800 s D) 1000 s
Answer: C) 800 s
11. If a heat shield tile expands by 0.1% when heated to 1000°C, what is its coefficient of thermal
expansion?
A) 1 × 10⁻⁶ /°C B) 5 × 10⁻⁶ /°C C) 1 × 10⁻⁵ /°C D) 5 × 10⁻⁵ /°C
Answer: C) 1 × 10⁻⁵ /°C
12. A spacecraft experiences a heat load of 100 MJ/m² during re-entry. If its heat shield has a heat
capacity of 2 MJ/(m²·K), what is the temperature rise assuming no heat loss?
A) 25°C B) 50°C C) 75°C D) 100°C
Answer: B) 50°C
13. If the drag coefficient of a spacecraft during re-entry is 1.2 and its frontal area is 10 m², what is
the drag force at an altitude where the air density is 1 × 10⁻⁴ kg/m³ and velocity is 5 km/s?
A) 10 kN B) 15 kN C) 20 kN D) 25 kN
Answer: B) 15 kN
14. A thermal protection system can withstand a maximum stress of 100 MPa. If it experiences a
thermal gradient of 1000°C/cm and has a thermal expansion coefficient of 5 × 10⁻⁶ /°C, what is the
maximum allowable Young's modulus?
A) 100 GPa B) 150 GPa C) 200 GPa D) 250 GPa
Answer: C) 200 GPa
15. If a spacecraft's kinetic energy is reduced by 90% during re-entry and 80% of this energy goes into
heating the thermal protection system, how much energy (as a percentage of initial kinetic energy) is
available for other processes?
A) 10% B) 18% C) 28% D) 38%
Answer: B) 18%
16. A heat shield tile has a thermal conductivity that varies with temperature according to k = 0.1 +
0.0002T W/(m·K), where T is in °C. What is the average thermal conductivity between 20°C and
1020°C?
A) 0.15 W/(m·K) B) 0.20 W/(m·K) C) 0.25 W/(m·K) D) 0.30 W/(m·K)
Answer: B) 0.20 W/(m·K)
17. If a spacecraft's heat shield mass is 15% of the total spacecraft mass, and the total mass is 6000
kg, what is the heat shield mass?
A) 600 kg B) 750 kg C) 900 kg D) 1050 kg
Answer: C) 900 kg
18. A spacecraft experiences a deceleration of 40 m/s² for 3 minutes during re-entry. What is its
change in velocity?
A) 5.2 km/s B) 6.2 km/s C) 7.2 km/s D) 8.2 km/s
Answer: C) 7.2 km/s
19. If the heat of ablation for a thermal protection material is 20 MJ/kg and the heat flux during re-
entry is 10 MW/m², what is the ablation rate in mm/s for a material with density 1600 kg/m³?
A) 0.25 mm/s B) 0.3125 mm/s C) 0.375 mm/s D) 0.4375 mm/s
Answer: B) 0.3125 mm/s
20. A spacecraft's heat shield has a mass of 500 kg and specific heat capacity of 1200 J/(kg·K). If it
absorbs 300 MJ of heat during re-entry, what is its temperature increase?
A) 400°C B) 450°C C) 500°C D) 550°C
Answer: C) 500°C
21. If a thermal protection system has an emissivity of 0.9 and radiates 2 MW/m² at a temperature of
2000 K, what is the Stefan-Boltzmann constant to two significant figures?
A) 5.6 × 10⁻⁸ W/(m²·K⁴) B) 5.8 × 10⁻⁸ W/(m²·K⁴) C) 6.0 × 10⁻⁸ W/(m²·K⁴) D) 6.2 × 10⁻⁸ W/(m²·K⁴)
Answer: A) 5.6 × 10⁻⁸ W/(m²·K⁴)
22. A spacecraft's heat shield loses 2 kg of mass during re-entry. If the heat of ablation is 15 MJ/kg,
how much energy was absorbed by the ablation process?
A) 20 MJ B) 25 MJ C) 30 MJ D) 35 MJ
Answer: C) 30 MJ
23. If a thermal protection tile has a thermal expansion coefficient of 3 × 10⁻⁶ /°C and expands by 0.3
mm when heated, what was its original length if the temperature change was 500°C?
A) 150 mm B) 175 mm C) 200 mm D) 225 mm
Answer: C) 200 mm
24. A spacecraft's heat shield has a thermal conductivity of 0.2 W/(m·K) and thickness of 10 cm. If
the outer surface is at 1500°C and the inner surface at 50°C, what is the heat flux through the shield?
A) 290 kW/m² B) 310 kW/m² C) 330 kW/m² D) 350 kW/m²
Answer: A) 290 kW/m²
25. If a heat shield tile has a density of 200 kg/m³ and a specific heat capacity of 1000 J/(kg·K), what
is its volumetric heat capacity?
A) 100 kJ/(m³·K) B) 150 kJ/(m³·K) C) 200 kJ/(m³·K) D) 250 kJ/(m³·K)
Answer: C) 200 kJ/(m³·K)
26. A spacecraft enters the atmosphere at 11 km/s and experiences a constant deceleration until it
reaches 300 m/s. If the deceleration takes 5 minutes, what is the average deceleration?
A) 35.8 m/s² B) 35.8 g C) 3.58 g D) 3.58 m/s²
Answer: A) 35.8 m/s²
27. If a heat shield's emissivity increases from 0.7 to 0.9 due to surface changes during re-entry, by
what factor does its radiative heat dissipation capability increase at a given temperature?
A) 1.14 B) 1.22 C) 1.29 D) 1.36
Answer: C) 1.29
28. A thermal protection system uses phase change material that absorbs 400 kJ/kg during melting. If
the total heat input during re-entry is 80 MJ and the heat shield mass is 500 kg, what percentage of
the material undergoes phase change?
A) 30% B) 35% C) 40% D) 45%
Answer: C) 40%
29. If a spacecraft's kinetic energy decreases from 50 GJ to 10 GJ during re-entry, and 75% of the
energy difference goes into heating the thermal protection system, how much heat does the system
absorb?
A) 20 GJ B) 25 GJ C) 30 GJ D) 35 GJ
Answer: C) 30 GJ
30. A heat shield tile has a thermal diffusivity of 4 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 5 cm thick layer?
A) 1562.5 s B) 2500 s C) 3125 s D) 3750 s
Answer: C) 3125 s
31. If a spacecraft's heat shield can withstand a maximum heat flux of 1.2 MW/m² and the actual
heat flux during re-entry peaks at 900 kW/m², what is the safety factor?
A) 1.2 B) 1.33 C) 1.5 D) 1.67
Answer: B) 1.33
32. A thermal protection system uses a material with a density of 300 kg/m³. If the heat shield has a
surface area of 20 m² and a thickness of 5 cm, what is its mass?
A) 250 kg B) 275 kg C) 300 kg D) 325 kg
Answer: C) 300 kg
33. If the temperature of a heat shield increases from 20°C to 1520°C in 2 minutes, what is the
average rate of temperature increase?
A) 10°C/s B) 12.5°C/s C) 15°C/s D) 17.5°C/s
Answer: B) 12.5°C/s
34. A spacecraft with a mass of 4000 kg experiences a drag force of 200 kN during re-entry. What is
its deceleration?
A) 40 m/s² B) 45 m/s² C) 50 m/s² D) 55 m/s²
Answer: C) 50 m/s²
35. If a heat shield's thermal conductivity increases by 5% for every 100°C rise in temperature, what
is its thermal conductivity at 1000°C if it was 0.2 W/(m·K) at 0°C?
A) 0.28 W/(m·K) B) 0.30 W/(m·K) C) 0.32 W/(m·K) D) 0.34 W/(m·K)
Answer: C) 0.32 W/(m·K)
36. A spacecraft's heat shield has a mass of 600 kg and absorbs 90 MJ of heat during re-entry. If its
temperature rises by 250°C, what is its specific heat capacity?
A) 500 J/(kg·K) B) 550 J/(kg·K) C) 600 J/(kg·K) D) 650 J/(kg·K)
Answer: C) 600 J/(kg·K)
37. If a thermal protection tile expands by 0.15% when heated from 20°C to 1020°C, what is its
coefficient of thermal expansion?
A) 1.5 × 10⁻⁶ /°C B) 2.0 × 10⁻⁶ /°C C) 2.5 × 10⁻⁶ /°C D) 3.0 × 10⁻⁶ /°C
Answer: A) 1.5 × 10⁻⁶ /°C
38. A spacecraft's velocity decreases from 10 km/s to 2 km/s during re-entry. What percentage of its
initial kinetic energy is converted to heat?
A) 80% B) 84% C) 88% D) 96%
Answer: D) 96%
39. If a heat shield material has a thermal diffusivity of 3 × 10⁻⁷ m²/s and a thermal conductivity of
0.3 W/(m·K), what is its volumetric heat capacity?
A) 0.5 MJ/(m³·K) B) 1.0 MJ/(m³·K) C) 1.5 MJ/(m³·K) D) 2.0 MJ/(m³·K)
Answer: B) 1.0 MJ/(m³·K)
40. A spacecraft experiences a constant deceleration of 30 m/s² during re-entry. How long does it
take to reduce its velocity from 7.5 km/s to 0.5 km/s?
A) 200 s B) 233 s C) 266 s D) 300 s
Answer: B) 233 s
. A spacecraft with a mass of 5000 kg experiences a deceleration of 50 m/s² during re-entry. What is
the force acting on the spacecraft?
A) 200 kN B) 250 kN C) 300 kN D) 350 kN
Answer: B) 250 kN
7. If the specific heat capacity of a heat shield material is 1000 J/(kg·K) and its mass is 100 kg, how
much energy is required to raise its temperature by 500°C?
A) 25 MJ B) 50 MJ C) 75 MJ D) 100 MJ
Answer: B) 50 MJ
8. A spacecraft's heat shield ablates at a rate of 0.1 mm/s. If the initial thickness is 20 mm, how long
will it last before being completely consumed?
A) 100 s B) 150 s C) 200 s D) 250 s
Answer: C) 200 s
9. If the emissivity of a thermal protection system is 0.8 and it radiates 1 MW/m² at temperature T,
what is T according to Stefan-Boltzmann law? (σ = 5.67 × 10⁻⁸ W/(m²·K⁴))
A) 1639 K B) 1823 K C) 2011 K D) 2205 K
Answer: B) 1823 K
10. A spacecraft's heat shield has a thermal diffusivity of 5 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 2 cm thick layer?
A) 400 s B) 600 s C) 800 s D) 1000 s
Answer: C) 800 s
11. If a heat shield tile expands by 0.1% when heated to 1000°C, what is its coefficient of thermal
expansion?
A) 1 × 10⁻⁶ /°C B) 5 × 10⁻⁶ /°C C) 1 × 10⁻⁵ /°C D) 5 × 10⁻⁵ /°C
Answer: C) 1 × 10⁻⁵ /°C
12. A spacecraft experiences a heat load of 100 MJ/m² during re-entry. If its heat shield has a heat
capacity of 2 MJ/(m²·K), what is the temperature rise assuming no heat loss?
A) 25°C B) 50°C C) 75°C D) 100°C
Answer: B) 50°C
13. If the drag coefficient of a spacecraft during re-entry is 1.2 and its frontal area is 10 m², what is
the drag force at an altitude where the air density is 1 × 10⁻⁴ kg/m³ and velocity is 5 km/s?
A) 10 kN B) 15 kN C) 20 kN D) 25 kN
Answer: B) 15 kN
14. A thermal protection system can withstand a maximum stress of 100 MPa. If it experiences a
thermal gradient of 1000°C/cm and has a thermal expansion coefficient of 5 × 10⁻⁶ /°C, what is the
maximum allowable Young's modulus?
A) 100 GPa B) 150 GPa C) 200 GPa D) 250 GPa
Answer: C) 200 GPa
15. If a spacecraft's kinetic energy is reduced by 90% during re-entry and 80% of this energy goes into
heating the thermal protection system, how much energy (as a percentage of initial kinetic energy) is
available for other processes?
A) 10% B) 18% C) 28% D) 38%
Answer: B) 18%
16. A heat shield tile has a thermal conductivity that varies with temperature according to k = 0.1 +
0.0002T W/(m·K), where T is in °C. What is the average thermal conductivity between 20°C and
1020°C?
A) 0.15 W/(m·K) B) 0.20 W/(m·K) C) 0.25 W/(m·K) D) 0.30 W/(m·K)
Answer: B) 0.20 W/(m·K)
17. If a spacecraft's heat shield mass is 15% of the total spacecraft mass, and the total mass is 6000
kg, what is the heat shield mass?
A) 600 kg B) 750 kg C) 900 kg D) 1050 kg
Answer: C) 900 kg
18. A spacecraft experiences a deceleration of 40 m/s² for 3 minutes during re-entry. What is its
change in velocity?
A) 5.2 km/s B) 6.2 km/s C) 7.2 km/s D) 8.2 km/s
Answer: C) 7.2 km/s
19. If the heat of ablation for a thermal protection material is 20 MJ/kg and the heat flux during re-
entry is 10 MW/m², what is the ablation rate in mm/s for a material with density 1600 kg/m³?
A) 0.25 mm/s B) 0.3125 mm/s C) 0.375 mm/s D) 0.4375 mm/s
Answer: B) 0.3125 mm/s
20. A spacecraft's heat shield has a mass of 500 kg and specific heat capacity of 1200 J/(kg·K). If it
absorbs 300 MJ of heat during re-entry, what is its temperature increase?
A) 400°C B) 450°C C) 500°C D) 550°C
Answer: C) 500°C
21. If a thermal protection system has an emissivity of 0.9 and radiates 2 MW/m² at a temperature of
2000 K, what is the Stefan-Boltzmann constant to two significant figures?
A) 5.6 × 10⁻⁸ W/(m²·K⁴) B) 5.8 × 10⁻⁸ W/(m²·K⁴) C) 6.0 × 10⁻⁸ W/(m²·K⁴) D) 6.2 × 10⁻⁸ W/(m²·K⁴)
Answer: A) 5.6 × 10⁻⁸ W/(m²·K⁴)
22. A spacecraft's heat shield loses 2 kg of mass during re-entry. If the heat of ablation is 15 MJ/kg,
how much energy was absorbed by the ablation process?
A) 20 MJ B) 25 MJ C) 30 MJ D) 35 MJ
Answer: C) 30 MJ
23. If a thermal protection tile has a thermal expansion coefficient of 3 × 10⁻⁶ /°C and expands by 0.3
mm when heated, what was its original length if the temperature change was 500°C?
A) 150 mm B) 175 mm C) 200 mm D) 225 mm
Answer: C) 200 mm
24. A spacecraft's heat shield has a thermal conductivity of 0.2 W/(m·K) and thickness of 10 cm. If
the outer surface is at 1500°C and the inner surface at 50°C, what is the heat flux through the shield?
A) 290 kW/m² B) 310 kW/m² C) 330 kW/m² D) 350 kW/m²
Answer: A) 290 kW/m²
25. If a heat shield tile has a density of 200 kg/m³ and a specific heat capacity of 1000 J/(kg·K), what
is its volumetric heat capacity?
A) 100 kJ/(m³·K) B) 150 kJ/(m³·K) C) 200 kJ/(m³·K) D) 250 kJ/(m³·K)
Answer: C) 200 kJ/(m³·K)
26. A spacecraft enters the atmosphere at 11 km/s and experiences a constant deceleration until it
reaches 300 m/s. If the deceleration takes 5 minutes, what is the average deceleration?
A) 35.8 m/s² B) 35.8 g C) 3.58 g D) 3.58 m/s²
Answer: A) 35.8 m/s²
27. If a heat shield's emissivity increases from 0.7 to 0.9 due to surface changes during re-entry, by
what factor does its radiative heat dissipation capability increase at a given temperature?
A) 1.14 B) 1.22 C) 1.29 D) 1.36
Answer: C) 1.29
28. A thermal protection system uses phase change material that absorbs 400 kJ/kg during melting. If
the total heat input during re-entry is 80 MJ and the heat shield mass is 500 kg, what percentage of
the material undergoes phase change?
A) 30% B) 35% C) 40% D) 45%
Answer: C) 40%
29. If a spacecraft's kinetic energy decreases from 50 GJ to 10 GJ during re-entry, and 75% of the
energy difference goes into heating the thermal protection system, how much heat does the system
absorb?
A) 20 GJ B) 25 GJ C) 30 GJ D) 35 GJ
Answer: C) 30 GJ
30. A heat shield tile has a thermal diffusivity of 4 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 5 cm thick layer?
A) 1562.5 s B) 2500 s C) 3125 s D) 3750 s
Answer: C) 3125 s
31. If a spacecraft's heat shield can withstand a maximum heat flux of 1.2 MW/m² and the actual
heat flux during re-entry peaks at 900 kW/m², what is the safety factor?
A) 1.2 B) 1.33 C) 1.5 D) 1.67
Answer: B) 1.33
32. A thermal protection system uses a material with a density of 300 kg/m³. If the heat shield has a
surface area of 20 m² and a thickness of 5 cm, what is its mass?
A) 250 kg B) 275 kg C) 300 kg D) 325 kg
Answer: C) 300 kg
33. If the temperature of a heat shield increases from 20°C to 1520°C in 2 minutes, what is the
average rate of temperature increase?
A) 10°C/s B) 12.5°C/s C) 15°C/s D) 17.5°C/s
Answer: B) 12.5°C/s
34. A spacecraft with a mass of 4000 kg experiences a drag force of 200 kN during re-entry. What is
its deceleration?
A) 40 m/s² B) 45 m/s² C) 50 m/s² D) 55 m/s²
Answer: C) 50 m/s²
35. If a heat shield's thermal conductivity increases by 5% for every 100°C rise in temperature, what
is its thermal conductivity at 1000°C if it was 0.2 W/(m·K) at 0°C?
A) 0.28 W/(m·K) B) 0.30 W/(m·K) C) 0.32 W/(m·K) D) 0.34 W/(m·K)
Answer: C) 0.32 W/(m·K)
36. A spacecraft's heat shield has a mass of 600 kg and absorbs 90 MJ of heat during re-entry. If its
temperature rises by 250°C, what is its specific heat capacity?
A) 500 J/(kg·K) B) 550 J/(kg·K) C) 600 J/(kg·K) D) 650 J/(kg·K)
Answer: C) 600 J/(kg·K)
37. If a thermal protection tile expands by 0.15% when heated from 20°C to 1020°C, what is its
coefficient of thermal expansion?
A) 1.5 × 10⁻⁶ /°C B) 2.0 × 10⁻⁶ /°C C) 2.5 × 10⁻⁶ /°C D) 3.0 × 10⁻⁶ /°C
Answer: A) 1.5 × 10⁻⁶ /°C
38. A spacecraft's velocity decreases from 10 km/s to 2 km/s during re-entry. What percentage of its
initial kinetic energy is converted to heat?
A) 80% B) 84% C) 88% D) 96%
Answer: D) 96%
39. If a heat shield material has a thermal diffusivity of 3 × 10⁻⁷ m²/s and a thermal conductivity of
0.3 W/(m·K), what is its volumetric heat capacity?
A) 0.5 MJ/(m³·K) B) 1.0 MJ/(m³·K) C) 1.5 MJ/(m³·K) D) 2.0 MJ/(m³·K)
Answer: B) 1.0 MJ/(m³·K)
40. A spacecraft experiences a constant deceleration of 30 m/s² during re-entry. How long does it
take to reduce its velocity from 7.5 km/s to 0.5 km/s?
A) 200 s B) 233 s C) 266 s D) 300 s
Answer: B) 233 s
. A spacecraft with a mass of 5000 kg experiences a deceleration of 50 m/s² during re-entry. What is
the force acting on the spacecraft?
A) 200 kN B) 250 kN C) 300 kN D) 350 kN
Answer: B) 250 kN
7. If the specific heat capacity of a heat shield material is 1000 J/(kg·K) and its mass is 100 kg, how
much energy is required to raise its temperature by 500°C?
A) 25 MJ B) 50 MJ C) 75 MJ D) 100 MJ
Answer: B) 50 MJ
8. A spacecraft's heat shield ablates at a rate of 0.1 mm/s. If the initial thickness is 20 mm, how long
will it last before being completely consumed?
A) 100 s B) 150 s C) 200 s D) 250 s
Answer: C) 200 s
9. If the emissivity of a thermal protection system is 0.8 and it radiates 1 MW/m² at temperature T,
what is T according to Stefan-Boltzmann law? (σ = 5.67 × 10⁻⁸ W/(m²·K⁴))
A) 1639 K B) 1823 K C) 2011 K D) 2205 K
Answer: B) 1823 K
10. A spacecraft's heat shield has a thermal diffusivity of 5 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 2 cm thick layer?
A) 400 s B) 600 s C) 800 s D) 1000 s
Answer: C) 800 s
11. If a heat shield tile expands by 0.1% when heated to 1000°C, what is its coefficient of thermal
expansion?
A) 1 × 10⁻⁶ /°C B) 5 × 10⁻⁶ /°C C) 1 × 10⁻⁵ /°C D) 5 × 10⁻⁵ /°C
Answer: C) 1 × 10⁻⁵ /°C
12. A spacecraft experiences a heat load of 100 MJ/m² during re-entry. If its heat shield has a heat
capacity of 2 MJ/(m²·K), what is the temperature rise assuming no heat loss?
A) 25°C B) 50°C C) 75°C D) 100°C
Answer: B) 50°C
13. If the drag coefficient of a spacecraft during re-entry is 1.2 and its frontal area is 10 m², what is
the drag force at an altitude where the air density is 1 × 10⁻⁴ kg/m³ and velocity is 5 km/s?
A) 10 kN B) 15 kN C) 20 kN D) 25 kN
Answer: B) 15 kN
14. A thermal protection system can withstand a maximum stress of 100 MPa. If it experiences a
thermal gradient of 1000°C/cm and has a thermal expansion coefficient of 5 × 10⁻⁶ /°C, what is the
maximum allowable Young's modulus?
A) 100 GPa B) 150 GPa C) 200 GPa D) 250 GPa
Answer: C) 200 GPa
15. If a spacecraft's kinetic energy is reduced by 90% during re-entry and 80% of this energy goes into
heating the thermal protection system, how much energy (as a percentage of initial kinetic energy) is
available for other processes?
A) 10% B) 18% C) 28% D) 38%
Answer: B) 18%
16. A heat shield tile has a thermal conductivity that varies with temperature according to k = 0.1 +
0.0002T W/(m·K), where T is in °C. What is the average thermal conductivity between 20°C and
1020°C?
A) 0.15 W/(m·K) B) 0.20 W/(m·K) C) 0.25 W/(m·K) D) 0.30 W/(m·K)
Answer: B) 0.20 W/(m·K)
17. If a spacecraft's heat shield mass is 15% of the total spacecraft mass, and the total mass is 6000
kg, what is the heat shield mass?
A) 600 kg B) 750 kg C) 900 kg D) 1050 kg
Answer: C) 900 kg
18. A spacecraft experiences a deceleration of 40 m/s² for 3 minutes during re-entry. What is its
change in velocity?
A) 5.2 km/s B) 6.2 km/s C) 7.2 km/s D) 8.2 km/s
Answer: C) 7.2 km/s
19. If the heat of ablation for a thermal protection material is 20 MJ/kg and the heat flux during re-
entry is 10 MW/m², what is the ablation rate in mm/s for a material with density 1600 kg/m³?
A) 0.25 mm/s B) 0.3125 mm/s C) 0.375 mm/s D) 0.4375 mm/s
Answer: B) 0.3125 mm/s
20. A spacecraft's heat shield has a mass of 500 kg and specific heat capacity of 1200 J/(kg·K). If it
absorbs 300 MJ of heat during re-entry, what is its temperature increase?
A) 400°C B) 450°C C) 500°C D) 550°C
Answer: C) 500°C
21. If a thermal protection system has an emissivity of 0.9 and radiates 2 MW/m² at a temperature of
2000 K, what is the Stefan-Boltzmann constant to two significant figures?
A) 5.6 × 10⁻⁸ W/(m²·K⁴) B) 5.8 × 10⁻⁸ W/(m²·K⁴) C) 6.0 × 10⁻⁸ W/(m²·K⁴) D) 6.2 × 10⁻⁸ W/(m²·K⁴)
Answer: A) 5.6 × 10⁻⁸ W/(m²·K⁴)
22. A spacecraft's heat shield loses 2 kg of mass during re-entry. If the heat of ablation is 15 MJ/kg,
how much energy was absorbed by the ablation process?
A) 20 MJ B) 25 MJ C) 30 MJ D) 35 MJ
Answer: C) 30 MJ
23. If a thermal protection tile has a thermal expansion coefficient of 3 × 10⁻⁶ /°C and expands by 0.3
mm when heated, what was its original length if the temperature change was 500°C?
A) 150 mm B) 175 mm C) 200 mm D) 225 mm
Answer: C) 200 mm
24. A spacecraft's heat shield has a thermal conductivity of 0.2 W/(m·K) and thickness of 10 cm. If
the outer surface is at 1500°C and the inner surface at 50°C, what is the heat flux through the shield?
A) 290 kW/m² B) 310 kW/m² C) 330 kW/m² D) 350 kW/m²
Answer: A) 290 kW/m²
25. If a heat shield tile has a density of 200 kg/m³ and a specific heat capacity of 1000 J/(kg·K), what
is its volumetric heat capacity?
A) 100 kJ/(m³·K) B) 150 kJ/(m³·K) C) 200 kJ/(m³·K) D) 250 kJ/(m³·K)
Answer: C) 200 kJ/(m³·K)
26. A spacecraft enters the atmosphere at 11 km/s and experiences a constant deceleration until it
reaches 300 m/s. If the deceleration takes 5 minutes, what is the average deceleration?
A) 35.8 m/s² B) 35.8 g C) 3.58 g D) 3.58 m/s²
Answer: A) 35.8 m/s²
27. If a heat shield's emissivity increases from 0.7 to 0.9 due to surface changes during re-entry, by
what factor does its radiative heat dissipation capability increase at a given temperature?
A) 1.14 B) 1.22 C) 1.29 D) 1.36
Answer: C) 1.29
28. A thermal protection system uses phase change material that absorbs 400 kJ/kg during melting. If
the total heat input during re-entry is 80 MJ and the heat shield mass is 500 kg, what percentage of
the material undergoes phase change?
A) 30% B) 35% C) 40% D) 45%
Answer: C) 40%
29. If a spacecraft's kinetic energy decreases from 50 GJ to 10 GJ during re-entry, and 75% of the
energy difference goes into heating the thermal protection system, how much heat does the system
absorb?
A) 20 GJ B) 25 GJ C) 30 GJ D) 35 GJ
Answer: C) 30 GJ
30. A heat shield tile has a thermal diffusivity of 4 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 5 cm thick layer?
A) 1562.5 s B) 2500 s C) 3125 s D) 3750 s
Answer: C) 3125 s
31. If a spacecraft's heat shield can withstand a maximum heat flux of 1.2 MW/m² and the actual
heat flux during re-entry peaks at 900 kW/m², what is the safety factor?
A) 1.2 B) 1.33 C) 1.5 D) 1.67
Answer: B) 1.33
32. A thermal protection system uses a material with a density of 300 kg/m³. If the heat shield has a
surface area of 20 m² and a thickness of 5 cm, what is its mass?
A) 250 kg B) 275 kg C) 300 kg D) 325 kg
Answer: C) 300 kg
33. If the temperature of a heat shield increases from 20°C to 1520°C in 2 minutes, what is the
average rate of temperature increase?
A) 10°C/s B) 12.5°C/s C) 15°C/s D) 17.5°C/s
Answer: B) 12.5°C/s
34. A spacecraft with a mass of 4000 kg experiences a drag force of 200 kN during re-entry. What is
its deceleration?
A) 40 m/s² B) 45 m/s² C) 50 m/s² D) 55 m/s²
Answer: C) 50 m/s²
35. If a heat shield's thermal conductivity increases by 5% for every 100°C rise in temperature, what
is its thermal conductivity at 1000°C if it was 0.2 W/(m·K) at 0°C?
A) 0.28 W/(m·K) B) 0.30 W/(m·K) C) 0.32 W/(m·K) D) 0.34 W/(m·K)
Answer: C) 0.32 W/(m·K)
36. A spacecraft's heat shield has a mass of 600 kg and absorbs 90 MJ of heat during re-entry. If its
temperature rises by 250°C, what is its specific heat capacity?
A) 500 J/(kg·K) B) 550 J/(kg·K) C) 600 J/(kg·K) D) 650 J/(kg·K)
Answer: C) 600 J/(kg·K)
37. If a thermal protection tile expands by 0.15% when heated from 20°C to 1020°C, what is its
coefficient of thermal expansion?
A) 1.5 × 10⁻⁶ /°C B) 2.0 × 10⁻⁶ /°C C) 2.5 × 10⁻⁶ /°C D) 3.0 × 10⁻⁶ /°C
Answer: A) 1.5 × 10⁻⁶ /°C
38. A spacecraft's velocity decreases from 10 km/s to 2 km/s during re-entry. What percentage of its
initial kinetic energy is converted to heat?
A) 80% B) 84% C) 88% D) 96%
Answer: D) 96%
39. If a heat shield material has a thermal diffusivity of 3 × 10⁻⁷ m²/s and a thermal conductivity of
0.3 W/(m·K), what is its volumetric heat capacity?
A) 0.5 MJ/(m³·K) B) 1.0 MJ/(m³·K) C) 1.5 MJ/(m³·K) D) 2.0 MJ/(m³·K)
Answer: B) 1.0 MJ/(m³·K)
40. A spacecraft experiences a constant deceleration of 30 m/s² during re-entry. How long does it
take to reduce its velocity from 7.5 km/s to 0.5 km/s?
A) 200 s B) 233 s C) 266 s D) 300 s
Answer: B) 233 s
. A spacecraft with a mass of 5000 kg experiences a deceleration of 50 m/s² during re-entry. What is
the force acting on the spacecraft?
A) 200 kN B) 250 kN C) 300 kN D) 350 kN
Answer: B) 250 kN
7. If the specific heat capacity of a heat shield material is 1000 J/(kg·K) and its mass is 100 kg, how
much energy is required to raise its temperature by 500°C?
A) 25 MJ B) 50 MJ C) 75 MJ D) 100 MJ
Answer: B) 50 MJ
8. A spacecraft's heat shield ablates at a rate of 0.1 mm/s. If the initial thickness is 20 mm, how long
will it last before being completely consumed?
A) 100 s B) 150 s C) 200 s D) 250 s
Answer: C) 200 s
9. If the emissivity of a thermal protection system is 0.8 and it radiates 1 MW/m² at temperature T,
what is T according to Stefan-Boltzmann law? (σ = 5.67 × 10⁻⁸ W/(m²·K⁴))
A) 1639 K B) 1823 K C) 2011 K D) 2205 K
Answer: B) 1823 K
10. A spacecraft's heat shield has a thermal diffusivity of 5 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 2 cm thick layer?
A) 400 s B) 600 s C) 800 s D) 1000 s
Answer: C) 800 s
11. If a heat shield tile expands by 0.1% when heated to 1000°C, what is its coefficient of thermal
expansion?
A) 1 × 10⁻⁶ /°C B) 5 × 10⁻⁶ /°C C) 1 × 10⁻⁵ /°C D) 5 × 10⁻⁵ /°C
Answer: C) 1 × 10⁻⁵ /°C
12. A spacecraft experiences a heat load of 100 MJ/m² during re-entry. If its heat shield has a heat
capacity of 2 MJ/(m²·K), what is the temperature rise assuming no heat loss?
A) 25°C B) 50°C C) 75°C D) 100°C
Answer: B) 50°C
13. If the drag coefficient of a spacecraft during re-entry is 1.2 and its frontal area is 10 m², what is
the drag force at an altitude where the air density is 1 × 10⁻⁴ kg/m³ and velocity is 5 km/s?
A) 10 kN B) 15 kN C) 20 kN D) 25 kN
Answer: B) 15 kN
14. A thermal protection system can withstand a maximum stress of 100 MPa. If it experiences a
thermal gradient of 1000°C/cm and has a thermal expansion coefficient of 5 × 10⁻⁶ /°C, what is the
maximum allowable Young's modulus?
A) 100 GPa B) 150 GPa C) 200 GPa D) 250 GPa
Answer: C) 200 GPa
15. If a spacecraft's kinetic energy is reduced by 90% during re-entry and 80% of this energy goes into
heating the thermal protection system, how much energy (as a percentage of initial kinetic energy) is
available for other processes?
A) 10% B) 18% C) 28% D) 38%
Answer: B) 18%
16. A heat shield tile has a thermal conductivity that varies with temperature according to k = 0.1 +
0.0002T W/(m·K), where T is in °C. What is the average thermal conductivity between 20°C and
1020°C?
A) 0.15 W/(m·K) B) 0.20 W/(m·K) C) 0.25 W/(m·K) D) 0.30 W/(m·K)
Answer: B) 0.20 W/(m·K)
17. If a spacecraft's heat shield mass is 15% of the total spacecraft mass, and the total mass is 6000
kg, what is the heat shield mass?
A) 600 kg B) 750 kg C) 900 kg D) 1050 kg
Answer: C) 900 kg
18. A spacecraft experiences a deceleration of 40 m/s² for 3 minutes during re-entry. What is its
change in velocity?
A) 5.2 km/s B) 6.2 km/s C) 7.2 km/s D) 8.2 km/s
Answer: C) 7.2 km/s
19. If the heat of ablation for a thermal protection material is 20 MJ/kg and the heat flux during re-
entry is 10 MW/m², what is the ablation rate in mm/s for a material with density 1600 kg/m³?
A) 0.25 mm/s B) 0.3125 mm/s C) 0.375 mm/s D) 0.4375 mm/s
Answer: B) 0.3125 mm/s
20. A spacecraft's heat shield has a mass of 500 kg and specific heat capacity of 1200 J/(kg·K). If it
absorbs 300 MJ of heat during re-entry, what is its temperature increase?
A) 400°C B) 450°C C) 500°C D) 550°C
Answer: C) 500°C
21. If a thermal protection system has an emissivity of 0.9 and radiates 2 MW/m² at a temperature of
2000 K, what is the Stefan-Boltzmann constant to two significant figures?
A) 5.6 × 10⁻⁸ W/(m²·K⁴) B) 5.8 × 10⁻⁸ W/(m²·K⁴) C) 6.0 × 10⁻⁸ W/(m²·K⁴) D) 6.2 × 10⁻⁸ W/(m²·K⁴)
Answer: A) 5.6 × 10⁻⁸ W/(m²·K⁴)
22. A spacecraft's heat shield loses 2 kg of mass during re-entry. If the heat of ablation is 15 MJ/kg,
how much energy was absorbed by the ablation process?
A) 20 MJ B) 25 MJ C) 30 MJ D) 35 MJ
Answer: C) 30 MJ
23. If a thermal protection tile has a thermal expansion coefficient of 3 × 10⁻⁶ /°C and expands by 0.3
mm when heated, what was its original length if the temperature change was 500°C?
A) 150 mm B) 175 mm C) 200 mm D) 225 mm
Answer: C) 200 mm
24. A spacecraft's heat shield has a thermal conductivity of 0.2 W/(m·K) and thickness of 10 cm. If
the outer surface is at 1500°C and the inner surface at 50°C, what is the heat flux through the shield?
A) 290 kW/m² B) 310 kW/m² C) 330 kW/m² D) 350 kW/m²
Answer: A) 290 kW/m²
25. If a heat shield tile has a density of 200 kg/m³ and a specific heat capacity of 1000 J/(kg·K), what
is its volumetric heat capacity?
A) 100 kJ/(m³·K) B) 150 kJ/(m³·K) C) 200 kJ/(m³·K) D) 250 kJ/(m³·K)
Answer: C) 200 kJ/(m³·K)
26. A spacecraft enters the atmosphere at 11 km/s and experiences a constant deceleration until it
reaches 300 m/s. If the deceleration takes 5 minutes, what is the average deceleration?
A) 35.8 m/s² B) 35.8 g C) 3.58 g D) 3.58 m/s²
Answer: A) 35.8 m/s²
27. If a heat shield's emissivity increases from 0.7 to 0.9 due to surface changes during re-entry, by
what factor does its radiative heat dissipation capability increase at a given temperature?
A) 1.14 B) 1.22 C) 1.29 D) 1.36
Answer: C) 1.29
28. A thermal protection system uses phase change material that absorbs 400 kJ/kg during melting. If
the total heat input during re-entry is 80 MJ and the heat shield mass is 500 kg, what percentage of
the material undergoes phase change?
A) 30% B) 35% C) 40% D) 45%
Answer: C) 40%
29. If a spacecraft's kinetic energy decreases from 50 GJ to 10 GJ during re-entry, and 75% of the
energy difference goes into heating the thermal protection system, how much heat does the system
absorb?
A) 20 GJ B) 25 GJ C) 30 GJ D) 35 GJ
Answer: C) 30 GJ
30. A heat shield tile has a thermal diffusivity of 4 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 5 cm thick layer?
A) 1562.5 s B) 2500 s C) 3125 s D) 3750 s
Answer: C) 3125 s
31. If a spacecraft's heat shield can withstand a maximum heat flux of 1.2 MW/m² and the actual
heat flux during re-entry peaks at 900 kW/m², what is the safety factor?
A) 1.2 B) 1.33 C) 1.5 D) 1.67
Answer: B) 1.33
32. A thermal protection system uses a material with a density of 300 kg/m³. If the heat shield has a
surface area of 20 m² and a thickness of 5 cm, what is its mass?
A) 250 kg B) 275 kg C) 300 kg D) 325 kg
Answer: C) 300 kg
33. If the temperature of a heat shield increases from 20°C to 1520°C in 2 minutes, what is the
average rate of temperature increase?
A) 10°C/s B) 12.5°C/s C) 15°C/s D) 17.5°C/s
Answer: B) 12.5°C/s
34. A spacecraft with a mass of 4000 kg experiences a drag force of 200 kN during re-entry. What is
its deceleration?
A) 40 m/s² B) 45 m/s² C) 50 m/s² D) 55 m/s²
Answer: C) 50 m/s²
35. If a heat shield's thermal conductivity increases by 5% for every 100°C rise in temperature, what
is its thermal conductivity at 1000°C if it was 0.2 W/(m·K) at 0°C?
A) 0.28 W/(m·K) B) 0.30 W/(m·K) C) 0.32 W/(m·K) D) 0.34 W/(m·K)
Answer: C) 0.32 W/(m·K)
36. A spacecraft's heat shield has a mass of 600 kg and absorbs 90 MJ of heat during re-entry. If its
temperature rises by 250°C, what is its specific heat capacity?
A) 500 J/(kg·K) B) 550 J/(kg·K) C) 600 J/(kg·K) D) 650 J/(kg·K)
Answer: C) 600 J/(kg·K)
37. If a thermal protection tile expands by 0.15% when heated from 20°C to 1020°C, what is its
coefficient of thermal expansion?
A) 1.5 × 10⁻⁶ /°C B) 2.0 × 10⁻⁶ /°C C) 2.5 × 10⁻⁶ /°C D) 3.0 × 10⁻⁶ /°C
Answer: A) 1.5 × 10⁻⁶ /°C
38. A spacecraft's velocity decreases from 10 km/s to 2 km/s during re-entry. What percentage of its
initial kinetic energy is converted to heat?
A) 80% B) 84% C) 88% D) 96%
Answer: D) 96%
39. If a heat shield material has a thermal diffusivity of 3 × 10⁻⁷ m²/s and a thermal conductivity of
0.3 W/(m·K), what is its volumetric heat capacity?
A) 0.5 MJ/(m³·K) B) 1.0 MJ/(m³·K) C) 1.5 MJ/(m³·K) D) 2.0 MJ/(m³·K)
Answer: B) 1.0 MJ/(m³·K)
40. A spacecraft experiences a constant deceleration of 30 m/s² during re-entry. How long does it
take to reduce its velocity from 7.5 km/s to 0.5 km/s?
A) 200 s B) 233 s C) 266 s D) 300 s
Answer: B) 233 s
. A spacecraft with a mass of 5000 kg experiences a deceleration of 50 m/s² during re-entry. What is
the force acting on the spacecraft?
A) 200 kN B) 250 kN C) 300 kN D) 350 kN
Answer: B) 250 kN
7. If the specific heat capacity of a heat shield material is 1000 J/(kg·K) and its mass is 100 kg, how
much energy is required to raise its temperature by 500°C?
A) 25 MJ B) 50 MJ C) 75 MJ D) 100 MJ
Answer: B) 50 MJ
8. A spacecraft's heat shield ablates at a rate of 0.1 mm/s. If the initial thickness is 20 mm, how long
will it last before being completely consumed?
A) 100 s B) 150 s C) 200 s D) 250 s
Answer: C) 200 s
9. If the emissivity of a thermal protection system is 0.8 and it radiates 1 MW/m² at temperature T,
what is T according to Stefan-Boltzmann law? (σ = 5.67 × 10⁻⁸ W/(m²·K⁴))
A) 1639 K B) 1823 K C) 2011 K D) 2205 K
Answer: B) 1823 K
10. A spacecraft's heat shield has a thermal diffusivity of 5 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 2 cm thick layer?
A) 400 s B) 600 s C) 800 s D) 1000 s
Answer: C) 800 s
11. If a heat shield tile expands by 0.1% when heated to 1000°C, what is its coefficient of thermal
expansion?
A) 1 × 10⁻⁶ /°C B) 5 × 10⁻⁶ /°C C) 1 × 10⁻⁵ /°C D) 5 × 10⁻⁵ /°C
Answer: C) 1 × 10⁻⁵ /°C
12. A spacecraft experiences a heat load of 100 MJ/m² during re-entry. If its heat shield has a heat
capacity of 2 MJ/(m²·K), what is the temperature rise assuming no heat loss?
A) 25°C B) 50°C C) 75°C D) 100°C
Answer: B) 50°C
13. If the drag coefficient of a spacecraft during re-entry is 1.2 and its frontal area is 10 m², what is
the drag force at an altitude where the air density is 1 × 10⁻⁴ kg/m³ and velocity is 5 km/s?
A) 10 kN B) 15 kN C) 20 kN D) 25 kN
Answer: B) 15 kN
14. A thermal protection system can withstand a maximum stress of 100 MPa. If it experiences a
thermal gradient of 1000°C/cm and has a thermal expansion coefficient of 5 × 10⁻⁶ /°C, what is the
maximum allowable Young's modulus?
A) 100 GPa B) 150 GPa C) 200 GPa D) 250 GPa
Answer: C) 200 GPa
15. If a spacecraft's kinetic energy is reduced by 90% during re-entry and 80% of this energy goes into
heating the thermal protection system, how much energy (as a percentage of initial kinetic energy) is
available for other processes?
A) 10% B) 18% C) 28% D) 38%
Answer: B) 18%
16. A heat shield tile has a thermal conductivity that varies with temperature according to k = 0.1 +
0.0002T W/(m·K), where T is in °C. What is the average thermal conductivity between 20°C and
1020°C?
A) 0.15 W/(m·K) B) 0.20 W/(m·K) C) 0.25 W/(m·K) D) 0.30 W/(m·K)
Answer: B) 0.20 W/(m·K)
17. If a spacecraft's heat shield mass is 15% of the total spacecraft mass, and the total mass is 6000
kg, what is the heat shield mass?
A) 600 kg B) 750 kg C) 900 kg D) 1050 kg
Answer: C) 900 kg
18. A spacecraft experiences a deceleration of 40 m/s² for 3 minutes during re-entry. What is its
change in velocity?
A) 5.2 km/s B) 6.2 km/s C) 7.2 km/s D) 8.2 km/s
Answer: C) 7.2 km/s
19. If the heat of ablation for a thermal protection material is 20 MJ/kg and the heat flux during re-
entry is 10 MW/m², what is the ablation rate in mm/s for a material with density 1600 kg/m³?
A) 0.25 mm/s B) 0.3125 mm/s C) 0.375 mm/s D) 0.4375 mm/s
Answer: B) 0.3125 mm/s
20. A spacecraft's heat shield has a mass of 500 kg and specific heat capacity of 1200 J/(kg·K). If it
absorbs 300 MJ of heat during re-entry, what is its temperature increase?
A) 400°C B) 450°C C) 500°C D) 550°C
Answer: C) 500°C
21. If a thermal protection system has an emissivity of 0.9 and radiates 2 MW/m² at a temperature of
2000 K, what is the Stefan-Boltzmann constant to two significant figures?
A) 5.6 × 10⁻⁸ W/(m²·K⁴) B) 5.8 × 10⁻⁸ W/(m²·K⁴) C) 6.0 × 10⁻⁸ W/(m²·K⁴) D) 6.2 × 10⁻⁸ W/(m²·K⁴)
Answer: A) 5.6 × 10⁻⁸ W/(m²·K⁴)
22. A spacecraft's heat shield loses 2 kg of mass during re-entry. If the heat of ablation is 15 MJ/kg,
how much energy was absorbed by the ablation process?
A) 20 MJ B) 25 MJ C) 30 MJ D) 35 MJ
Answer: C) 30 MJ
23. If a thermal protection tile has a thermal expansion coefficient of 3 × 10⁻⁶ /°C and expands by 0.3
mm when heated, what was its original length if the temperature change was 500°C?
A) 150 mm B) 175 mm C) 200 mm D) 225 mm
Answer: C) 200 mm
24. A spacecraft's heat shield has a thermal conductivity of 0.2 W/(m·K) and thickness of 10 cm. If
the outer surface is at 1500°C and the inner surface at 50°C, what is the heat flux through the shield?
A) 290 kW/m² B) 310 kW/m² C) 330 kW/m² D) 350 kW/m²
Answer: A) 290 kW/m²
25. If a heat shield tile has a density of 200 kg/m³ and a specific heat capacity of 1000 J/(kg·K), what
is its volumetric heat capacity?
A) 100 kJ/(m³·K) B) 150 kJ/(m³·K) C) 200 kJ/(m³·K) D) 250 kJ/(m³·K)
Answer: C) 200 kJ/(m³·K)
26. A spacecraft enters the atmosphere at 11 km/s and experiences a constant deceleration until it
reaches 300 m/s. If the deceleration takes 5 minutes, what is the average deceleration?
A) 35.8 m/s² B) 35.8 g C) 3.58 g D) 3.58 m/s²
Answer: A) 35.8 m/s²
27. If a heat shield's emissivity increases from 0.7 to 0.9 due to surface changes during re-entry, by
what factor does its radiative heat dissipation capability increase at a given temperature?
A) 1.14 B) 1.22 C) 1.29 D) 1.36
Answer: C) 1.29
28. A thermal protection system uses phase change material that absorbs 400 kJ/kg during melting. If
the total heat input during re-entry is 80 MJ and the heat shield mass is 500 kg, what percentage of
the material undergoes phase change?
A) 30% B) 35% C) 40% D) 45%
Answer: C) 40%
29. If a spacecraft's kinetic energy decreases from 50 GJ to 10 GJ during re-entry, and 75% of the
energy difference goes into heating the thermal protection system, how much heat does the system
absorb?
A) 20 GJ B) 25 GJ C) 30 GJ D) 35 GJ
Answer: C) 30 GJ
30. A heat shield tile has a thermal diffusivity of 4 × 10⁻⁷ m²/s. How long does it take for a
temperature change to propagate through a 5 cm thick layer?
A) 1562.5 s B) 2500 s C) 3125 s D) 3750 s
Answer: C) 3125 s
31. If a spacecraft's heat shield can withstand a maximum heat flux of 1.2 MW/m² and the actual
heat flux during re-entry peaks at 900 kW/m², what is the safety factor?
A) 1.2 B) 1.33 C) 1.5 D) 1.67
Answer: B) 1.33
32. A thermal protection system uses a material with a density of 300 kg/m³. If the heat shield has a
surface area of 20 m² and a thickness of 5 cm, what is its mass?
A) 250 kg B) 275 kg C) 300 kg D) 325 kg
Answer: C) 300 kg
33. If the temperature of a heat shield increases from 20°C to 1520°C in 2 minutes, what is the
average rate of temperature increase?
A) 10°C/s B) 12.5°C/s C) 15°C/s D) 17.5°C/s
Answer: B) 12.5°C/s
34. A spacecraft with a mass of 4000 kg experiences a drag force of 200 kN during re-entry. What is
its deceleration?
A) 40 m/s² B) 45 m/s² C) 50 m/s² D) 55 m/s²
Answer: C) 50 m/s²
35. If a heat shield's thermal conductivity increases by 5% for every 100°C rise in temperature, what
is its thermal conductivity at 1000°C if it was 0.2 W/(m·K) at 0°C?
A) 0.28 W/(m·K) B) 0.30 W/(m·K) C) 0.32 W/(m·K) D) 0.34 W/(m·K)
Answer: C) 0.32 W/(m·K)
36. A spacecraft's heat shield has a mass of 600 kg and absorbs 90 MJ of heat during re-entry. If its
temperature rises by 250°C, what is its specific heat capacity?
A) 500 J/(kg·K) B) 550 J/(kg·K) C) 600 J/(kg·K) D) 650 J/(kg·K)
Answer: C) 600 J/(kg·K)
37. If a thermal protection tile expands by 0.15% when heated from 20°C to 1020°C, what is its
coefficient of thermal expansion?
A) 1.5 × 10⁻⁶ /°C B) 2.0 × 10⁻⁶ /°C C) 2.5 × 10⁻⁶ /°C D) 3.0 × 10⁻⁶ /°C
Answer: A) 1.5 × 10⁻⁶ /°C
38. A spacecraft's velocity decreases from 10 km/s to 2 km/s during re-entry. What percentage of its
initial kinetic energy is converted to heat?
A) 80% B) 84% C) 88% D) 96%
Answer: D) 96%
39. If a heat shield material has a thermal diffusivity of 3 × 10⁻⁷ m²/s and a thermal conductivity of
0.3 W/(m·K), what is its volumetric heat capacity?
A) 0.5 MJ/(m³·K) B) 1.0 MJ/(m³·K) C) 1.5 MJ/(m³·K) D) 2.0 MJ/(m³·K)
Answer: B) 1.0 MJ/(m³·K)
40. A spacecraft experiences a constant deceleration of 30 m/s² during re-entry. How long does it
take to reduce its velocity from 7.5 km/s to 0.5 km/s?
A) 200 s B) 233 s C) 266 s D) 300 s
Answer: B) 233 s
41. If a heat shield's emissivity is 0.85 and it radiates 1.5 MW/m² at temperature T, what is T
according to Stefan-Boltzmann law? (σ = 5.67 × 10⁻⁸ W/(m²·K⁴))
A) 1823 K B) 1932
