Orbits and Gravity: Gravity Puzzle

Astro 112/114/120 KEY AACC Levine

Gravity Ranking Task #1

Ranking Instructions: Rank the asteroid pairs in order of the strength of the gravitational force exerted on the asteroid on the left side of each pair.

Greatest Force 1_____ 2_____ 3_____ 4_____ 5 _____ Least Force

Or, the strength of the gravitational force exerted in each case is the same. ______

Explain your reasoning for ranking this way: Since the distance is the same for all pairs, the strength of the gravitation force is proportional to the combination of the two masses (multiplied together) so the most total mass creates the greatest force on EITHER member of the pair.

E B C A D

Astro 112/114/120 KEY AACC Levine

Gravity Ranking Task #2

The figure below shows five different locations (A-E) for a satellite orbiting the Earth. The Earth has a mass ME and the satellite has a constant mass m, only the distance varies.

Ranking Instructions: Rank the satellite locations in order of the strength of the gravitational force exerted on the satellite by the Earth form least force to greatest force.

Least Force 1_____ 2_____ 3_____ 4_____ 5 _____ Greatest Force

Or, the strength of the gravitational force exerted in each case is the same. ______

Explain your reasoning for ranking this way: Since the masses are the same in all pairs, the gravitational force is inversely proportional to the distance (it decreases with increasing distance) so these are ranked from largest distance to smallest distance.

Earth

A

d=4

C d=2

D B

d=1d=1.5

E

d=3

A E C D B

Astro 112/114/120 KEY AACC Levine

Gravity Ranking Task #3

The table below shows the masses and distances for four different pairs of stars (A-D). The masses and distances are in arbitrary units.

Ranking Instructions: Rank the pairs of stars in order of the strength of the gravitational force exerted between the pairs from least force to greatest force.

Least Force 1_____ 2_____ 3_____ 4_____ Greatest Force

Or, the strength of the gravitational force exerted in each case is the same. ______

Explain your reasoning for ranking this way: Here both distance and mass are changing so you need to multiply the masses together and divide by the distance squared to combine the two effects. That means that you rank in order of the number you calculate in the rightmost column from least to greatest.

Case Star #1 Mass Distance between Star #1 and Star #2

Star #2 Mass d2 Mm/d2

A 2 1 2 1 4

B 2 2 2 4 1

C 2 4 2 16 1/4

D 4 2 2 4 2

C B D A

Astro 112/114/120 KEY AACC Levine

Gravity Ranking Task #4

This diagram shows the Earth and Moon (not to scale) and 5 positions where a spacecraft might be located. Point C is exactly halfway between the Earth and the Moon.

Ranking Instructions: Rank the lettered positions in order of how strong the combined gravitational pull from both the Earth and the Moon on the spaceship would be at that position.

Least Force 1_____ 2_____ 3_____ 4_____ 5 _____ Greatest Force

Or, the strength of the gravitational force exerted in each case is the same. ______

Additional Question: Is the combined pull from Earth and Moon at position C towards the Earth or towards the Moon? Towards Earth

Explain your reasoning: The gravitational pull of the Earth pulls the spaceship towards it (down and to the left) and the gravitational pull of the Moon on the spaceship pulls it up and to the right. At point C, the distances are equal, and the pull towards Earth is greater due to Earth’s greater mass. As you move from C to B to A, the pull from the Earth gets stronger and the pull from the Moon weaker, so the strongest pull is towards the Earth at point A. Moving the other direction, from C to D to E increases the pull towards the Moon and decreases the pull towards the Earth. The pull towards the Moon is subtracted from the pull towards the Earth and the total force is weaker. If you go far enough towards the Moon the forces will be equal and will cancel out. Closer to the Moon from there, and the pull will be towards the Moon.

A B C D E

Astro 112/114/120 KEY AACC Levine

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