Astrology Assignment

Brief Overview of Activity: Using a modified version of Kepler's Third Law and orbital data from several of Saturn's moons, the mass of Saturn can be determined.

Required Items: a scientific calculator

Procedure:

You have learned that Kepler's third law, P2 = a3, applies to any object orbiting the Sun. Newton was able to derive Kepler's third law using his law of gravity. Newton's version includes the masses of both objects, P2 = a3 / (M1 + M2) and can be used for any object that orbits any astronomical body. In this formula, the masses are measured in special units called solar mass units. The mass of the Sun is equal to one solar mass unit (SU). 

If the mass of the second object is very small compared to the first mass, then to a good approximation P2 = a3 / M1. Solving for the mass we get M1 = a3 / P2. Use this mass formula to determine the mass of Saturn using data from five of its moons. The following data will be used:

To use Kepler’s Third Law, you must first calculate the distances in AU and the periods in years. Use 1.5 × 108 km for the AU and 365.25 d for the year. Then calculate the mass in solar units (SU) for each satellite and Saturn’s mass in kilograms by multiplying each result by the Sun’s mass (2.0 × 1030 kg)*. Calculate the mean values for Saturn’s mass in solar units and in kg and fill in the last two columns of the table. For example, for Dione, divide 377,400 by 1.5E8 to get “a” in AU. Then divide 2.737 d by 365.25 d/yr to “p” in years. Cube “a” and square “p” to get M in SU. Note that M (SU) must be much smaller than 1 and that the values for all moons must agree closely. If they don’t agree or if the SU values are larger than 1, then you’ve done something wrong.

Your mean calculated mass of Saturn is ____________________ solar mass units.

Your mean calculated mass of Saturn is ____________________ kg.

Compare your calculated mass of Saturn (kg) to the actual value, which you can look up by Googling “mass of Saturn”. Since the superscripts are all the same in the formula below, you don’t need to use them in the calculation. Keep the sign, however, because that gives important information. Show your calculation below.

Percent Difference = 100 x (your calculated value - actual value ) / ( actual value )

Your calculated Percent Difference is __________ %.

How close did you get? Explain any possible difference.

Consult the rubric for this project for detailed information on what to do and the points for individual parts of the project.

Turn in this form to your submission folder.

* You can calculate cubes easily if you have an x3 key on your calculator. You can also use the xy or the yx key, whichever you have. Enter the exponent first, press the xy key, then enter the value and press the = key, or enter the exponent, press enter, then key in the value and press yx. Test your method by cubing 3 to get 27.