Brief overview of activity using a modified version of

Question

Mass of Saturn Activity-

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

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 mass 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.

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 its moon Phoebe: period of orbit is 1.507 years, average orbital distance is 0.0863 astronomical units.

Your calculated mass of Saturn is ____________________ solar mass units.

You can convert your result above into kilograms by multiplying it by the mass of the Sun in kilograms, 2.00 x 10³⁰ kg.

Your calculated mass of Saturn is ____________________ kg.

Compare your calculated mass of Saturn (kg) to the actual value.

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.