Mass of Jupiter Activity (Project 4) Brief Overview of Activity : Using a modifi
ID: 2298400 • Letter: M
Question
Mass of Jupiter Activity (Project 4)
Brief Overview of Activity: Using a modified version of Kepler's third law, and orbital data from one of Jupiter's moons, the mass of Jupiter can be determined.
Required Items: a calculator, your textbook, pencil & paper.
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 Jupiter using data from its moon Sinope: period of orbit is 2.075 years, average orbital distance is 0.158 astronomical units.
Your calculated mass of Jupiter 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 10 30 kg.
Your calculated mass of Jupiter is ____________________ kg.
Compare your calculated mass of Jupiter (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.
Explanation / Answer
mass units = 0.158^3/2.075^2=9.16E-4
so 9.16E-4*2.0E30=1.83E27
mas of jupiter is actually 1.89E27
so % difference is (1.89E27-1.83E27)/1.89E27=0.0317 = 3.17%