You have learned that Kepler\'s third law, P 2 = a 3 , applies to any object orb

Question

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.

Explanation / Answer

a.)M=(0.158)^3/(2.075)^2=9.16 x10^-4 Solar mass units

b.)mass of jupiter=9.16 x10^-4*2 x10^30=1.832 x10^27 Kg

c.) actual mass of Jupiter=1.8987 x 10^27 kg

Difference=0.0667 x10^27

So very close we got

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