Question

A satellite of mass 3.00 x 10⁴ kg is placed in orbit around Jupiter. The mass of Jupiter is 2.90 x 10²⁷ kg. The distance between the satellite and the centre of Jupiter is 9.24 x 10⁷ m.

1. Determine the force of gravitational attraction between the satellite and Jupiter.
2. One of the moons of Jupiter is Io. The distance between the centre of Jupiter and the centre of Io is 5.22 x 10⁸ m. If the force of gravitational attraction between Io and Jupiter is 6.35 x 10²² N, what must be the mass of Io?
3. If the mass of Io were to suddenly double, by what amount would the force of gravitational attraction change? (Do not actually calculate the force of attraction; just determine how much more or less the force of gravity would change.)
4. One of the other moons that orbit Jupiter is Callisto. Its mass, m_C, is 2.08 x 10²³ kg. If the force of gravity between Jupiter and Callisto is 2.87 x 10²¹ N, then what must be the distance between the centre of Jupiter and the centre of Callisto? (This represents the radius of orbit R_o)
5. If the distance between (R_o) Jupiter and Callisto doubles, by what amount would the force of gravitational attraction (F_g) change?

Answer 1

This Problem requires the application of Newton's Law of Gravitation.

We can clearly see that the Force of Gravity directly depends on the product of masses and inversely depends on the square of the distance between the centres of two objects under consideration.

Hope This Helps!!