How to find acceleration due to gravity on jupiter

Question

Jupiter is the largest planet in the solar system, with a mass of 1.90 x 10²⁷kg and a radius of 7.18 x 10⁷ m. A space probe of mass 185 kg is sent to the planet's surface to examine its atmosphere. What acceleration due to gravity will this probe detect near Jupiter's surface?

I'm getting a different answer every time and don't know what the actual formula for this is.

Answer 1

From Newton's law of gravity, the force of gravity between two bodies is found by the equation:

F = (G x m₁ x m₂)/r²

Where F is the gravitational force, G is the gravitational constant 6.67 x 10^-11, m₁ and m₂ are the masses of the bodies, and r is the distance between them.

The force between Jupiter and the probe on the surface of Jupiter would be:

F = (6.67 x 10^-11) (1.9 x 10²⁷) (185) / ( 7.18 x 10⁷)²

= 4547.8 N

This would also be the weight of the probe since it's on the surface of Jupiter and the force we just found is the force of gravity on the surface between the two.

Since F = mg:

4547.8 = 185g

24.58 m/s² = g