Question: A very small moon with a mass of 5 tons orbits Jupiter. Another small

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Question: A very small moon with a mass of 5 tons orbits Jupiter. Another small moon with the same mass also orbits Jupiter, but with an orbit radius 3 times larger than the orbit radius for the first moon. What is the ratio of the gravitational force Jupiter exerts on the first moon compared to the gravitational force it exerts on the second moon?

What I have done so far:

Use the formula F= GM1M2/ r^2 where G= 6.67 x 10^-11; 5 tons= 4535.92 kg.; Jupiter's mass= 1.8987 x 10^27 kg.

Moon #1:

Mass= 4535.92 kg.
Radius= 2 m. (made up)

So... 6.67x10^-11(4535.92)(1.8987x10^27)/ 2^2 = 1.43610958 x 10^20

Moon #2:

Mass= 4535.92 kg.
Radius= 6 m. (made up x 3)

So... 6.67x10^-11(4535.92)(1.8987x10^27)/ 6^2 = 1.595677311 x 10^19

To get the ratio: divide moon #1 gravitational force by moon #2's gravitational force to get .900

Did I do this correctly?

Thank you for your help!

Explanation / Answer

you did it right, im assuming you just made a typing error in the end. everything is constant except for the radius, there is no reason to use numbers and make things more complicated than it needs to be. always try to do a problem with variables first. it greatly reduces the chance of error.

Gm1m2/(1r)2 gives you the force of the first moon.

Gm1m2/(3r)2 gives you Gm1m2/9r2, which is the force on the second moon.

you can rewrite this as 1 * Gm1m2/r2 : 1/9 * Gm1m2/r2 in order to see it more clearly

this gives you a ratio of 1:9

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