Question

On earth, two parts of a space probe weigh 12500 N and 8400 N. These parts are separated by a center-to-center distance of 23 m and are spherical. How do you find the magnitude of the gravitational force that each part exerts on the other out in space?

Answer 1

`0.13` microNewtons
And that's the same force they exert on each other on earth when set 23 meters apart.

Explanation:

Let's assume that `g=10 m/s^2` to simplify some of our math.

The gravitational force between two objects can be calculates as a function of the product of their masses (`M` and `m`), the square of the distance between them (`r`), and the universal gravitational constant. In the case of spherical objects, this is exactly correct. For more complicated shapes you might have to analyze different parts separately.

`F = G(Mm)/r^2`

The mass of the objects can be found by dividing their weight by the gravitational acceleration at the surface of the earth. I'm using `10m/s^2` to make the mass easy.

`M = (12500 N)/(10 m/s^2) = 1250 kg`
`m = (8400 N)/(10 m/s^2) = 840 kg`

The distance was given:
`r = 23 m`

We can look up a value for G:
`G = 6.67408 × 10^-11 m^3/ (kg s^2)`

And plug that all into the first equation:
`F = 6.67408 × 10^-11 (1250*840)/23^2 N`
`F = 1.325 × 10^-7 N`

That seems very small, but in space, that could eventually draw these two objects together.