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?
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Answer:
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=10ms2 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=GMmr2
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 10ms2 to make the mass easy.
M=12500N10ms2=1250kg
m=8400N10ms2=840kg
The distance was given:
r=23m
We can look up a value for G:
G=6.67408×10−11m3kgs2
And plug that all into the first equation:
F=6.67408×10−111250⋅840232N
F=1.325×10−7N
That seems very small, but in space, that could eventually draw these two objects together.
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