At what distance from the Earth and the moon have zero net force?

AI Thread Summary
To determine the distance from Earth where a spacecraft experiences zero net force due to equal gravitational pulls from both Earth and the Moon, the gravitational force equations for both bodies must be set equal. The ratio of the masses of Earth and the Moon is approximately 81.3, which can be used to derive the relationship between the distances involved. The equation GM(earth)/(R-d)^2 = GM(moon)/d^2 is central to solving the problem. The user expresses confusion about how to proceed with the calculations, seeking assistance in applying the relevant equations. The discussion emphasizes the importance of understanding gravitational forces and their balance in space travel.
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Homework Statement



At what distance from the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?

Homework Equations



GM(earth)/(R-d)^2=GM(moon)/d^2

The Attempt at a Solution


Me/Mm=81.3
root 81.3=(R-d)/d

I have no idea how to figure out the rest of the question. Please help.
 
Physics news on Phys.org
(a-b)/c = a/c - b/c

use this and solve
 
(a-b)/c = a/c - b/c

use this and solve
 

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