What is the force of gravity, $F_g$, if the distance between two objects is $0$? Wouldn't that mean that the fraction: $m_1m_2/d^2$ is undefined? And in that case, how would you escape Earth's gravity field unless you had no mass?
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Two objects can't be zero distance away. Even if they could, you would be well within the regime where classical gravity failed at that point, so Newton's law of gravity wouldn't apply anyway.
To be clear, the distance $d$ here is between the center of gravity of two objects, so several thousand kilometers on the earth. So whatever gravity does at $d=0$, it isn't relevant for escaping the earth's gravity.
Chris
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The gravitational force will never be 0. Typically what you will see is that the force of gravity approaches 0 as d goes to infinity. Therefore, to escape Earth's gravity, you would need a speed that puts you infinitely far away from Earth, thus reducing the force and potential energy to 0.
In the case when d is equal to 0, the gravitational force is undefined like you said, but this is not an issue since this would mean the objects are at the same point in space.
BioPhysicist
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