-2

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?

Kyle Kanos
  • 28,229
  • 41
  • 68
  • 131
Athreya
  • 21
  • 1
  • What do you mean by Fg? This question will be easier to answer if you explain in more detail what you want to know. – ZachMcDargh Jan 05 '18 at 03:31
  • 2
    how would the distance between two objects be 0? – pentane Jan 05 '18 at 04:28
  • With the Earth gravity, the only case of a zero distance is if you drill a tunnel to the center of the Earth and lower your object there. In this case the gravitational force would be zero, because the mass of the Earth in the formula is only the mass below the object that would be zero in the center. No mass under the feet, no gravity. As you pull the object back to the surface, it would become gradually heavier until it gets its full weight at the surface. – safesphere Jan 05 '18 at 10:00

2 Answers2

2

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
  • 17,189
0

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
  • 56,248
  • 2
    I don't think the OP is asking for when is the gravitational force 0, but rather what happens when the distance between the objects is 0. – ZeroTheHero Jan 05 '18 at 02:48
  • I think you are right. I just got confused with the wording and with the mention of escaping Earth's gravity. – BioPhysicist Jan 05 '18 at 03:35