Expert: Steve Johnson - 9/19/2006

Question
How strongly, and in what direction does a 1-newton apple pull on the earth?  I understand that the earth pulls on the apple and the apple pulls on the earth with a force equal to the mass of the earth divided by the distance squared between them. I believe the answer to be upward with a force of more than 1-newton, but since the direction of the apple is downward it seems possible to me that the force could be downward 1-newton.

Answer
Hello Joelle,

The apple exerts a 1-Newton pull on the Earth - toward the apple. It's fitting that we're talking about an apple because my answer is based on Newton's 3rd Law: "To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts." (They talked funny back then.)

If you could place 2 moon-sized objects 20 Km from each other out in inter-galactic space with no relative velocity, each would be pulled toward the other by an equal force. Even if one were made of lead and the other of styrofoam. The force on each would be the same, although the acceleration and final velocity of the heavy one would be much less than the other. (The statement about comparing acceleration needs to be related to a reference system in which the original position of the moons is stationary.)

I need to disagree with 2 details of how you state the Law of Universal Gravitation. You said, "... force equal to the mass of the earth divided by the distance squared between them". Better would be "... force **proportional** to the mass of the earth **times the mass of the apple** divided by the distance squared between them". There is a constant G called the Constant of Universal Gravitation. If G is included in the formula, then the expression is equal to the force.

F = G*m1*m2/r^2

I hope this helps,
Steve