Gravity Rocks!
Three friends were talking about gravity. One friend
held up a rock and asked his friends whether the gravi-
tational force on the rock depended on where the rock
was located. Each friend had a different idea about a
place where the gravitational force on the rock would
be the greatest. This is what they said:
Lorenzo: "I think if you put the rock on the top of a very tall mountain, the gravita-
tional force on the rock will be greatest."
Eliza: "I think the gravitational force will be greatest when the rock is resting on
the ground near sea level."
Flo: "I think you have to go really high up. If you drop the rock out of a high-
flying plane, the gravitational force will be greatest."
Explain why you agree with
Which friend do you most agree with?
that friend.

Newton’s law of universal gravitation is [tex]F = G\frac{m_1m_2}{r^2}[/tex] where G is a constant and both masses are constant in this experiment as well. So it only depends on r, the distance between the center of mass of both objects.

Bringing it high in the sky, as Flo suggests, is definitely not a good idea because it only increases the distance from the center of the Earth mass.

A mountain contains significant mass, so the center of the Earth mass is somewhat shifted to regions with the largest mountains. However, standing on top of a mountain, as Lorenzo suggests, doesn’t help since the shift of the center of mass, if any, is far smaller than the height of the mountain.

Standing near sea level, as Eliza suggests, is a good way to minimize the distance to the center of the Earth mass.