Weight Changes with Position On/In Earth

## Question:

1. At what point on the Earth do you weigh the most?
2. If you dig a hole to the center of the Earth how would your
weight change as you went towards the center.

## Answer:

Define weight to be the net force with which you are pressed
against the surface of the Earth. That force is made up of the
force due gravity and the apparent force due to the rotation of
the Earth. The Earth's surface tends to pull away from you
due to its rotation so the apparent (centrifugal) force due to
rotation is directed directly away from the Earth's axis of
rotation. The strength of this centrifugal force is proportional
to your distance from the Earth's axis of rotation. At the
equator the centrifugal force is maximum and directed exactly
opposite to the gravitational force. At the poles the centrifugal
force goes to zero.
The force of gravity depends on the actual distribution of the
mass of the Earth and your distance from the center of that mass.
Assuming the Earth to be spherical and homogeneous, meaning that
the mass is uniformly distributed throughout the sphere, your
weight will be maximum at the poles. In fact the gravitational
force varies a bit over the surface of the Earth depending on
altitude and mass distribution. In practice the variations in
weight over the Earth's surface are so small compared to the
total weight that they may be neglected for most purposes.

If there were a hole drilled through the center of a solid
sphere and you jumped into the hole, your weight would become
zero since the force pressing against the Earth would disappear.
It would stay zero as long as you stayed in the hole. To see how
your acceleration depends on your position relative to the center
of the sphere, look at our Physics 1
course on the web.

J. D. Jones

M. Casco Associates