ExpErdMann

2004-Aug-19, 02:59 PM

For a body in orbit around the Earth the forces of gravity and centrifugal motion are balanced:

(1) mv^2/r = GMm/r^2 ,

where M is the Earth, m is the body and r is the distance from the Earth's centre.

We then have

(2) mv^2 = GMm/r ,

and the kinetic energy of the body is equal to the gravitational potential energy (except for a factor of 2).

Now if the same body is lying on the Earth's surface, the gravitational force on it is still GMm/r^2. To prevent the body from falling into the Earth's centre, there must be an equal outward force to balance this. This force must be related to the stress energy of the Earth that was built up during the Earth's formation. As each piece of mass was added to the young Earth, it caused a compression of the existing Earth body. If this is true, then would it be correct to say that the total stress energy of the Earth is equal to the total gravitational potential energy of the Earth? The latter is about - 10^32 J.

(1) mv^2/r = GMm/r^2 ,

where M is the Earth, m is the body and r is the distance from the Earth's centre.

We then have

(2) mv^2 = GMm/r ,

and the kinetic energy of the body is equal to the gravitational potential energy (except for a factor of 2).

Now if the same body is lying on the Earth's surface, the gravitational force on it is still GMm/r^2. To prevent the body from falling into the Earth's centre, there must be an equal outward force to balance this. This force must be related to the stress energy of the Earth that was built up during the Earth's formation. As each piece of mass was added to the young Earth, it caused a compression of the existing Earth body. If this is true, then would it be correct to say that the total stress energy of the Earth is equal to the total gravitational potential energy of the Earth? The latter is about - 10^32 J.