kenmoore22 Posts: 2, Reputation: 1 New Member #1 Oct 24, 2007, 12:33 PM
The gain of kinetic energy
Taking a practice ASVAB test and this one has stumped me. HELP!!

14: The gain in kinetic energy if a 400-kilogram satellite moves from a distance of 3 × 106 meters above the surface of the Earth to a point 1.50 × 106 meters above the surface is _______ J. The mass of the Earth is 5.98 × 1024 kilograms and the radius of the Earth is 6.37x106 meters.

I don't even know where to start on this one. I'd appreciate some guidance. Thanks
 ebaines Posts: 12,131, Reputation: 1307 Expert #2 Oct 24, 2007, 01:12 PM
The gain in kinetic energy is equal to the loss in potential energy of the satellite, as it moves closer to the earth. The change in potential energy of an object in a gravitational field is GMm(1/R1 - 1/R2), where R1 and R2 are the distances from the center of mass of the earth.

If you need to understand why the potential energy is of the form GMm/R, post back.
 systm11eleven Posts: 1, Reputation: 1 New Member #3 Jul 27, 2009, 03:17 PM

M is the mass of the earth and m is the mass of the satellite and G is the radius of the earth?
 ebaines Posts: 12,131, Reputation: 1307 Expert #4 Jul 28, 2009, 05:44 AM
Originally Posted by systm11eleven
M is the mass of the earth
Yes
Originally Posted by systm11eleven
and m is the mass of the satellite
Yes
Originally Posted by systm11eleven
and G is the radius of the earth?
No - G is the gravitational constant. See: Gravitational constant - Wikipedia, the free encyclopedia
The radius of the earth has nothing to do with it.

EDIT: However, the distance from the center of the earth to the satellite (R1 or R2 in the formula) is equal to the radius of the earth plus the height of the satellite above the earth's surface.

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