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    kenmoore22's Avatar
    kenmoore22 Posts: 2, Reputation: 1
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    #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's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #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's Avatar
    systm11eleven Posts: 1, Reputation: 1
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    #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's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #4

    Jul 28, 2009, 05:44 AM
    Quote Originally Posted by systm11eleven View Post
    M is the mass of the earth
    Yes
    Quote Originally Posted by systm11eleven View Post
    and m is the mass of the satellite
    Yes
    Quote Originally Posted by systm11eleven View Post
    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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