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Homework Help: Physics Gravitation Problem

  1. Apr 7, 2005 #1
    How would i go about doing a problem like this?

    A 1500 kg satellite is orbiting the earth at a height of 250 km. How much work would it take to move it into an 800 km orbit?
     
    Last edited: Apr 7, 2005
  2. jcsd
  3. Apr 7, 2005 #2
    Use the gravitational potential energy. If the radius increases, this energy will become less negative, ergo, the energy rises...

    marlon
     
  4. Apr 7, 2005 #3
    The formula is [tex]- \frac{GMm}{R}[/tex]

    G is the universal gravitational constant
    M is the mass of the first object
    m is the mass of the second object
    r is the radius

    be sure to treat the earth as a point mass with all mass centered in that point. Thus, you will also need the earth's radius...

    marlon
     
  5. Apr 7, 2005 #4
    that is just the equation for gravitational potential energy at one point. wouldn't it have kinetic? and it asks for work in the question. also, its worth 10 marks, so i don't think it can be that simple.

    i've done some where you take it off the surface and throw it into orbit, and i used

    Etotal(orbit) = Epotential(surface) + W
     
  6. Apr 7, 2005 #5

    dextercioby

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    The total mechanical energy (KE + gravitational potential) that a body has is found,when solving the Kepler problem in CM,

    [tex] \mbox{Tot \ E}=-G\frac{m_{body}M_{Earth}}{2a} [/tex]

    ,where "a" is the big semiaxis of the elliptical orbit.However,it can be proven really easliy that "a" goes to R (radius of orbit) for a circular orbit.

    It's all u need to know.The work done is simply the variation in total energy of the body.

    Daniel.
     
  7. Apr 7, 2005 #6
    isn't that just its total energy at that point? what is the work used to bring it up into a higher orbit? this is the equation my professor gave me for moving something from the surface up into an orbit: Etotal(orbit) = Epotential(surface) + W
     
  8. Apr 7, 2005 #7

    dextercioby

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    Mind that there's a trick here.The height is given wrt Earth's surface,while R in the formulas is the distance between the Earth's center & the orbit (the circle's radius).

    So u need to add the mean Earth's radius

    [tex] \bar{R}_{Earth}\simeq 6371 \ \mbox{Km} [/tex]

    Daniel.


    P.S.Of course,for consistency of units,u need to transform every length from Km to m...
     
  9. Apr 7, 2005 #8

    dextercioby

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    The sattelite is already in orbit...W is just the diff.between total energies...

    Daniel.
     
  10. Apr 7, 2005 #9
    so its just Etotal(2nd orbit) - Etotal(1st orbit)? using the equation you said, except using the larger value 800km for R for the 2nd orbit and smaller 250km for 1st orbit?
     
  11. Apr 7, 2005 #10

    dextercioby

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    Yeah,that's right...

    Daniel.
     
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