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Energy of orbiting satellites

  1. Apr 2, 2005 #1
    this is the problem...
    What is the change in gravitational potential energy of a 6200kg satellite that lifts off from Earth's surface into a circular orbit of altitude2500km?

    i did this...
    r = rE +h
    =6.38 x10^6m + 2.5 x10^6m
    r=8.88 x10^6m

    Eg= -GMm
    r
    =-6.673x10-11N m2/kg2 (5.98 x10^24kg)(6200kg)
    8.88 x10^6m
    Eg=-2.786127793 x10^11J

    Eg=mgh
    =6200kg(9.82m/s2)(-2.5 x10^6m)
    Eg=-1.52055 x10^11J

    Change in Gravitational Potential Energy
    ∆ Eg = Eg - Eg
    =-2.786127793 x10^11J – (-1.52055 x10^11J)
    ∆ Eg =-1.265577793 x10^11J

    but the answer on my book is 1.1x10^11J, can anyone check this, coz im not sure where is the mistake.. thanks for the help
     
    Last edited: Apr 2, 2005
  2. jcsd
  3. Apr 2, 2005 #2

    Janus

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    Staff Emeritus
    Science Advisor
    Gold Member

    Your problem is here:

    Eg=mgh
    =6200kg(9.82m/s2)(-2.5 x10^6m)
    Eg=-1.52055 x10^11J

    You should have just the used the same form used in the prior Eg formula

    [tex]E_g = \frac{GMm}{R}[/tex]

    with a different value for R
     
  4. Apr 2, 2005 #3
    satellites

    thanks for the help... i get the answer now...
     
  5. Apr 2, 2005 #4
    another problem is... a rocket is launched vertically from earth's surface with a velocity of3.4km/s. How high it go a)from Earth's centre and b) from Earth's surface.
    a)r = 2GM
    V^2
    = 2(6.673x10^-11N m^2/kg^2) (5.98 x10^24kg)
    (3400m/s)^2
    r=7.0x107m

    i dont know waht to do with b), i am thinking to add the raduis of the earth, but my answer is wrong... the answer should be 650km.
     
    Last edited: Apr 2, 2005
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