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Calculating Height, Velocity of mass in orbit.

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  1. Dec 7, 2014 #1
    The problem is from a practice exam given to us by our professor to prepare for our final this coming week.

    1. The problem statement, all variables and given/known data


    A satellite in a circular geostationary orbit
    above the Earth’s surface (meaning it has the
    same angular velocity as the Earth) explodes
    in to three pieces of equal mass. One piece
    remains in a circular orbit at the same height
    as the satellite’s orbit after the collision, but
    the velocity of this piece is in the opposite direction
    to the velocity of the satellite before
    the explosion. After the explosion the second
    piece falls from rest in a straight line directly
    to the Earth. The third piece has an initial velocity in the same direction as the original direction of
    the satellite, but now has a different magnitude of velocity. The diagram is obviously not remotely to
    scale!
    (a) At what height above the Earth does the satellite orbit?
    (b) What is the magnitude of the velocity of the satellite along it’s original circular path?


    2. Relevant equations
    Fg = (GMeMs)/(R^2)
    Ms*a = GMeMs / R^2
    a= v^2/R
    v = 2piR/Period
    3. The attempt at a solution
    I messed around with the equations to get =
    v^2 = GMe/R
    after which i used v = 2piR/Period.

    To find the period, I did 24*60*60 / 1 complete oscillation (=86,400). The answer key for some reason is saying: 24*60*60/ 2 (=43,200) . That's something I am having trouble understanding.

    Anyways, I continued with 43,200. I messed with the equations again to get:

    v^2 = 4pi^2R^2 / (43,200^2) = GMe/R. I solved the equation, and got 2.66*10^7.

    The answer key decided to multiply Me by .1. How come?



    I am posting the answer key link here: http://www.ic.sunysb.edu/class/phy141md/doku.php?id=phy141:examprep:final10sols (it's the first problem)
     
  2. jcsd
  3. Dec 7, 2014 #2
    JK. I figured it out! I was looking at the wrong solutions! Can a Mod Please delete this thread!!!
     
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