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Period of Elliptical Orbit

  1. Apr 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 400 km above the earth's surface; at the high point, or apogee, it is 4000 km above the earth's surface.

    1. What is the period of the spacecraft's orbit?

    2. Relevant equations

    Kepler's 3rd Law: T=(2*pi*a3/2)/ sqrt(GME)

    where a=semi-major axis

    3. The attempt at a solution

    So the first thing I did was find the semi-major axis (value a of the eqn above):
    (1/2)*(4000+400)=2200 km or 2.2*106 m

    Then I plugged it into the equation along with the following constants:
    G=6.67*10-11 m2/kg2,
    ME=5.97*1024kg

    T=(2*pi*2.2*10(6)3/2)/ sqrt(6.67*10-11*5.97*1024)= 1027 seconds

    I checked the back of the book and the answer is wrong. I have no clue what I am doing wrong....:( Any help would be greatly appreciated.
     
  2. jcsd
  3. Apr 21, 2009 #2

    LowlyPion

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    Homework Helper

    Perigee = 6380 + 400 in km
    Apogee = 6380 + 4000 in km
     
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