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Semi-major axis of an Orbit

  1. Aug 6, 2015 #1
    1. The problem statement, all variables and given/known data
    (a) A satellite is initially in a geostationary orbit around the Earth, so that the satellite always remains above the same point on the Earth’s equator. Show that the radius of the orbit is ##4.22\times 10^7##


    (b)An engine is briefly fired in the direction of the satellite’s motion, making the speed of the satellite suddenly increase to a speed ##v_p## and sending the satellite into an elliptical orbit with eccentricity ##e = 0.35##. What is the semi-major axis of the new orbit?

    2. Relevant equations
    Period: ##T=2\pi\sqrt{\frac{r^3}{GM_E}}##

    Escape Velocity: ##V_{esc}=\sqrt{\frac{2GM_E}{r}}##

    Eccentricity: ##e=\sqrt{1+\frac{2{\epsilon}L^2}{(GM_E)^2}}##

    ##e=\frac{r_a-r_b}{r_a+r_b}## where ##r_a=a(1-e)## and ##r_b=a(1+e)##

    3. The attempt at a solution
    Done the (a) part straight forward enough with the period formula.
    So I subbed in my values to get:

    ##r=4.22\times 10^7 m##

    ##V_{esc}=4345 ms^{-1}##

    What I don't understand is how to get the semi major axis. If someone could point me in the right direction that would be great. I think I have to get the new period of the orbit but I don't know how.
     
    Last edited: Aug 6, 2015
  2. jcsd
  3. Aug 6, 2015 #2

    SteamKing

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    Have you posted the complete problem statement and/or all the information you were furnished?
     
  4. Aug 6, 2015 #3
    Hey SteamKing I edited my post and put in more,I didn't think it was necessary sorry.
     
  5. Aug 6, 2015 #4

    SteamKing

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    It normally wouldn't make a difference if this were Psychic Forums, rather than Physics Forums.

    But, the additional information clarifies this thread greatly.
     
  6. Aug 6, 2015 #5
    Ouch
     
  7. Aug 7, 2015 #6

    andrevdh

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    Hint: The transfer occur at perihelion.
     
  8. Aug 7, 2015 #7
    What do you mean by transfer?
     
  9. Aug 7, 2015 #8

    andrevdh

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    From the one orbit to the other.
     
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