Semimajor Axis and Eccentricity after increased velocity

  1. Question:

    A space shuttle is in an orbit about the Earth. At its apogee, it uses thrusters and increases its velocity by 400 m/sec. What is the new orbit semimajor axis, eccentricity and how much will the next perigee altitude be increased?


    Original semimajor axis: 7000 km -> a
    Original eccentricity: 0.05 -> e
    Earth's Radius: 6378 km
    u= GxEarth's Mass=3.986x10[tex]^{5}[/tex]

    What I have done so far:

    I figured out the apogee and perigee of the orbit, as well as the velocity at the apogee before the firing of the thrusters.

    i) apogee: a(1+e) = 7350 km
    ii) perigee: a(1-e) = 6650 km
    iii) velocity at apogee:

    [tex]\sqrt{u*((2/r)-(1/a))}/[/tex] where r = apogee.

    I got v=7.17 km/s

    Now after the thrusters are fired, the new velocity is 7.57 km/s

    Using [tex]\epsilon[/tex] = V[tex]^{2}[/tex][tex]/2[/tex] - u[tex]/r[/tex] where r is the current position, aka the apogee and plugging [tex]\epsilon[/tex] into

    a = -u[tex]/2\epsilon[/tex]

    I found the new semimajor axis to be 7809 km. But then here is the problem. How do I find out the new eccentricity? Thanks!
  2. jcsd
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