1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Semimajor Axis and Eccentricity after increased velocity

  1. Jan 23, 2008 #1

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted