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: Gravitation - change of orbit

  1. Jul 13, 2015 #1
    1. The problem statement, all variables and given/known data
    A spaceship is in a circular orbit of radius ##r_0## about a planet of mass M. A brief but intense firing of its engine in the forward direction decreases the spaceship's speed by 50%. This causes the spaceship to move into an elliptical orbit.
    a) What is the spaceship's, just after the rocket burn is completed, in terms of M, G and ##r_0##?
    b) In terms of ##r_0##, what are the spaceship's minimum and maximum distance from the planet in its new orbit?

    2. Relevant equations

    3. The attempt at a solution
    Let's look at part a first. This is an even numbered problem and I'm not sure about the answer.
    Let ##v_i = 2v_f## and the mass of the ship be m
    Just after firing, the movement can still be considered circular and the ship experiences a centripetal acceleration of
    ##a_r = \frac{F}{m}##, leading to
    ##\frac{GmM}{r_0^2} = m\frac{(2v_f)^2}{r_0}##
    ##v_f = \sqrt{\frac{GM}{4r_0}}##
    Is this correct?
  2. jcsd
  3. Jul 13, 2015 #2


    User Avatar
    2017 Award

    Staff: Mentor

    This statement is a bit misleading. Just calculate the initial velocity in terms of M, G and r0, then you don't need assumptions about the orbit (you know the initial orbit) to find vf.

    The answer is right.
  4. Jul 14, 2015 #3
    Looking at now I can see just how obvious and simple it is. But that's what happens when doing physics problems as the time approaches midnight. Thanks for the input.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted