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: Planetary motion

  1. Jun 5, 2007 #1
    1. The problem statement, all variables and given/known data

    Two masses, m and M, are initially at rest at a great distance from each other. The gravitational force between them causes them to accelerate towards each other. Using conservation of energy and momentum, show that at any instant the speed of one of the particles relative to the other is:

    v=sqrt(2G (M+m)/d)

    where d is the distance between them at that instant.

    3. The attempt at a solution

    I have the solution sheet but am stuck as to what happens between:

    0 = -GMm/d +1/2m v^2(1+m/M)


    v^2 = 2GM^2/d(M+m)

    where v is v_m, but that's not relevant again till the end of the question.

    what I've gotten the top to reduce to is

    v^2= 2GM[(m+M)/dm]

    Am I missing some math trick here?
  2. jcsd
  3. Jun 5, 2007 #2
    The answer should be v=sqrt(2G (M+m)/d)*M, and you've made a calculation mistake somewhere...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook