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Homework Help: Determining work of a 3 particle system

  1. Oct 9, 2016 #1
    1. The problem statement, all variables and given/known data
    on a spherical astroid with a radius of 500km and an acceleration due to gravity of 3.0m/s2
    How far from the surface will a particle go if it leaves the asteroid’s surface with a radial speed of 1000m/s?
    2. Relevant equations
    conservation of energy
    Ui + ki=Uf +kf
    (can apply to h height)

    r=radius of astroid
    h=height above center
    m=mass of rocket
    M=mass of astroid
    G=gravitational constant
    a=acceleration due to astroids gravity
    3. The attempt at a solution
    Ui + ki=Uf +kf
    Ui + ki=Uf + 0
    -(GmM)/r +(1/2)mvi2=-(GmM)/h
    the m masses cancel
    -(GM)/r +(1/2)vi2=-(GM)/h
    -ar +(1/2)vi2=-ah
    plugging in the values gives me

    5166666.667meters from the center of the astroid. so 166666.667 meters above its surface. Which is the incorrect answer. the right answer is 250000 meters above the surface.

    I know this should be a pretty simple problem, Not too sure where I went wrong. Thanks ahead of time
  2. jcsd
  3. Oct 9, 2016 #2
    Okay so I realized that I cannot use mgh fro the U final because the acceleration due to gravity is different here. So I found the mass of the astroid. If I use U=-(GmM)/r and solve for h will I get the correct answer?

    and btw the title is wrong for this post.
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