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Escape speed from the Earth

  1. Oct 12, 2008 #1
    1. The problem statement, all variables and given/known data

    The escape speed from the surface of the Earth is 11.2 km/s. What would be the escape speed be from another planet of the same density (mass per unit volume) as Earth but with a radius 5 times that of Earth's?

    2. Relevant equations

    I know I have to use v=sqrt2GM/R

    3. The attempt at a solution

    I wasn't really sure how to go about this problem, but I did v1/v2 = 11.2/v2 = sqrt5

    So I solved for v2 by doing 11.2/(sqrt5) and I got 5.00879227.
    I have tried 5, 5.0, and 5.009 as answer submissions and got them all incorrect. I am not even sure if I am setting the problem up right, so any guidance or hints would be much appreciated. Thanks!!
  2. jcsd
  3. Oct 12, 2008 #2

    D H

    Staff: Mentor

    Rather than guessing, use the equation you supplied. It is indeed very relevant to the problem, but you didn't use it at all.

    To go about using that equation you need to know each term involved in the equation. Which terms do you know, and which don't you know? Can you solve for the ones you don't know?
  4. Oct 12, 2008 #3


    User Avatar
    Science Advisor

    Did you account for the new planet's mass? I think the volume of a sphere is (4/3)(pi)(r^3). A planet with 5x the radius is 125x as heavy. I don't actually know how to solve this problem, but this is probably important.
  5. Oct 12, 2008 #4

    D H

    Staff: Mentor

    Yes, it is, Shawn. This however, is homework and you shouldn't have given so much info, at least at the onset.
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