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Mass of object in Escape velocity

  1. Dec 4, 2011 #1
    Why doesn't the escape velocity depend upon the mass of body?
     
  2. jcsd
  3. Dec 4, 2011 #2

    Doc Al

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    Staff: Mentor

    Why doesn't the height reached by a tossed ball depend on the mass of the ball? Same thing. (As is often the case when dealing with gravity, the mass drops out.)
     
  4. Dec 4, 2011 #3

    D H

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    Staff Emeritus
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    It does. The correct equation is

    [tex]v_e = \sqrt{\frac{2\,G(M+m)}r}[/tex]

    The capital M denotes the mass of the central body, the little m, the mass of the escaping body.

    Now think about how big that little m needs to be to make any measurable difference in the velocity needed to escape Earth orbit. Escape velocity from LEO is about 11 km/s. Suppose we can measure velocity down to the micrometer/second range, or 10 significant digits. That corresponds to a mass of 1015 kg, or the mass of about 100 mountains.

    We aren't going to launch a 100 mountain mass out of Earth orbit any time soon.
     
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