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Determine its escape velocity in miles/s?

  1. Feb 7, 2015 #1
    1. The problem statement, all variables and given/known data
    A space probe is to be launched from a space station 200 miles above Earth. Determine its escape velocity in miles/s. Take Earth's radius to be 3960 miles.

    2. Relevant equations
    None.

    3. The attempt at a solution
    m(dv/dt)=-(mgR^2)/(x+R)^2
    dv/dt=-(gR^2)/(x+R)^2
    Now what?
    The answer is 6.76 miles/s.
     
  2. jcsd
  3. Feb 7, 2015 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    What is the condition for escape? (hint: what is the potential energy and what is the kinetic energy of the body when it has reached a distance where the earth's gravity is negligible and the body is just barely moving?). Use the principle of conservation of total energy to determine what its speed must be initially in order to achieve that distance.

    Suggestion: I would convert to metric, do the calculations and convert back.

    AM
     
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