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Homework Help: Object falling towards moon

  1. Mar 13, 2010 #1
    1. The problem statement, all variables and given/known data
    An object is dropped from a distanse of 2*R(moon radius) from moon senter.
    How many seconds does it take until impact with moon, and in what speed will it hit?

    The distanse of the fall will be 1.74*10^6 m. The problem is the not so constant accleration.. ;)

    gravity constant: G := 6.67*10^(-11)
    moon mass M := 0.0735^24 kg
    moon radius R := 1.74*10^6 m



    2. Relevant equations

    gravity(accleration) is
    g=G*M/R^2

    So a(x)=(G*M)/(2*R - x)^2 , x = meter fallen x{0..R)


    3. The attempt at a solution
    I've calculated the speed at impact:

    Average accleration:
    > A:=(G*M)/(2*R - x)^2
    > Aa := (int(A, x = 0 .. R))/R;
    0.8096264368

    Time using x= 0.5*a*t^2
    > T := solve(R = 0.5*Aa*t^2, t);
    -2073.229031, 2073.229031

    This time is found using constant accleration, so it isnt the correct one...
    but it will work for finding the speed of impact.

    Speed
    > V := T*Aa;
    -1678.541033, 1678.541033
    So it will hit at 1678,54 m/s

    but for how long will it fall?
     
  2. jcsd
  3. Mar 13, 2010 #2
    You have acceleration as a function of distance. Put it in the expression a = v*dv/dx.That way you can obtain velocity as a function of distance by integrating. That will solve the first part of your problem. For time you can write v as dx/dt. Now if you put that and integrate you have distance as a function of time.
     
  4. Mar 13, 2010 #3
    Thanks aim!

    I got the correct velocity using your method, but i dont figure out the distanse as a function of time...

    Could you please try to explain it again, a bit more detailed? :)
     
  5. Mar 13, 2010 #4
    Ok you figured out velocity as a function of distance(x). Now what you do is write v as dx/dt. You will notice that the equation now contains x and t only. A little rearrangement and integration and you can express x as function of t.
     
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