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Distance - Using net force

  1. Feb 18, 2007 #1
    1. The problem statement, all variables and given/known data

    At what distance from the earth should an astronaut be placed so that he will feel no net force when the Earth and the Moon and he are aligned?

    2. Relevant equations


    3. The attempt at a solution

    I assume I'm gonna do a force annalysis, I'm just not sure how to. Also I thought that maybe if the pull from the moon to the astronaut and the pull from the earth to the astronaut were equal, he should feel no force.
  2. jcsd
  3. Feb 18, 2007 #2
    Thats exactly right. Youve got the equations, youve figured it out. Just do the math.
  4. Feb 19, 2007 #3
    I got a problem though. I have no way of knowing the distance from the moon to the astronaut. If the forces are equal, and I need to know the distance from the astronaut to the earth, then the resulting equation cleared for d1 (d1 being the distance from the earth to the astronaut), ends up as this:


    m2 being the mass of the earth, m3 being the mass of the moon and d2 being the distance from the astronaut to the moon. I got that equation clearing this in terms of d1 :


    G is the gravitational constant and m1 is the mass of the astronaut.
    Last edited: Feb 19, 2007
  5. Feb 19, 2007 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Hint: What's d1 + d2 equal?
  6. Feb 19, 2007 #5
    Chaos, he has the right equations however there's some things that aren't apparent.

    Draw a picture first of all of this happening and some things will become apparent.
  7. Feb 19, 2007 #6
    I did it :biggrin: All I needed was what Doc Al said. d2 would be the distance from the earth to the moon minus d1, and since I had only one variable left, the rest was algebra. Thanks!
  8. Feb 19, 2007 #7
    I'd solve it like this instead ->

    ( G*Mm*m ) / Rm^2 = (G*Me*m) / Re^2

    Rm = Re * sqrt( Mm / Me );

    Alpha = Rm + Re = 3.84x10^8 m.

    Alpha = Re * sqrt(Mm / Me) + Re; Algebraically pull out the Re.

    Alpha = Re * [ sqrt(Mm / Me) + 1 ]

    Re = Alpha / [ sqrt(Mm / Me) + 1 ]

    Mm = 7.35x10^22 Kg; Me = 5.98x10^24 Kg
    Re = 3.84x10^8 / [ sqrt(7.35x10^22 / 5.98x10^24) + 1 ]

    Re = 3.46x10^8 m
    Last edited: Feb 19, 2007
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