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Circular Motion - Satellites Problem

  1. Apr 30, 2007 #1
    1. The problem statement, all variables and given/known data
    Two satellites of equal mass, S1 and S2, orbit the earth. S1 is orbiting at a distance r from the earth's center at speed v. S2 orbits at a distance 2r from the earth's center at speed (v/squareroot2) . The ratio of the centripetal force on S1 to the centripetal force on S2 is,

    A. 1/8

    B. 1/4

    C. 4

    D. 8

    2. Relevant equations

    F = mvsqrd/r

    3. The attempt at a solution

    I just couldn't figure this one out at all... its frustrating, i tried playing around with the equation but i kept getting nonsense.
  2. jcsd
  3. Apr 30, 2007 #2

    Doc Al

    User Avatar

    Staff: Mentor

    You have the correct equation. Show what you did to find F_1 and F_2 (the two centripetal forces).
  4. Apr 30, 2007 #3
    Ok. So since the mass is equal its constant, so we just have

    F = Vsquared/r

    So then, S1 = Vsquared/r

    S2 = (v/squareroot2)squared/2r
    = (vsquared/2)/2r
    = (2vsquared*r)/2

    S1 = Vsquared/r

    S2 = (2vsquared*r)/2

    Hmm.. so now?
  5. Apr 30, 2007 #4
    Ultimately, that's all you need, but it would be more correct to leave the mass in until the very end.


    Correcct until [tex]F_{S2}=m\frac{\frac{v^2}{2}}{2r}[/tex]
    Then you have an algebra error.

    The problem asks you to take calculate a ratio, ie, divide one of the forces by the other. (Incidentally, that's why you can leave the mass in until the very end: both forces have the term 'm' so the masses cancel).
  6. Apr 30, 2007 #5
    Oh, yeah, algebra got me there.

    So it'd have to then be:

    [tex] S2 = {\frac{v^2}{4r}}[/tex]

    Ah, so now it gives me a much simpler division to do. When i divide those S1/S2 after multiplying and cancelling i get 4r/r.

    Awesome, so the answer is 4. Thanks for pointing out the algebra mistake.
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