Mass of planet, given only Earth's mass?

  1. This is a past paper exam question:

    1. The problem statement, all variables and given/known data
    One of the moons of Saturn is in an orbit which has approximately the same radius as that of the Earth's moon. Given that the speed of the saturn moon is ten times the speed of the Earth's moon, calculate a value for the mass of Saturn.
    (Mass of the Earth=6x10^24kg)



    2. Relevant equations
    GmmE/r^2=mv^2/r


    3. The attempt at a solution
    Mass of earth=6x10^24
    r satmoon=r earthmoon
    v satmoon=v earthmoon/10



    I did try this, but it's obviously wrong:
    tau^2=4pi^2r^3/Gme


    G=(6.67x10^-11) me=(6x120^24)

    period of revolution of the moon=24hrs

    hence (24)^2=4pir^3/4x10^14

    576=4pi r^3
    144=pir^3

    even without going further, you can tell that it's going to be faaar too small to represent the radius of the moon.

    Without being given anything else-- do you need to memorise the radius of the moon's orbit for the exam? I can't really see any other way! I'm stumped...please help!
     
  2. jcsd
  3. Doc Al

    Staff: Mentor

    You don't need to know the radius of the moon's orbit. Since both Earth and Saturn moons have the same orbital radius, treat that radius as a constant.

    How does planetary mass affect the moon's speed? Hint: Set up a ratio, using this equation (generalize it for any planet, of course):
    Also:
    You seem to have that last relationship reversed--Saturn's moon is 10x faster, not slower, than Earth's moon.
     
  4. Thanks so much for your help. I went back and tried it again:
    if v=(sqrt)Gme/r, then set up ratio:

    10(sqrtGmearth/r)= sqrt Gmsaturn

    Remove r as it is a a constant
    This gives us
    10(sqrt G.mearth)=G.msaturn Remove G as it is another constant.
    10(sqrt mearth)=sqrt msaturn
    10 (sqrt 6x10^24=sqrt msaturn
    2.45x10^13=sqrt msaturn (square both sides)
    (2.45x10^13)^2=msaturn=6x10^26

    therefore mass of saturn=6x10^26. Yay or nay?
     
  5. tony873004

    tony873004 1,585
    Science Advisor
    Gold Member

    Wikipedia says: Yay!
    Don't forget your units.
     
  6. Hm... 6x10^24mg? Just kidding.

    6x1-^24kg it is then!
     
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