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Satellite Orbit Problem what am I doing wrong?

  1. Apr 5, 2010 #1
    I have a satellite orbit problem I'm not quite understanding...any help would be appreciated.

    1. The problem statement, all variables and given/known data

    Suppose a spacecraft orbits the moon in a very low, circular orbit, just a few hundred meters above the lunar surface. The moon has a diameter of 3500 km, and the free-fall acceleration at the surface is 1.60 m/s^2.


    2. Relevant equations

    1. How fast is this spacecraft moving?


    3. The attempt at a solution

    To find the speed, I used the equation v= square root of (G X M/R), with M being the mass of the moon (I had to look that up) and G being the gravitational constant.

    v= square root of (6.674E-11)(7.36E22/1750)=52980.125=>52.9 m/s

    The answer I got was an available option under the answer choices; however, I got it wrong. I can't figure out another way to come up with the velocity.

    I also tried using the equation mg=mv^2/R; however, I got the same number as before.
    m's cancel;
    g=v^2/R
    v= square root of g*R
    Acceleration = g in freefall
    V = square root of 1.60*1750km=>52.9 m/s

    Both of these answers are incorrect. What am I doing wrong?
     
    Last edited: Apr 5, 2010
  2. jcsd
  3. Apr 5, 2010 #2

    D H

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    Science Advisor

    Watch your units! Kilometers and meters are not the same.
     
  4. Apr 5, 2010 #3
    Didn't I convert between them? For the first equation I used, 52980.125 is in kilometers, then I moved the decimals 3 places over to convert to meters.
     
  5. Apr 5, 2010 #4

    D H

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    Staff Emeritus
    Science Advisor

    No, it is not. It is in goofy units. G is not just a number, and you used it is such. It has units. You used G=6.674E-11, more correctly, G=6.674×10-11 m3 kg-1 s-2.
     
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