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Calculating the escape speed and gravity of a planet / moon

  1. Jul 20, 2012 #1
    Problem:
    One of the asteroids, Ida, looks like an elongated potato. Surprisingly it has a tiny (compared to Ida) spherical moon! This moon called Dactyl has a mass of 4.20x1016kg, and a radius of 1.57x104 meters, according to Wikipedia.
    Solve:
    - Find the acceleration of gravity on the surface of Dactyl.
    - Find the escape speed on Dactyl.
    - If you are 10,000 meters above the surface of Dactyl, what must your orbital speed be?

    I wanna make sure that I've solved the problem correctly. Can anyone check my work?

    What have I done:
    - Calculate the acceleration of gravity:
    F = (G*M)/R2 = (6.67384*10-11 * 4.20*1016) / (1.57*104)2 = 0.0113717 m/s2 = 11.3717 * 10-3 m/s2

    Escape Speed:
    I saw on wikipedia that the formula for escape speed is:
    ve = sqrt((2*G*M)/r)
    That would give = sqrt((2*6.67384*10-11 * 4.20*1016) / 1.57*104) = 18.8963 m/s

    Orbital Speed:
    Formula for orbital speed:
    vo = sqrt((G*M)/r)
    That would give = sqrt(6.67384*10-11 * 4.20*1016) / 1.57*104 + 10000) = 10.4434 m/s
     
    Last edited: Jul 20, 2012
  2. jcsd
  3. Jul 20, 2012 #2

    gneill

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    Staff: Mentor

    Values look okay!

    Be sure to use use an appropriate number of significant figures when you report your results.
     
  4. Jul 20, 2012 #3

    TSny

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    Homework Helper
    Gold Member

    [Removed: Question already answered]
     
  5. Jul 20, 2012 #4
    thx for the replies. The teacher didn't specify how many significant figures...
     
  6. Jul 20, 2012 #5

    D H

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    Staff Emeritus
    Science Advisor

    The teacher doesn't have to say how many significant figures to use. It's right there in the question. How many significant figures are used in the question?
     
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