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Density of Asteroids, Escape Velcoity and Jumping

  1. Feb 7, 2008 #1

    TFM

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    [SOLVED] Density of Asteroids, Escape Velcoity and Jumping

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

    The question wants to know the maximum radius of an asteroid that you can escape from by simply jumpibng off.

    The Variables given:
    densities = 2500 kg/m cubed
    radii = 470km downwards
    height of jump = 1m

    2. Relevant equations

    v(Escape) = sqrt(GM/r)
    m = d/r cubed
    V squared = U squared + 2as (for initial jump speed)

    3. The attempt at a solution
    using a = 9.8 and s = 1, I calculated the initial jump speed is 4.43
    rearranging the equation for EScape Velocity:
    v(escape) = sqrt[(G(d/r cubed))/r]
    v sqyared = (G(d/r cubed))/r
    v squared = GD/r squared
    r squared = Gd/v sqyared
    r = sqrt [GD/v squared]

    but this isn't giving me the right answer?
     
  2. jcsd
  3. Feb 7, 2008 #2
    This isn't right. mass is density * volume. and the volume of a sphere is?
     
    Last edited: Feb 7, 2008
  4. Feb 7, 2008 #3

    Shooting Star

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    Homework Helper

    HI TFM,

    It's given that you can jump 1 m on earth. Using that, find the speed you can generate at the start of the jump. Then apply that speed for v_escape to find r. All other data are given.
     
  5. Feb 7, 2008 #4

    TFM

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    The question assumes the asteroids are speherically symmetrical - which is why I should use the volume of a sphere, 4/3 Pi r cubed.

    i.e:

    (escape) = sqrt[(G(d/(4/3) pi r cubed))/r]

    TFM
     
  6. Feb 7, 2008 #5

    Shooting Star

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    Yes, spherically symmetrical and of uniform density. However, the following formula you've written is not correct.

    >
    2. Relevant equations

    v(Escape) = sqrt(GM/r)

    >
     
  7. Feb 7, 2008 #6

    TFM

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    I've just checked -its sqrt[(2GM)/r]

    this all gives:

    R squared = (3*V escape squared)/(8*G*density*pi)

    TFM
     
    Last edited: Feb 7, 2008
  8. Feb 8, 2008 #7

    TFM

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    I have now got the (right) answer of 3.7km (using a 10^-3 conversion factor):smile:

    Thanks all,

    TFM
     
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