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Math Help - Calculating Escape Velocity

  1. #1
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    Calculating Escape Velocity

    Using the formula Ve = sqrt 2 mu/r

    Where Ve is the escape velocity, mu is the Gravitational constant times the mass of the object to be escaped from, and r is the radius of said object.

    I now have the following:

    Ve = sqrt 2(6.6742 x 10^-11 N m^2/kg^2 (12.1kg))/0.106780959m

    N Being Newtons, one newton equivalent to: 1kg x m/s^2

    What would be the next step in solving this?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Thrawn View Post
    Using the formula Ve = sqrt 2 mu/r

    Where Ve is the escape velocity, mu is the Gravitational constant times the mass of the object to be escaped from, and r is the radius of said object.

    I now have the following:

    Ve = sqrt 2(6.6742 x 10^-11 N m^2/kg^2 (12.1kg))/0.106780959m

    N Being Newtons, one newton equivalent to: 1kg x m/s^2

    What would be the next step in solving this?
    First of all you need parenthesis:
    Ve = sqrt(2mu/r)

    Ve = sqrt(2*6.6742 x 10^(-11)*12.1/0.106780959) m/s

    Now just plug the numbers into a calculator:
    Ve = sqrt(1.5125884 x 10^(-8)) m/s

    Ve = 1.22987 x 10^(-4) m/s

    -Dan
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  3. #3
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    So in this equation I just ignore the kg, m, and stuff like that, rather than cancelling or combining?
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  4. #4
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    Quote Originally Posted by Thrawn View Post
    So in this equation I just ignore the kg, m, and stuff like that, rather than cancelling or combining?
    They are the units of the given quantities, and as long as you are using
    a consistent set of units all they do is collectively tell you the units of the
    final answer but do not effect it.

    If you have inconsistent units (as luck would have it you don't here) you will need a fist full of
    conversion factors to get the final answer, but if you stick to SI everything
    will come out in the wash (usually).

    RonL
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Thrawn View Post
    So in this equation I just ignore the kg, m, and stuff like that, rather than cancelling or combining?
    Typically (that is to say, unless you are adding or subtracting) you can do two problems: one with numbers and one with units. The unit analysis on this problem goes like this:

    [Ve] = sqrt{(Nm^2/kg^2 * kg)/m} <-- [Ve] indicates the unit for the quantity Ve.

    [Ve] = sqrt{Nm/kg}

    Now N = kgm/s^2, so:

    [Ve] = sqrt{(kgm/s^2)m/kg}

    [Ve] = sqrt{(m/s^2)m}

    [Ve] = sqrt{m^2/s^2}

    [Ve] = m/s

    Which is the unit for a speed, just like we needed.

    -Dan
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