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Math Help - Help calculating acceleration due to gravity.

  1. #1
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    Help calculating acceleration due to gravity.

    Hi there.

    I'm looking for an equation to calculate the rate at which 2 bodies of known mass m1 and m2 will accelerate towards each other for any given distance. Just want to check that I've got this right.

    Using the gravitational equation

    F=G*m1*m2/r2

    then substitute

    F=ma where m = m1+m2

    therefore

    (m1+m2)a = G * m1 * m2/r2

    therefore

    a = G * m1 * m2 / (m1+m2)r2
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  2. #2
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    Re: Help calculating acceleration due to gravity.

    Quote Originally Posted by Ollie999 View Post
    Hi there.

    I'm looking for an equation to calculate the rate at which 2 bodies of known mass m1 and m2 will accelerate towards each other for any given distance. Just want to check that I've got this right.

    Using the gravitational equation

    F=G*m1*m2/r2

    then substitute

    F=ma where m = m1+m2

    therefore

    (m1+m2)a = G * m1 * m2/r2

    therefore

    a = G * m1 * m2 / (m1+m2)r2

    each mass has its own acceleration dependent upon the magnitude of the other mass.

    your substitution of (m_1+m_2) into Newton's 2nd law equation is incorrect.


    case 1 ... if m_1 = m_2 = m , then a_1 = a_2 = a = \frac{Gm}{r^2}

    case 2 ... if m_1 \ne m_2, then a_1 \ne a_2 ...

    a_1 = \frac{Gm_2}{r^2}

    a_2 = \frac{Gm_1}{r^2}
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