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Thread: 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 $\displaystyle (m_1+m_2)$ into Newton's 2nd law equation is incorrect.


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

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

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

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