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al mustafa publick school

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two planets of masses m and respectively.have a centre to center separation of r.at what distance from the center of the pianet of mass m do the gravitational force of planets cancel each other???

  • al mustafa publick school - ,

    Assuming you meant masses M and m, then we need at distance d from M,

    M/d^2 + m/(r-d)^2 = 0
    M(r-d)^2 + md^2 = 0
    (M+m)d^2 - 2Mrd + Mr^2 = 0

    d = r/2 * (M+√Mm)/(M+m)

    just as a sanity check, it's easy to see that d=r/2 when M=m

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