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Planetary motion: h = |dr/dt|^2/2 - μ/r is a constant.

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Starting from the formula d^r/dt^2 = -μ (r/r^3) show by differentiation that the quantity h = |dr/dt|^2/2 - μ/r is a constant. It is useful to recall that |dr/dt|^2 = dr/dt . dr/dt. You will need to use your calculus skills to find an expression for the derivative of 1/r with respect to time t, after which the fact that rdr/dt = r.dr/dt is likely to be useful.

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Solution Summary

Solution to this problem is in a scanned file. I have shown each and every step of this calculation. Knowledge of calculus has been abundantly used in solving this problem.