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Suppose gravity were modified so that the force of attraction between two particles varied inversely as the (5/2)th power of the distance between them. For a satellite in a circular orbit, the orbital speed v0 is plotted against the orbital radius r on a log-log graph (a straight line). Find the slope of this line.

1. -5/4
2. -5/2
3. -3/4
4. -1

Correct answer: -3/4

Solution

Equating the central force (proportional to 1/r^(5/2)) to m*v0²/r gives v0² proportional to 1/r^(3/2), so v0 proportional to r^(-3/4). On a log-log plot the slope equals this exponent.

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