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Form of Kepler’s in a different universe!

Mukta asked:

“imagine a planetary system in which gravitational force varied as 1/r instead of 1/r2 .what relation would correspond to KEPLER’S THIRD LAW (SQUARE OF TIME PERIOD / CUBE OF SEMI MAJOR AXIS.?”

(Answer)

If the gravitational force varied as 1/r instead of 1/r2 , then Kepler’s Law of periods would have to be modified accordingly and it would give T proportional to r.

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