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If the gravitational force between two objects were proportional to 1/R (and not as 1/R²) where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to

1. 1/R²
2. R⁰
3. R¹
4. 1/R

Correct answer: R¹

Solution

If the gravitational force is proportional to 1/R, the centripetal force required for circular motion (mv²/R) must equal the gravitational force. This gives v² proportional to R, so v is proportional to R¹.

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