Question

Let the period of revolution of
planet at
at a distance Rrom
star be I prove that the
a distance of 2R from
the star its
star. its period of revolution
be under root 8T
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Answer 1

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Answer 2

According to Kepler’s third law

T²∝a³

T is time period of planet and a is semi major axis of its orbit.

So, according to question

T² = KR³...... (1)

When distance is 2R then

T²= K(2R³)

T’²= 8R³K.....(2)

Taking ratios of (1) and (2)

T²/T'²= KR³/8R³K

T²/T'²= 1/8

T'²= 8T²

T'= √8T