Question

4. Let the period of revolution of a planet
at a distance R from a star be T. Prove
that if it was at a distance of 2R from
the star, its period of revolution will be
√8 T.

pls answer step wise

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Answer 1

Answer:

√8T

Explanation:

According to the Kepler's law , T² ∝ a³

where T is the time period and a is the distance between two objects

When distance between planet and star is R then time period is T

means T² = kR³ [ k is proportionality constant ]----(1)

Let the time period is T' when distance between planet and star is 2R, thus

T'² = k(2R)³ = k × 8R³ -----(2)

Dividing equation (1) by (2)

T²/T'² = kR³/k × 8R³ = 1/8

T'² = 8T²

Square root both sides,

T' = √8T

Thus, when distance between planet and star will be 2R, the time period will be √8T.