Question

The period of revolution of two satellites are 3 hours and 24 hours the ratio of their velocities will be​

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Answer 1

hence, ratio of their velocities will be 2 : 1.

explanation : from Kepler's 3rd law, square of orbital time period is directly proportional to cube of the semi major axis of its orbit.

i.e., T² ∝ r³

here, T1 = 3hrs , T2 = 24 hrs

so, (T1/T2)² = (r1/r2)³

⇒ (3/24)² = (r1/r2)³

⇒1/64 = (1/4)³ = (r1/r2)³

⇒r1/r2 = 1/4

we also know, orbital velocity , v ∝ 1/√r

so, v1/v2 = √(r2/r1) = √(4/1) = 2/1

hence, ratio of their velocities will be 2 : 1

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Answer 2

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from Kepler's 3rd law, square of orbital time period is directly proportional to cube of the semi major axis of its orbit.

i.e., T² ∝ r³

here, T1 = 3hrs , T2 = 24 hrs

so, (T1/T2)² = (r1/r2)³

⇒ (3/24)² = (r1/r2)³

⇒1/64 = (1/4)³ = (r1/r2)³

⇒r1/r2 = 1/4

we also know, orbital velocity , v ∝ 1/√r

so, v1/v2 = √(r2/r1) = √(4/1) = 2/1

hence, ratio of their velocities will be 2 : 1