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PHY 101 PHY 101 Past Questions Objective Question
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Question

Newton discovered that Kepler's laws could be derived; they are consequences of Newton's laws of motion and the law of gravitation. Let us see how Kepler's third law arises, for instance. Consider a planet of mass m_p with a circular orbit around the Sun of mass M_s. Centripetal force is supplied by the force of gravity that is: m_p v²/r = G M_s m_p / r². Then:
Options
A T² ∝ r³
Correct Answer
B T ∝ r³/²
C T² ∝ r
D T ∝ r²
Correct Answer

Option A is the correct answer.

Detailed Explanation

From m_p v²/r = G M_s m_p / r², we get v² = G M_s / r. For circular orbit, v = 2πr/T, so (2πr/T)² = G M_s / r → 4π²r²/T² = G M_s / r → 4π²r³ = G M_s T² → T² = (4π²/G M_s) r³, so T² ∝ r³ (Kepler's third law).

Hint

Combine centripetal force with gravitational force and relate period to radius.

Question Info

Course: PHY 101
Topic: PHY 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 892 of 1250
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