Kepler's third law of planetary motion states that the square of the orbital period T is proportional to
A{'text': 'The radius of the orbit r', 'label': 'A'}
B{'text': '1 / a²', 'label': 'B'}
C{'text': '1 / r', 'label': 'C'}
D{'text': 'The cube of the semi-major axis a³', 'label': 'D'}
Answer & Solution
Correct answer: D. {'text': 'The cube of the semi-major axis a³', 'label': 'D'}
1. Kepler analysed Tycho Brahe's planetary data.
2. His third law: T² ∝ a³, where a is the semi-major axis of the elliptical orbit.
3. Equivalently: T² / a³ = 4 π² / (G M) is the same for all planets around the Sun.
4. For circular orbits, a is simply the orbital radius.
_Source: NCERT Class 11 Physics, Ch 7 "Gravitation", §7.5_
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