According to the Law of Periods, the square of a planet's time period is proportional to:
Show answer & explanation
Correct answer: B
Explanation
Answer: The cube of the semi-major axis of its orbit.
Explanation
According to Kepler’s Third Law of Planetary Motion (Law of Periods), the square of the orbital period (T²) of a planet is directly proportional to the cube of the semi-major axis (a³) of its orbit.
Mathematically:
T² ∝ a³
This means planets that are farther from the Sun take disproportionately longer to complete one orbit compared to those closer.
Additional Key Facts
Formulated by Johannes Kepler in the early 17th century.
Applies to all orbiting bodies, including moons and artificial satellites.
More general form using Newton’s law of gravitation:
T² = (4π² / GM) × a³
First two laws of Kepler:
Orbit of planets is elliptical and Equal areas are swept in equal time
Kepler’s laws laid the foundation for Newton’s Law of Gravitation.
Potential Exam-Oriented Questions & Answers
Q. Who proposed the Law of Periods?
A. Johannes Kepler
Q. What is the mathematical form of Kepler’s Third Law?
A. T² ∝ a³