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What are Kepler's laws of planetary motion?

Class 11 PhysicsNCERT chapter: Gravitationइसे हिंदी में पढ़ें

Exam-ready answer

Kepler's three laws: (1) Law of orbits: all planets move in elliptical orbits with the Sun situated at one of the foci. (2) Law of areas: the line joining any planet to the Sun sweeps equal areas in equal intervals of time. (3) Law of periods: the square of a planet's time period is proportional to the cube of the semi-major axis of its orbit, T² ∝ a³.

Explanation

Law of orbits: an ellipse is a closed curve with two foci. The Sun sits at one focus, not at the centre. The point of the orbit closest to the Sun is the perihelion and the farthest point is the aphelion. Half of the longest diameter is the semi-major axis, a. A circle is a special ellipse in which the two foci coincide, so circular orbits also obey this law.

Law of areas: in equal time intervals, the line from the Sun to the planet sweeps out equal areas. So when the planet is near the Sun (perihelion) it moves faster, and when it is far (aphelion) it moves slower. This law follows from conservation of angular momentum. The gravitational force on the planet is directed towards the Sun (a central force), so it exerts no torque about the Sun and angular momentum stays constant.

Law of periods: T² ∝ a³, so T²/a³ has nearly the same value for all planets of the solar system. A planet farther from the Sun therefore takes much longer to complete one revolution; the Earth takes one year, while outer planets take many years. Newton later showed that this law follows from his inverse-square law of gravitation, which helped confirm the law of gravitation itself.

Points to remember

  1. Law of orbits: planets move in elliptical orbits with the Sun at one focus.
  2. Law of areas: the Sun–planet line sweeps equal areas in equal time intervals.
  3. Law of areas is a consequence of conservation of angular momentum (gravity is a central force).
  4. Law of periods: T² ∝ a³, where a is the semi-major axis.
  5. A planet moves fastest at perihelion (nearest the Sun) and slowest at aphelion (farthest).

Exam tip

Write each law with its name (orbits, areas, periods) and draw an ellipse showing the Sun at one focus, the perihelion, the aphelion and the semi-major axis a.

Questions students also ask

Why does a planet move faster when it is closer to the Sun?
By the law of areas, equal areas are swept in equal times. Near the Sun, the line joining the planet to the Sun is short, so the planet must cover a longer arc in the same time to sweep the same area. Hence its speed is greater.
What is the semi-major axis of an orbit?
It is half the length of the major axis, the longest diameter of the ellipse. For a planet, it equals the average of its nearest and farthest distances from the Sun. For a circular orbit, the semi-major axis is simply the radius.
Do Kepler's laws apply to satellites around the Earth?
Yes. They apply to any body moving under an inverse-square central gravitational force. Artificial satellites and the Moon orbiting the Earth follow the same three laws, with the Earth at one focus of the orbit.

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