Q.

Kepler’s Laws of Planetary Motion are three fundamental principles that describe how planets orbit the Sun. These laws were formulated by Johannes Kepler in the early 17th century and are based on astronomical observations.

Kepler’s Laws

1. The Law of Ellipses

• Statement: The orbit of a planet around the Sun is an ellipse, with the Sun at one of the two foci.
• Explanation: Unlike a perfect circle, a planet's orbit is slightly elongated. The Sun is not at the center but at one of the focal points of the elliptical orbit.

2. The Law of Equal Areas

• Statement: A line segment joining a planet and the Sun sweeps out equal areas in equal intervals of time.
• Explanation: Planets move faster when they are closer to the Sun (perihelion) and slower when farther from the Sun (aphelion). This ensures that the area covered over a given time is the same, regardless of the planet's position in its orbit.

3. The Law of Harmonies

• Statement: The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
• Mathematical Formula:

T²∝r³

Where:

• T = Orbital period of the planet.
• r = Average distance of the planet from the Sun (semi-major axis).

Explanation: This law establishes a relationship between the time a planet takes to complete one orbit and its distance from the Sun.

Solution

Kepler’s Laws explain the motion of planets as follows:

1. Shape of Orbits (Law of Ellipses): Helps us understand the elliptical nature of planetary paths.
2. Planetary Speed (Law of Equal Areas): Explains why planets move faster when closer to the Sun and slower when farther.
3. Time-Distance Relationship (Law of Harmonies): Relates a planet's orbital period to its average distance from the Sun.