Questions: Which of Kepler's Laws explains: Mercury has a shorter orbital period than Neptune

Solution Steps

Kepler's Laws of Planetary Motion consist of three laws:

1. First Law (Law of Ellipses): Planets move in elliptical orbits with the Sun at one focus.
2. Second Law (Law of Equal Areas): A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
3. Third Law (Law of Harmonies): The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

The question asks which of Kepler's Laws explains why Mercury has a shorter orbital period than Neptune. This involves comparing the orbital periods of two planets.

Kepler's Third Law relates the orbital period of a planet to the size of its orbit. Specifically, it states that the square of the orbital period (\( T^2 \)) is proportional to the cube of the semi-major axis (\( a^3 \)) of its orbit: \[ T^2 \propto a^3 \] Since Mercury is closer to the Sun than Neptune, it has a smaller semi-major axis, resulting in a shorter orbital period according to the Third Law.

Final Answer