Halley’s Comet appears around the sun about once every 76 years. It passes through the part of its orbit nearest the sun in just a few months but then moves out to great distances and takes more than half a century for the rest of its orbit. Explain these time differences in terms of Kepler’s laws.

There are actually three, Kepler’s laws that is, of planetary motion: 1) every planet’s orbit is an ellipse with the Sun at a focus; 2) a line joining the Sun and a planet sweeps out equal areas in equal times; and 3) the square of a planet’s orbital period is proportional to the cube of the semi-major axis of its orbit. As it’s the third which is most often used, Kepler’s law usually means Kepler’s third law (of planetary motion).

Explanation:

Kepler's third law would tell us that Halley's comet has an average distance much greater than that of the Earth. However, there is a time in Halley's comet's orbit that brings it closer to the Sun than the Earth. Kepler's third law is a mathematical relation between a planet's period and its average distance.