Question

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.

Answer 1

Halley's Comet's orbit is explained by Kepler's laws, where the time differences arise due to its highly eccentric elliptical orbit and the law of equal areas, resulting in faster movement near the Sun and slower movement when farther away.

Step-by-step explanation:

The time differences in Halley's Comet's orbit can be explained through Kepler's laws of planetary motion. According to Kepler's second law, also known as the law of equal areas, a line segment joining a planet (or comet in this case) to the Sun sweeps out equal areas during equal intervals of time. As Halley's Comet has an eccentric orbit with an eccentricity of 0.967, it moves rapidly when it is near the Sun at perihelion and much more slowly when at the aphelion, which is beyond the orbit of Neptune.

Kepler's first law, stating that planets orbit the Sun in ellipses with the Sun at one focus, indicates that Halley's Comet's orbit is highly elongated. Therefore, when the comet is close to the Sun, it travels a shorter arc of its elliptical path but covers larger distances compared to when it is far from the Sun, resulting in rapid movement through the perihelion but a slower trek for the rest of its orbit. This is also why the comet takes only a few months to pass through the part of its orbit nearest the Sun but more than half a century to complete the rest of its orbit.

Answer 2

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).

Step-by-step 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.