A comethas an orbital period of 78 years. Whatis its average distance (in AU) from the Sun?AUIf the comet last came closest to the Sun in 1982, when will it reach its furthestpoint from the Sun? (Enter your answer as a date in years.)

Answered: AU If the comet last came closes

Applications and Investigations in Earth Science (9th Edition)

9th Edition

ISBN:9780134746241

Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Chapter1: The Study Of Minerals

Section: Chapter Questions

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A comethas an orbital period of 78 years. Whatis its average distance (in AU) from the Sun?
AU
If the comet last came closest to the Sun in 1982, when will it reach its furthestpoint from the Sun? (Enter your answer as a date in years.)

Expert Solution

Step 1

Kepler's third law states that the planets' orbital periods' square is directly proportional to the semi-major axes' cubes and their orbits. It also states that a planet's period to orbit the sun increases rapidly with its orbit's radius. Short-period comets are the ones having an orbital period of fewer than 200 years. It is also known as the periodic comet.

Step 2

The third law of Kepler relates the orbital period T in years to the semi-major axis distance in AU using the equation $T^{2} = R^{3}$ . If T=78 years then R=18.26AU
- Given,
The comet last came closest to the sun in 1982.

We know that short period comets take 200 years or less to complete one orbit, and long-period comets take more than 200 years.

As the given comet is a short-period comet, the time it takes to reach the sun's furthest point is around 1982+200=2182.