A comet has an orbital period of 78 years. What is its average distance (in AU) from the Sun?[Blank space for answer] AUIf the comet last came closest to the Sun in 1982, when will it reach its furthest point from the Sun? (Enter your answer as a date in years.)[Blank space for answer]

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

Problem 1LR

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A comet has an orbital period of 78 years. What is its average distance (in AU) from the Sun?

[Blank space for answer] AU

If the comet last came closest to the Sun in 1982, when will it reach its furthest point from the Sun? (Enter your answer as a date in years.)

[Blank space for answer]

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.