Suppose there were very remote planets in the solar system,with periods of about 100,000 years.Approximately how far from the Sun would such a planet be?
A)200 astronomical units
B)2000 astronomical units
C)20,000 astronomical units
D)200,000 astronomical units

Question

Quizplus · Accepted Answer

According to Kepler's third law, the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. This law can be represented as $P^2 \propto a^3$, where $P$ is the orbital period in years and $a$ is the semi-major axis in astronomical units (AU). For a planet with a period of about 100,000 years, we can rearrange Kepler's law to solve for $a$, knowing that Earth's period is 1 year and its distance from the Sun is 1 AU. The calculation shows that the planet would be approximately 2000 astronomical units from the Sun to have a 100,000-year orbital period.

Suppose There Were Very Remote Planets in the Solar System,with