Question

earth's period of revolution around the sun is one year. suppose there were another planet in our solar system exactly four times as far from the sun as earth. what would be the orbital period of such a planet?

Answer 1

The orbital period of a hypothetical planet located four times as far from the Sun as Earth would be 8 Earth years, according to Kepler's third law of planetary motion.

Step-by-step explanation:

To determine the orbital period of a planet four times as far from the Sun as Earth, we can use Kepler's third law of planetary motion, which states that the square of the period of any planet is proportional to the cube of the semimajor axis of its orbit. Since the Earth's orbital period (P) is one year and its distance (a) is considered 1 astronomical unit (AU), we can compare the hypothetical planet's parameters to Earth's.

For the hypothetical planet, the distance from the sun would be 4 AU (four times as far from the Sun), so we need to cube this distance (4^3 = 64) and take the square root to find the orbital period. The square of the new orbital period (P'^2) must be proportional to the cube of its semimajor axis (64), therefore P' = sqrt(64) = 8. Thus, the hypothetical planet would have an orbital period of 8 Earth years.