Which statement correctly states Kepler’s Third Law of Planetary Motion?
A.
The square of the orbital periods of the planets are inversely proportional to the squares of their mean distances from the Sun.
B.
The square of the orbital periods of the planets are directly proportional to the masses of the planets.
C.
The square of the orbital periods of the planets are inversely proportional to the squares of the masses of the planets.
D.
The square of the orbital periods of the planets are directly proportional to the cubes of their average distances from the Sun.
E.
The cube of the orbital periods of the planets are directly proportional to the squares of their average distances from the Sun.

D.

The square of the orbital periods of the planets are directly proportional to the cubes of their average distances from the Sun.

Explanation:

Kepler laws of planetary motion are three laws describing the motion of the planets around the Sun.

The three laws are:

1) The orbits of the planets around the Sun are ellipses, with the Sun being at one of the two focii

2) A line connecting the center of each planet to the center of the Sun sweeps out equal areas in equal intervals of time

3) The square of the orbital periods of the planets are directly proportional to the cubes of their average distances from the Sun.

Mathematically, the third law can be rewritten as:

where

T is the orbital period of a planet

r is the average distance of the planet from the Sun

This law is valid for all planets orbiting around the Sun: this means that the farther a planet is from the Sun, the longer its orbital period is.

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