Question

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

Answer 1

Answer:

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

Explanation:

Kepler's third law of planetary motion can be summarized as follows:

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

In formula, this is written as follows:

$r^3 = \frac{GM}{4 \pi^2} T^2$

where:

r is the average distance of the planet from the Sun

G is the gravitational constant

M is the mass of the Sun

T is the orbital period of the planet

From the formula, we see that the factor $\frac{GM}{4 \pi^2}$ is constant for every planet. So, if we call this constant factor k, the equation can be rewritten as

$r^3 = k T^2$

which means that the cube of the mean distance of the planet from the Sun (r) is directly proportional to the square of the orbital period (T).

Answer 2

Based on the options given, the most likely answer to this query is The square of the orbital periods of the planets are directly proportional to the cubes of their average distances from the Sun. 

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