Question

Kepler's harmonic law states that the distance of a planet from the Sun corresponds to the period of time it takes the planet to orbit the Sun. The formula looks like this: . Which statement best describes this formula summarizing Kepler's harmonic law?

A. The square of the orbital period of a planet around the sun is proportional to the cube of the planet's orbital radius.
B. The square of the orbital radius of a planet to the sun is proportional to the cube of the planet's orbital period.
C. The cube of the planet's orbital radius equals the orbital period of a planet around the sun.
D. The orbital period to the second power of a planet around the sun is proportional to the planet's orbital radius to the fourth power.

Answer 1

A. The square of the orbital period of a planet around the sun is proportional to the cube of the planet's orbital radius.

Step-by-step explanation:

Kepler's third law states that the square of the orbital period of a planet around the sun is proportional to the cube of the planet's orbital radius. This law can be expressed with the following equation:

`(r^3)/(T^2)=const.`

where

r is the orbital radius of the planet

T is the orbital period of the planet

This law tells that the ratio in the formula is constant for all the planets orbiting the same star, therefore if we know for example the orbital radius and period of one planet, and the radius of the orbit of a second planet, it is possible to calculate the orbital period of the second planet.