How does Kepler’s third law compare the periods and orbital radii of two planets within a solar system?(1 point)

Responses

The ratio of the periods equals the square of the ratio of the radii.
The ratio of the periods equals the square of the ratio of the radii.

The cube of the ratio of the periods equals the square of the ratio of the radii.
The cube of the ratio of the periods equals the square of the ratio of the radii.

The square of the ratio of the periods equals the ratio of the radii.
The square of the ratio of the periods equals the ratio of the radii.

The square of the ratio of the periods equals the cube of the ratio of the radii.

1 answer

Kepler's third law states that the squares of the orbital periods of two planets are proportional to the cubes of the semi-major axes of their orbits. In mathematical terms, this can be expressed as:

\[ \frac{T_1^2}{T_2^2} = \frac{R_1^3}{R_2^3} \]

Where \( T \) is the orbital period and \( R \) is the orbital radius (semi-major axis).

From this relationship, one can infer that:

  • The ratio of the squares of the periods equals the ratio of the cubes of the radii.

Thus, the correct choice based on the options provided would be:

The squares of the ratio of the periods equals the cubes of the ratio of the radii.