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

Question

Responses

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. - no response given

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. - incorrect

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. - no response given

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

Answer 1

Kepler's third law states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (r) of its orbit. This can be expressed mathematically as:

\[ \frac{T_1^2}{T_2^2} = \frac{r_1^3}{r_2^3} \]

From this, we can deduce that the cube of the ratio of the periods equals the square of the ratio of the radii. Therefore, the correct interpretation of Kepler's third law in terms of the periods and orbital radii of two planets is:

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

So, the correct response is:

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