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

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.

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

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.

1 answer

Kepler's third law states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit (which can be thought of as the orbital radius for circular orbits). Mathematically, this is often expressed as:

\[ \frac{T_1^2}{T_2^2} = \frac{a_1^3}{a_2^3} \]

Where:

  • \( T_1 \) and \( T_2 \) are the orbital periods of the two planets,
  • \( a_1 \) and \( a_2 \) are the orbital radii (or semi-major axes).

From this relationship, we can see that the correct correlation is:

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

Thus, the correct response is: The square of the ratio of the periods equals the cube of the ratio of the radii.