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 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 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 correct response is: The square of the ratio of the periods equals the cube of the ratio of the radii.
The correct answer is: The square of the ratio of the periods equals the cube of the ratio of the radii.
To understand how Kepler's third law compares the periods and orbital radii of two planets within a solar system, we need to look at the formula for this law.
Kepler's third law states that the square of the period (T) of a planet's orbit is proportional to the cube of its average distance (R) from the sun. Mathematically, it can be expressed as:
T^2 ∝ R^3
This means that if we have two planets within a solar system, we can compare their periods and orbital radii by taking the ratio of these values and examining the relationship between them.
If we have two planets with periods T1 and T2, and orbital radii R1 and R2 respectively, then the ratio of their periods squared (T1^2/T2^2) will be equal to the ratio of their radii cubed (R1^3/R2^3):
(T1^2 / T2^2) = (R1^3 / R2^3)
Therefore, the square of the ratio of the periods will be equal to the cube of the ratio of the radii. This is how Kepler's third law compares the periods and orbital radii of two planets within a solar system.