Question

How do I use Kepler’s law to find t² and r³?

a) By taking the square of time and the cube of radius
b) By taking the square root of time and the cube root of radius
c) By squaring both time and radius
d) By cubing both time and radius

Answer 1

Kepler's Third Law states T² (the square of the orbital period) is proportional to r³ (the cube of the orbital radius). To find T² and r³, square the period and cube the radius respectively.

Step-by-step explanation:

To use Kepler's law to find the relation between the square of the orbital period (T²) and the cube of the orbital radius (r³), we refer to Kepler's Third Law, which states that the square of a planet's orbital period is directly proportional to the cube of the semi-major axis of its orbit. This can be represented mathematically as T² ≈ r³. Therefore, the correct way to find T² and r³ is by taking the square of the orbital period and the cube of the orbital radius respectively, which corresponds to option a).