Which expression best represents Kepler's third law with a planet's period T and radius r in our solar system?(1 point) Responses
A) T^2 = 4π^2r^3
B) T^2 = 4π^2r
C) T^2 = 4π^2r^2
D) T^2 = 4πr^2
Kepler's third law, also known as the Law of Harmonies, states that the square of a planet's period is directly proportional to the cube of its semi-major axis. Mathematically, it can be represented as:
T^2 = k * r^3
Where T represents the period of the planet (time taken to complete one orbit around the sun) and r represents its average distance from the sun (radius of its orbit).
In this equation, k is a constant of proportionality. For the specific case of planets in our solar system, the value of k is the same for all planets and is obtained by using the observed values of T and r for a reference planet, usually Earth.
Hence, the expression that best represents Kepler's third law with a planet's period T and radius r in our solar system is:
T^2 = k * r^3