1 point) One of Kepler's three laws of planetary motion states that the square of the period, P, of a body orbiting the sun is proportional to the cube of its average distance, d, from the sun. The Earth has a period of 365 days and its distance from the sun is approximately 93,000,000 miles. (a) Find P as a function of d. P(d)

P = √1.66 * 10^-19 days^2miles^-3d^3

Explanation:

The mathematical statement of Kepler's third law is;

P^2 α d^3

Where;

P = Period of the body orbiting the sun

d = its average distance from the sun

Introducing a constant of proportionality K, known as Kepler's constant then;

P^2 = Kd^3

K = P^2/d^3

P=365 days

d = 93,000,000 miles

K = (365)^2/(93,000,000)^3

K=1.66 * 10^-19 days^2miles^-3

P = √1.66 * 10^-19 days^2miles^-3d^3