can you help me with math I don't understand that.

Question

It follows from Kepler's Third Law of planetary motion that the average distance from a planet to the sun (in meters)

where M = 1.99 × 1030 kg is the mass of the sun, G = 6.67 × 10−11 N · m2/kg2 is the gravitational constant, and T is the period of the planet's orbit (in seconds). Use the fact that the period of the earth's orbit is about 365.25 days to find the distance from the earth to the sun. (Round your answer to one decimal place.)

Answer 1

Kepler's 3rd law:

 

T²/a³ = 4π²/(GM) ⇒

 

a = [GMT² /(4π²)]^1/3

 

You know G and M.

 

T = (365.25 days)(24 hours/day)(3600 sec/hour) = 31,557,600 sec

 

Plug in the numbers and get the distance "a" in meters.  Be careful with the algebra.