How do I solve this word problem

Question

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

d =	GM
4π2
	1/3

T^2/3

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

Hi Elina,

Keplers third law is

T²=4π²R³/GM_s

T=period of rotation in sec

R= distance from the planet to the sun

M_s=Mass of the sun

solving this equation for R gives

R=(GM_sT²/4π²)^1/3

You were given M_s=1.99x10³⁰kg

T=365 days =3.15x10⁷sec

If you substitute these values into the equation for R you should get R=1.5x10¹¹ m (93 million miles)

Hope this helps

Jim