# Mass of the Earth

## Homework Statement

Earth is a satellite of the Sun with an orbit radius of approximately 1.5×1011 m.
a) What is the Sun’s mass?
b) If the Sun’s radius is 6.96×108 m, how does the Sun’s density compare with Earth’s density?

v^2 / r = ac

GMm / r^2 = Fg

## The Attempt at a Solution

For a) I know Fg has to = ac for the planet to orbit without crashing into it or moving away.

I set them equal to each other and simplified.

v^2 / r = GMm / r^2

Which simplified to

v^2 / G = M

I found the velocity of earth using the v = d / t

d = the distance around one orbit
t = the number of seconds in 1 year

The using the expression

v^2 / G = M

I derived the sun's mass which was 2.0058 x 10^30

Part b)

I know Density = m / v

I have the mass of the sun

To find the volume I just used the formula for the volume of a sphere

which is = 4/3Pir^3

Volume of the sun was = 1.41 x 10^27

Since I have volume of the sun and the mass, I can also get the density

What's causing me trouble is finding the mass of the Earth.

I tried using this method.

ma = GMm / r^2

Where m = 1kg
a = 9.8m/s^2

But the problem was the radius of earth. Is there a way to finding the radius? I've tried everything I can possibly do. Any help would be appreciated. Thanks in advance. :)