# 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. :)

## Answers and Replies

gneill
Mentor
There's not enough information given in the question statement for you to find the density of the Earth. You'll have to refer to some resource that gives Earth's mass and radius.

There's not enough information given in the question statement for you to find the density of the Earth. You'll have to refer to some resource that gives Earth's mass and radius.

Thank you! I thought that might be the problem, but since I found an answer to a) without any outside source (except G which I knew), I thought I could solve this with my previous knowledge. Thank you. :)