Sun-Earth System given center of mass

Homework Statement

Consider the Sun and the Earth as a 'system' of two 'particles'. The center of mass of this system lies a distance L from the center of the Sun. Find L and compare it to the radius of the Sun.

The center of mass of the Earth-Sun system lies?
A. inside the radius of the Sun
B. inside the radius of the Sun
C. inside the radius of the Earth

The Attempt at a Solution

I have no clue where to start, I know the center of mass equation but I don't know if that has any significance or what. Thank you in advance!

D H
Staff Emeritus
What is that equation? Try using it. We can't help you until you make some kind of start.

Well, center of mass equation is (m_1r_1+m_2r_2)/(sigma)m_1)

I know the center of mass of the 2 is in the radius of the sun because the suns size compared to earth, but i dont know the first part still?

D H
Staff Emeritus
How do you know that unless you do the calculations? If you do the calculations the answer will pop right out. The distance from the center of the Sun to the Sun-Earth center of mass will either be smaller than or larger than the radius of the Sun. If it's smaller the center of mass is inside the Sun. Larger, and the center of mass is outside of the Sun.

In short, you need to do the calculation.

Im having the same problem, I know the center of mass equation

(M1r1+M2r2)/ sigma (m)

but is the center of the sun the origin? so would M1xR1 just be 0?

What im confused about is what do I plug in for what?

I already tried calculating the distance from the center of the sun to the center of the earth to use as r2 but it didn't work.

D H
Staff Emeritus