Sun-Earth System given center of mass

[disque]

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

Homework Equations

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]

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

 

[disque]

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

 

[disque]

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 don't know the first part still?

 

[D H]

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.

 

[shaanyr]

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 I am 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]

In answering this question it does not matter one bit which point you choose as the origin of your reference frame in the sense that they will all the same answer. However, one specific choice will make it much easier to answer the question.

You picked that "best" choice, shaanyr.

Show your work.