# Am I right?

1. Mar 23, 2009

### aguycalledwil

First off, I'd like to apologize if this topic is against the rules. It's not a homework question, it's just something I decided to do in my spare time, so I figured it's okay to post here, but please tell me if not and I won't do it again.
Being a young physicist (14) I don't have much knowledge in math, so forgive me if this seems like a straight forward, simple question to you.

So my aim was to find how far underground the barycentre between the moon and the Earth was. I gathered several pieces of information as follows....

The mass of the Earth is 5.9742X10^24 KG
The mass of the Moon is 7.36X10^22 KG
The distance between the centre of the Earth and the centre of the Moon is 384,403 KM.
The radius of the Earth is 6378.1 KM

I then did the following...

r1 = a*m2/(m1+m2)

Where 'a' is the distance between the two objects, 'm1' is the mass of the first object and 'm2' is the mass of the second respectively.

So using my values I did...

r1 = 384,403*(5.9742*10^24)/((7.36*10^22)+(5.9724*10^24)). This gave me (supposedly) the distance from the moon to the barycentre. It came to 379,724 KM. I appreciate that it would have made a lot more sense for me to reverse some figures in the second half of the expression to give me the distance from the centre of the Earth to the barycentre, but I wasn't thinking properly. :p

Anyway, so I then did 384,403-379,724 to give me the distance from the centre of the Earth to the barycentre. This gave me 4679 KM. I then took this distance away from the radius of the Earth (6378.1 KM) to give me a final answer of 1699.1 KM underground.

So I was wondering if anyone could tell me how accurate/inaccurate my math is here? Does anyone know as a fact where the barycentre is?

Regards,
Will

Last edited: Mar 23, 2009
2. Mar 23, 2009