# Thread: Finding a Common centre of gravity

1. ## Finding a Common centre of gravity

Hi there, i have a problem that needs solving. Put simply it goes like this:
I have lots of objects all referenced from there own centres of gravity to a point in 3D space and i need to know the common centre of gravity of all these objects combined.

I dont know if i am just not seeing the easy solution to this or whether it is genuinely a complicated problem...

Any ideas on an explanation or a formula, that Excel could handle to do this, would be awesome.

All the points have an X,Y,Z position on Right hand coordinate system.

2. Are all these constituent centers of gravity referencing the same point in 3D space? If so, let $\mathbf{r}_{j}$ be the vector from the common reference point $O$ to mass $m_{j}$. Then the vector $\mathbf{R}$ from point $O$ to the overall center of gravity is given by

$\displaystyle \mathbf{R}=\frac{\sum_{j}\mathbf{r}_{j}m_{j}}{\sum _{j}m_{j}}.$

3. Yes after doing a bit of research i came up with the same formula, thanks for confirming it.

But now im struggling in putting that into an excel format to deal with the list of co-ordinates i have!

4. You can do everything component-wise with the sumproduct and sum functions in Excel. Look at the help (hit F1 in Windows, anyway) to look up the syntax. The vector equation I gave is valid if you only look at one component at a time. Make sense?

5. Yeh that makes sense, i take it you dont have to take the mass as a vector too, as that would surely give errors (well, zeros) as it only acts in one direction? you just leave it as kg.. yeh i think i get it :P ill crack on with it tomorrow, thanks very much.

6. Right. Mass is not a vector quantity, at least not in your context. Let me know how it goes.

7. Worked a treat, Thankyou!

8. You're welcome. Have a good one!