# How to find the centre of mass of 3 masses (astronauts and a rock) connected by a rope

To be more specific on the problem, a 50kg astronaut, an 80kg astronaut and a 20kg rock are tied together by a light rope during a space walk. I am asked to find the center of mass.

Now, I've chosen my reference point as the 50kg astronaut and I've used the formula $(m_1r_1+m_2r_2+m_3r_3)/(m_1+m_2+m_3)$ to find the position of the center of mass ($r$) of the system. I am uncertain if this is the correct method used.

If someone could just inform me if i am on the right track. Thanks.

You are on the right track. Mathematically, the center of mass $\vec{c}$ is defined as
$$\vec{c} \sum_i m_i = \sum_i m_i \vec{r}_i$$
where $m_i$ are the individual masses and $\vec{r}_i$ the individual position vectors.
• Or more clearly $$\vec{c} = \frac{\sum_i m_i \vec{r}_i}{\sum_i m_i}$$ – Floris Mar 11 '15 at 19:16
• The reason I stated it as I did because it describes the fact that the net mass at $\vec{c}$ equals all the masses at their own $\vec{r}$ – ja72 Mar 11 '15 at 21:08