# Missing something obvious in this derivation

1. Nov 10, 2015

Hi,

I've attached a file displaying a derivation to make the kinetic energy of a two-body problem into a kinetic energy only involving the reduced mass. When plugging 8.3 into 8.1, I just don't quite see how this derivation makes sense. Shouldn't there be a $$\mu^2$$ term? Since when squaring the absolute value of r1, aren't the mass terms also squared? If I'm not mistaken, it simply looks like the mass terms are not squared when plugging in 8.3 into 8.1.

I feel like I'm missing something painfully obvious here, so any help is appreciated!

#### Attached Files:

• ###### Screen Shot 2015-11-10 at 6.42.34 PM.png
File size:
56.2 KB
Views:
45
2. Nov 10, 2015

### sophiecentaur

Isn't it just a matter of dimensions? Why would you expect mass2 to come into the energy formula?

3. Nov 10, 2015

### fzero

There's a factor of $m_1+m_2$ that cancels against one of the factors in the denominator.

4. Nov 10, 2015

### andrewkirk

Yes, they are squared. But if you make the substitutions and work through the algebra, you just end up with $\frac{m_1m_2}{m_1+m_2}$

5. Nov 10, 2015

### Let'sthink

I agree with fzero.

6. Nov 11, 2015

### Chandra Prayaga

Right. Just put it down on paper, instead of imagining what will happen, and it comes out very easily.