# Angular momentum in close binaries

1. Apr 22, 2004

### Kurdt

Staff Emeritus
Does anybody know how the angular momentum of close binaries was calculated as:

$$L=M_sM_p(\frac{GD}{M})^\frac{1}{2}$$

This is something which is plaguing me so any input would be appreciated.

$$M=M_s+M_p$$, D= total seperation between the two stars.

Thanks guys

2. Apr 22, 2004

### Labguy

Don't know if that formula always holds as there is almost always angular momentum loss in close binaries with either filled Roche Lobes or actual mass transfer. Too many types (variables) of binary stars to lump into one catagory. Take a look at: http://www.rri.res.in/ph217/binary.pdf and:
http://www-astro.physics.ox.ac.uk/~podsi/lecture11_c.pdf for a lot on this.

3. Apr 22, 2004

### Kurdt

Staff Emeritus
Yeah I know the gravitational waves leak angular momentum away from the system and also stellar winds from the secondary trapped in magnetic loops. The momentum equation should hold as the radius of orbit changes when the angular momentum is leaked away thus allowing the secondary to fill its Roche lobe and maintain contact with the L1 point. I will have a look at the links though, thanks for replying.

4. May 13, 2004

### Kurdt

Staff Emeritus
Ahh. Forgot I posted this. I managed to work it out and for anyone who was interested heres the derivation.

First we start with summing the $$\mathbf{v}\times \mathbf{r}$$ for each star in the system. This gives.

$$\mathbf{L_{orb}} = M_sr_sv_s\mathbf{e}_k+M-pr_pv_p\mathbf{e}_k$$

now $$v_s=r_s\Omega$$ and similarly for the primary also we can substitute $$r_s=\frac{M_p}{M}D$$ into the equation and again a similar relation is found for the primary to yield.

$$\mathbf{L_{orb}} =(M_s\frac{M^2_p}{M^2}D^2+M_p\frac{M^2_s}{M^2}D^2)\Omega\mathbf{e}_k$$

and manipulation gives

$$\mathbf{L_{orb}} =\frac{M_sM_p}{M^2}D^2\Omega(M_s+M_p)\mathbf{e}_k$$

$$(M_s+M_p)=M$$ and $$\Omega=(\frac{GM}{D^3})^{1/2}$$

So

$$\mathbf{L_{orb}} =\frac{M_sM_p}{M^2}D^2(\frac{GM}{D^3})^{1/2}\mathbf{e}_k$$

$$\mathbf{L_{orb}} =M_sM_p(\frac{GD}{M})^{1/2}\mathbf{e}_k$$

Last edited: May 13, 2004
5. May 18, 2004

### Pinkline Jones

Kurdt,

The angular momentum of close binaries was calculated by a modest young diesel mechanic working in a sheltered workshop in Yorkshire. The young man - Winthrop Spencer Flibberdigit has since gone on to write some fascinating books released in sanskrit by "Absolutely No Frills and Assoc. Publishers". Here's just a short list of his books to date:

"The Peripatetic Life of the Sandwich Island Penguins"

"Low Orbital-Decibel ratios of Semi-Diametric Rolling Hub Caps"

"Desperate and Dateless Conversations - How My Electromagnetic Spectrum Theorem sent my Lover into a Coma"

"Dangers of The Spiral Galaxy - Fifty Bucks to Clean the Cab"

My pleasure...

DR PINKLINE JONES a.l.s.c.

6. May 19, 2004

### Kurdt

Staff Emeritus
Thank you for your input Pinkline I shall certainly investigate these publications when I next visit the library. I have several exams in the coming three weeks though so I doubt I will be able to spare any time soon. The titles definitely look interesting.

Last edited: May 19, 2004
7. May 19, 2004

### Kurdt

Staff Emeritus
Would you believe it! I managed to find one of his publications in my own personal library. "Dangers of The Spiral Galaxy - Fifty Bucks to Clean the Cab" is a most interesting journey through the derivation of angular momentum in the andromeda galaxy all on a wild night out. I particularly like the climax when he reaches his conclusions in the taxi on the way home. Also the last chapter about his abduction by aliens is well worth the read alone.

8. May 19, 2004

### Pinkline Jones

LOL Kurdt - I'm glad you found the book and happy to be of assistance wherever I can in cyber world. But obviously I have to fine you for possessing a sense of humour - that's a very dangerous attribute to have in this mixed up world - people look at you funny.

PINKLINE JONES

9. May 20, 2004

### Kurdt

Staff Emeritus
Well I may never have to show it again as I think I have learned a valuable lesson to read peoples posts thoroughly first time. So if you don't tell i won't.