1. Jun 8, 2007

### Magister

Is it possible to calculate the radii of a star knowing its mass, luminosity and effective temperature?
Thanks

2. Jun 8, 2007

### marcus

try this

The answer to your question is yes, if it is a "main sequence" star.

Most of the stars we see are main sequence, in fact. It is basically just a technical term for the set of normal usual stars.
After a star forms and settles down to steadily fusing hydrogen then it becomes an ordinary (main sequence) star until later in life when it has used up a lot of the hydrogen in its core----later in life it can LEAVE the main sequence and start acting weird, becoming a red giant and such. Even later it might become a white dwarf or neutron start, they aren't part of the main sequence either.

So if you just look at ORDINARY stable hydrogen-fueled stars during their normal lifetime, then the answer is YES you can relate radius to mass, and mass to luminosity, and so on.

and DavidDarling at his website gives a simple approximate relation for relating mass to radius.

the formula he gives is expressed in solar units and says R = M0.8
in other words the radius is almost proportional to the mass. If you have a star with about half the mass of the sun, then it will have a radius which is about half the radius of the sun. (not exactly, because the exponent is 0.8 instead of exactly one)

Last edited: Jun 8, 2007
3. Jun 8, 2007

### Magister

Uoh!
Do you have any idea where this formula cames from?

$$R=M^{0.8}$$

4. Jun 8, 2007

### marcus

IIRC I first met the mass-radius relation in an astronomy textbook by Frank Shu, where it was explained in some detail. It is an old-but-good textbook going back to the 1980s. I will get the name. The title is something like "The Physical Universe"

yeah, here is the amazon page for it
https://www.amazon.com/Physical-Universe-Introduction-Astronomy-Books/dp/0935702059

the formula is based on a hydrostatic model of the insides of a star, the model has been checked empirically, so we know it fits.
if all stars were the same density, then you would expect that the mass would go as the CUBE of the radius
so then R = M^{0.333}
but evidently they aren't all the same density. As you add mass the pressure in the core increases and fusion occurs faster and it gets hotter and this may cause expansion making the more massive stars less dense. I should go upstairs and check my old textbook.

Last edited by a moderator: May 2, 2017
5. Jun 8, 2007

### Magister

From their mass I can know the nuclear energy, assuming that the the star is all made from hydrogen and knowing the percentage of the mass that would be converted to energy in forming helium. From that, assuming that the star is in equilibrium (not expanding), I can get the potential energy, due to gravity, that is needed to balance the pressure caused by the nuclear energy. From the potential energy I can get the radiis of the star. Am I wrong?

PS
Yes, I am talking about a main sequence star.

Edit: Thanks for the book recommendation

6. Jun 8, 2007

### marcus

Magister, I actually can't recommend that book now because it is an old book (1982) but I liked it a whole lot back when i read it.

I wish I could recommend a recent textbook! there is a lot of new information.
I also would like to be able to recommend something online, that you don't have to buy or go find at the library.

I think it is better to say radius is roughly proportional to mass

DavidDarling's formula is only approximate and it looks too precise with his exponent of 0.8

maybe it would be better to say simply
R~M

7. Jun 8, 2007

### Magister

Thanks any way.

What about the above idea? Am I non sense?

8. Jun 15, 2007

### mgb_phys

No I think thats pretty much how stellar hydrodynamics works - and you can usually treat the star as a 1d column of gas.