## Stars : distance, size, weight, density, luminosity ..... page [ 1 , 2 ]

>> Because this page is becoming too big, I've split it in two..all links will redirect you correctly ... you can also navigate by page number. <<

Normally when you read non-technical book about Stars you mostly get pretty pictures and may be some explanation, but not much more. I have been interested for long time about the details of how exactly we know the thing that we know about stars in more detailed way and finally I had some time to pursue this interest. Let me take you with me in this exploration. The first article will concentrate on how do we find about the different properties of the Stars, things like mass, distance, temperature etc... then the next on how exactly normal stars generate energy, how they stay in equilibrium and don't explode for billions of years, then may be we will explore the evolution of the stars. This is not meant to be full thesis on Stars, just something more than simple star-overview. Again the idea is to fill a gap I think exists.
Because there is so many interconnections between how you can deduce one property of a star from another, I want to point your attention toward the flowchart on the right, as you go trough the text below I'm almost sure you will get lost in this maze of information. I know I'm ;)
For this reason I created this shortcut diagram of some of the basic relations, so you can orient yourself of what you can derive from what and by what means.
For more detailed formulas you can also consult the table at the end of the article.

Another helpful tool is this mini-toc, so you can easily jump around :

To give you some idea before we start with the meat of the matter, the things we can infer about stars come mostly from several major places, namely direct observations for the closest stars using simple geometry, then comes the spectral analysis. Also knowledge of the Universal law of gravitation and Kepler laws give us glimpse of the mass, periods of rotation, distances in gravitationally bound systems . And finally modeling the interior and exterior of stars from our knowledge of fundamental physics and principles of Quantum mechanics, ideal gases and similar help us guess how exactly stars work and compare the results with our observations.
Now that you've got general idea what we will be looking for let start ...

I got in alot of trouble mixing data from different sources...so at the end I decided to only consult Wikipedia for source data. Also I'm limiting myself to three decimal places and this round off in most of the cases causes some small discrepancies with the final values and Wikipedia. Anyway if you find any calculation error please let me know .. all those numbers give me headache ;)

### Hertzsprung-Russell diagram ^

We know already how to measure :
• the star brightness
• and the distribution of light with respect to wavelength/color and from there calculate the surface temperature
It is time to learn the most important tool in Astrophysics, the Hertzsprung Russell diagram shown here on the right. The x-axis represent the spectral-class (temperature) of the star and the y-axis represent the brightness (magnitude).
Again on the x-axis the temperature grows from right-to->left ;(. In our current image the brightness is represented in a number scale comparative to the Sun brightness.
But on other HR-diagrams you may encounter on the Internet the y-axis uses magnitudes, in those cases don't forget that the values will go from positive to negative numbers.
Here is the cool part about the diagram once we pinpoint were a star is positioned we can get a wealth of information at a glance.
Do you see the diagonal lines, which allow us to guesstimate the star radius..niiice !
The big line that crosses the diagram from right-down corner to the upper-left corner is called main sequence, it get very important when we start talking about star life-cycle and provides very strong predictive power.
You can see also marks for the mass along the main sequence.
The theory on stars says that the position on the diagram depends on two and only two things the star mass and the composition of materials contained inside it.
Let's do quick experiment by just looking at the diagram.
Locate Sirius, now you can "eye-pick" that it is ~20 times brighter than the Sun, ~9000 K i.e. hotter, ~2 times more massive, and a little bigger in size.
Stars that are twice more massive are ten times more brighter, stars ten times more massive are thousand time more brighter.

### Velocity ^

TODO
- radial velocity (towards/away) : doppler effect.
- transverse (sideways)

### Density ^

Water density is : 1 g /(cm^3)
Average human body density : 1.02 g/(cm^3)
Sun density is : 1.4 g/(cm^3)

T_c prop M/R Another method is to use Mass/Luminosity to gauge the lifespan of a star.

### Spin ^

How fast stars spin around their own axis and why they rotate with the speed they do ? The theory says that Stars are formed from interstellar gas clouds. The clouds spiral towards the center of the mass as the star start to form. The gas has rotational velocity/momentum (called angular momentum). We know that when object is closer to the center of mass it tend to speed up but the distance it has to travel gets shorter and so we say the angular momentum stays the same, is preserved. There is even conservation law about this.
But if that is the case then as the gas cloud shrink its rotational speed will gets faster and faster. If we follow that train of thought when it shrinks to the size of a star like the Sun it has to speed up to ~100 km/s, even if the initial rotational velocity of the gas was just 1 cm/s.
This contradict observation. The rotation speed of the Sun is just 2 km/s.
Why the discrepancy then ? Overall the argument goes like this, once the star is born from the rotating maelstrom it blasts the nearby gas away, so the star and the accretion disk split. But the electro-magnetic field created by the star drags the dust of the disc around at least the closest parts, in a sense transferring angular momentum. The net result of all this is that the star spin slows down and the accretion-disk rotation speeds up.
Problem solved ;)

[ PAGE 1 ]

## Final notes ^

I'm nowhere near with finishing this article ... as I have time I will try to add some more explanation and other examples. Some more graphs and images would be good too...
As you can see star characteristics we can glance are many and there is myriad ways of finding them, I hope with this article I was able to show how using basic algebra you can discover them and possibly gain some understanding of the the mighty furnaces giving us light and life.
And now summarized in one place the basic relations that we used tr-ought...

L ~~ M^3.5Mass-luminosity ratioAverage for main sequence stars
E = tau T^4Stefan-Boltzmann law (flux)Luminosity-temperature relation (per unit area)
L = 4 pi R^2 tau T^4Luminosity of a starBoltzmann law applied to a sphere.
R = sqrt(L/(4 pi tau T^4)Radius from Temperature and Luminositythe above formula rearranged
F = (G M m)/r^2Universal gravitational law
G M T^2 = 4 pi R^3Kepler 3rd law
lambda_max = k / TWien lawFind temperature from spectrum.
m - M = 5 log d - 5Distance from apparent and absolute magnitudesDistance in parsecs
(m_1 + m_2) * T^2 = (d_1 + d_2)^3 = R^3Mass of stars in binary systemKepler 3rd law
M = (r*v^2)/GCentrifugal force : F = (mv^2)/r and G-law

Next time we will explore how Stars work, the principles involved and some physics rule that stays behind it.

### Space references

Orbital mechanics