# D.1 Stellar Quantities

### Light year (Ly) & Astronimical unit (AU)

• A Light year is the distance travelled by light in one year, which is 9.46×10^15^m

• An Astronimical unit is the average radius of the Earth’s orbit around the Sun, which is 1.5×10^11^m = 3.26ly

### Stellar parallax

The parallax angle is the angle, at the position of the star, that is subtended by a distance equal to the radius of the Earth’s orbit around the Sun (1AU).

A parsec is the distance to a star whose parallax is 1 arc second, which is 3.09×10^16^m

An arc second is 1/3600 of a degree

• The average distance between stars in a galaxy is about 1pc
• Obveratory on Earth could see star within 100pc (Because of the distortion caused by atmosphere)
• High resolution satellite could see star within 100,000pc
• Distance toward the edge of milky way galaxy is 30,000pc
• Galaxy cluster (30 galaxies): 1,000,000pc

The parallax method is also a means of measuring astronomical distances:

$$d \textcolor{grey}{\text{ (parsecs)}}=\frac{1}{p\textcolor{grey}{\text{ (arc seconds)}}}$$

But if the star is too far, p would be too small to be measured accureately!

### Apparent brightness & Luminosity

Apparent brightness: The received power per unit area $$b=\frac{L}{4\pi d^2}$$ $b$: Apparent brightness ($Wm^{-2}$)

$L$: Luminosity ($W$)

$d$: Distance ($m$)

Luminosity: Total power radiated by the star

$$L=\sigma AT^4$$

$\sigma$: Stefan-Boltzmann constant

$A$: Area of the star ($m^2$)

$T$: Temperature ($K$)

A star is assumed to radiate like a black body.

$L_{\bigodot}$ symbolized the luminosity of the sun, the same for other variables.

### The nature of stars

The stability of a star depends on the equilibrium between radiation pressure and gravitational pressure

• Radiation pressure make the star expand
• Nuclear fusion provides the energy the star needs to keep it hot so that the star’s radiation pressure is high enough to oppose gravitational contraction.
• Gravitation make the star collapse

#### Proton–proton cycle (fusion reactions)

• $^1_1\text H+^1_1\text H\rightarrow^2_1\text H+^0_1e^++v_e$
• $^2_1\text H+^1_1\text H\rightarrow^3_2\text He+\gamma$
• $^3_2\text He+ ^3_2\text He\rightarrow^4_2\text He+2^1_1\text H$