→ A black body is a body which absorbs all the electromagnetic radiation incident upon it and which also emits all wavelengths of electromagnetic radiation. The temperature of a blackbody determines its colour.

If a star is cooler then it will be more red, higher $\lambda$, and if a star is hotter it will be more blue, lower $\lambda$.

→ The surface temperature of the Sun is $5800 \space K$. NB: $K=C\degree + 273$.

Based on the the assumption that stars behave as black bodies, the following relationships can be used to solve problems relating to luminosity, $L$ (measured in $W$), apparent brightness, $b$ (measured in $W \space m^{-2}$), distance between the observer and the star, $d$, power per unit area, $\frac{P}{A}$, stellar radius, $r$, and stellar surface temperature, $T$ (measured in $K$).

$$ b=\dfrac{L}{4\pi d^2} $$

→ There is an inverse square relationship between $b$ and $d$, meaning that $b$ will decrease rapidly as $d$ is increased.

$$ \dfrac{P}{A}=\sigma T^4 $$

$$ L=4\pi r^2 \sigma T^4 $$

→ The units for the Stefan-Boltzmann’s constant are $W \space m^{-2} \space K^{-4}$.

Stars are formed in interstellar clouds when gravitational forces overcome thermal pressure and cause a molecular cloud to contract until the core becomes hot enough to sustain nuclear fusion, which then provides a thermal pressure that balances the gravitational force.

Hydrostatic equilibrium

Several types of stars produce energy by converting hydrogen into helium by the process of nuclear fusion termed the proton-proton chain (p—p chain). There are three stages in this type of stellar fusion reaction.

→ Two hydrogen nuclei (protons) fuse together, ejecting a positron ($^0_{+1}e$) and a neutrino ($v_e$) in the process to form a deuterium nucleus (a proton and a neutron).

Then the deuterium nucleus fuses with another proton to produce a light form of helium, helium-3 (two protons and one neutron). A gamma ray is also released.

Then, two helium-3 atoms fuse into a normal helium atom, helium-4 (two protons and two neutrons). Two protons are also ejected.

→ The following is an example of a p—p chain.

$$ ^1_1H \space + \space ^1_1H \space \rarr \space ^2_1H \space + \space ^0_{+1}e \space + \space v_e $$