Astrophysics Fundamentals

What is Astrophysics?

Astrophysics is the branch of science that applies the laws of physics and mathematics to understand celestial objects and phenomena. It investigates stars, planets, galaxies, black holes, dark matter, and the evolution of the universe itself.

Astrophysicists use observations from telescopes and spacecraft along with theoretical models to explain how the cosmos works.

Newton's Law of Gravitation

Gravity governs the motion of planets, stars, and galaxies. Newton's Law of Universal Gravitation describes the attractive force between two masses.

\[ F = G\frac{m_1m_2}{r^2} \]

\(F\) = gravitational force
\(G\) = gravitational constant
\(m_1,m_2\) = masses
\(r\) = distance between centers

Luminosity and Brightness

A star's luminosity is the total energy it emits each second. The observed brightness depends on the distance from Earth.

\[ B=\frac{L}{4\pi d^2} \]

This relationship explains why distant stars appear dimmer even if they are intrinsically very powerful.

The Electromagnetic Spectrum

Region	Typical Astrophysical Sources
Radio	Pulsars, gas clouds
Microwave	Cosmic Microwave Background
Infrared	Dust clouds, forming stars
Visible	Stars and galaxies
Ultraviolet	Hot stars
X-ray	Black holes, neutron stars
Gamma Ray	Supernovae and gamma-ray bursts

Stellar Classification

Stars are categorized according to temperature and color using the spectral sequence:

O - B - A - F - G - K - M

Class	Color	Approx. Temperature (K)
O	Blue	30,000+
B	Blue-White	10,000–30,000
A	White	7,500–10,000
F	Yellow-White	6,000–7,500
G	Yellow	5,200–6,000
K	Orange	3,700–5,200
M	Red	Below 3,700

Worked Examples

Example 1

A star is twice as far away as another identical star. How much brighter does it appear?

Using:

\[ B \propto \frac{1}{d^2} \]

Doubling the distance decreases brightness by:

\[ \frac{1}{2^2}=\frac14 \]

The star appears four times dimmer.

Example 2

A star emits \(8 \times 10^{26}\) watts of power. What property does this represent?

It represents the star's luminosity.

Life Cycle of a Star

Nebula
Protostar
Main Sequence Star
Red Giant or Supergiant
Planetary Nebula or Supernova
White Dwarf, Neutron Star, or Black Hole

Practice Problems

Problem 1:
What force keeps planets orbiting the Sun?

Gravity.

Problem 2:
What spectral class is the Sun?

Class G.

Problem 3:
If distance doubles, brightness changes by what factor?

Brightness becomes one-fourth as large.

Problem 4:
Which electromagnetic region is commonly used to study black holes?

X-rays.

Problem 5:
What remains after a low-mass star exhausts its fuel?

A white dwarf.