properties of stars

Astronomy Notes

Electromagnetic Spectrum

Order from shortest wavelength/highest energy to longest wavelength/lowest energy:

  1. Gamma rays

  2. X-rays

  3. Ultraviolet

  4. Visible light

  5. Infrared

  6. Microwaves

  7. Radio waves

Key ideas:

  • Short wavelength → high energy

  • Long wavelength → low energy


Inverse Square Law

Light becomes weaker as distance increases.

I∝1d2I \propto \frac{1}{d^2}I∝d21​

  • Double distance → 1/4 intensity

  • Triple distance → 1/9 intensity


Telescope Properties

Objective

Main lens or mirror that collects light.

Larger objective:

  • Collects more light

  • Makes dim objects easier to see

Objective area:

A=π4D2A=\frac{\pi}{4}D^2A=4π​D2


Light-Gathering Power

Depends on objective diameter.

Larger diameter = more light collected.


Resolving Power

Ability to see fine details clearly.

θR∼λD\theta_R \sim \frac{\lambda}{D}θR​∼Dλ​

  • Larger diameter → sharper images

  • Longer wavelength → lower resolution


Magnification

Makes image larger.

Does NOT increase brightness.


Spectroscopy

Study of light spectra to determine:

  • Composition

  • Temperature

  • Motion

  • Distance


Types of Spectra

Continuous Spectrum

  • Full rainbow

  • Produced by hot dense objects like stars


Emission Spectrum

  • Bright lines on dark background

  • Produced by hot thin gas

Electron drops to lower energy level:

  • Releases light


Absorption Spectrum

  • Dark lines on rainbow background

Occurs when:

  • Light passes through cooler gas

  • Gas absorbs certain wavelengths

Each element has unique spectral lines.


Kirchhoff’s Laws

  1. Hot dense object → continuous spectrum

  2. Hot thin gas → emission spectrum

  3. Continuous light through cool gas → absorption spectrum


Blackbody Radiation

Blackbody:

  • Perfect absorber and emitter of radiation

Blackbody curves show:

  • Wavelength

  • Energy emitted

Hotter stars:

  • Emit more energy

  • Peak at shorter wavelengths

  • Appear blue

Cooler stars:

  • Peak at longer wavelengths

  • Appear red/orange

Approximate temperatures:

  • 3000 K → red

  • 4000 K → orange

  • 5000+ K → blue-white


Doppler Effect

Redshift

Object moving away:

  • Wavelength increases

  • Light shifts red

Blueshift

Object moving toward:

  • Wavelength decreases

  • Light shifts blue

Rotating stars:

  • One side blueshifted

  • One side redshifted

  • Spectral lines smear out


Magnitude System

Apparent Magnitude

Brightness seen from Earth.

  • Smaller/negative number = brighter

  • Larger positive number = dimmer

Difference of 5 magnitudes:

  • 100× brightness difference

Brightness ratio:

2.512m2−m12.512^{m_2-m_1}2.512m2​−m1​


Absolute Magnitude

True brightness of a star.

Defined as:

  • Brightness if star were 10 parsecs away

Formula:

m−M=5log⁡(d10)m-M=5\log\left(\frac{d}{10}\right)m−M=5log(10d​)

  • mmm = apparent magnitude

  • MMM = absolute magnitude

  • ddd = distance in parsecs


Parallax

Method for measuring nearby star distances.

As Earth orbits the Sun:

  • Nearby stars appear to shift

Closer star:

  • Larger parallax angle

Farther star:

  • Smaller parallax angle

Formula:

D∝1pD \propto \frac{1}{p}D∝p1​


Arc-Second

Tiny angle measurement.

1 arc-second=13600∘1\text{ arc-second}=\frac{1}{3600}^{\circ}1 arc-second=36001​∘


Measuring Distances

Cepheid Variable Stars

Brightness changes periodically.

Period relates to luminosity.

Used for:

  • Nearby galaxy distances


Supernovae

Exploding stars.

Extremely bright.

Used for:

  • Very large distances


Hubble’s Redshift

More distant galaxies:

  • Have larger redshift

  • Move away faster

Used to measure:

  • Galaxy velocity

  • Distance


Characteristics of Stars

Composition

Typical stars:

  • 71% hydrogen

  • 27% helium


Luminosity

Total energy emitted.

Depends on:

  • Size

  • Temperature


Size

  • White dwarfs ≈ Earth size

  • Neutron stars ≈ 20 km wide

  • Supergiants much larger than Sun


Temperature and Color

  • Red stars → cooler

  • Blue stars → hotter

Approximate:

  • 3000°C → red

  • 20,000°C+ → blue


Important Relationships

  • Hotter star → bluer

  • Cooler star → redder

  • Larger star → often more luminous

  • Closer star → larger parallax

  • Moving away → redshift

  • Moving toward → blueshift