Astronomy cheat sheet

Light-year

A light-year is a distance: the distance light travels through vacuum in one year.

It is not a unit of time.

Gravity and orbits

Gravity changes the direction of an orbiting object’s velocity. An orbit is continuous free fall around another body.

A nearly circular orbit requires inward acceleration.

Spectra

A spectrum separates light by wavelength. Spectral features provide evidence about composition, temperature and motion.

A shifted spectral line can indicate motion along the line of sight.

Stars and planets

Stars generate energy through nuclear fusion during their main-sequence lives. Planets orbit stars and generally shine by reflected light.

A planet’s brightness alone does not make it a star.

Brightness and luminosity

Luminosity is total emitted power. Apparent brightness depends on luminosity and distance; for isotropic emission without absorption it follows an inverse-square relation.

Twice the distance gives one-quarter the apparent brightness for the same source.

Stellar parallax

For nearby stars, distance in parsecs is approximately the reciprocal of parallax in arcseconds. The observed shift is measured against a distant reference background.

d(pc) = 1/p(arcsec); a parallax of 0.2 arcsec corresponds to 5 pc.

The H–R diagram

A Hertzsprung–Russell diagram relates stellar luminosity to temperature or spectral type. It groups evolutionary states; it is not a map of stars’ positions in space.

Main-sequence stars fuse hydrogen in their cores.

Redshift

Redshift means that observed wavelengths are longer than a reference wavelength. Doppler motion, cosmological expansion and gravitational effects require different interpretations.

z = (λobserved − λrest)/λrest.

Worked example: light travel

A signal travelling at approximately 300,000 km/s takes 500 s to cover 150 million km: time = distance/speed. This is about 8.3 minutes.

A light-year is a distance; a light-travel time must be expressed in units of time.

Common mistake: seasons and distance

Earth’s seasons primarily result from axial tilt changing sunlight angle and day length, not from Earth moving markedly closer to the Sun in one hemisphere’s summer.

The northern and southern hemispheres have opposite seasons at the same point in Earth’s orbit.

Check your understanding

If a star is moved three times farther away, how does its apparent brightness change?

It becomes one-ninth as bright under the inverse-square model, assuming unchanged luminosity and no intervening absorption.

Curriculum connections

Sources