Stars Galaxies and the Universe Cheat Sheet

A printable reference covering star properties, H-R diagrams, galaxy types, redshift, Hubble’s law, and cosmic expansion for grades 9-11.

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This cheat sheet covers how astronomers describe stars, galaxies, and the large-scale universe. Students need these ideas to connect observations, such as brightness and color, to physical properties like temperature, distance, and motion. It is especially useful for reviewing star life cycles, galaxy classification, redshift, and evidence for an expanding universe. The goal is to make common astronomy relationships easy to find and apply.

Key Facts

Apparent brightness decreases with distance according to b = L/(4 pi d^2), where L is luminosity and d is distance.
A star’s luminosity is related to its radius and temperature by L = 4 pi R^2 sigma T^4.
Wien’s law gives peak wavelength as lambda_max = b/T, where b = 2.9 x 10^-3 m K and T is temperature in kelvin.
Parallax distance is found with d = 1/p, where d is in parsecs and p is parallax angle in arcseconds.
On an H-R diagram, hot blue stars are on the left, cool red stars are on the right, and luminosity increases upward.
For small redshifts, z = (lambda_observed - lambda_rest)/lambda_rest = v/c, where v is recession speed and c is the speed of light.
Hubble’s law is v = H0 d, meaning more distant galaxies generally move away faster.
A star’s mass is the main factor that determines its lifetime, brightness, and final stage.

Vocabulary

Luminosity: The total amount of energy a star emits each second.
Apparent brightness: How bright an object looks from Earth, which depends on both luminosity and distance.
H-R diagram: A graph that compares stars by temperature or color and luminosity.
Redshift: The stretching of light to longer wavelengths when a light source moves away from the observer or space expands.
Galaxy: A large collection of stars, gas, dust, and dark matter held together by gravity.
Main sequence: The stable stage of a star’s life when it fuses hydrogen into helium in its core.

Common Mistakes to Avoid

Confusing apparent brightness with luminosity is wrong because a dim-looking star may actually be very luminous but far away.
Reading the H-R diagram backward is wrong because temperature usually decreases from left to right, unlike most standard graphs.
Treating redshift as only a change in color is wrong because it measures wavelength change and can show motion or cosmic expansion.
Using Hubble’s law for nearby stars is wrong because v = H0 d applies to distant galaxies on large cosmic scales, not objects inside the Milky Way.
Assuming bigger stars always live longer is wrong because very massive stars burn fuel much faster and usually have shorter lifetimes.

Practice Questions

1 A star has a parallax angle of 0.25 arcseconds. What is its distance in parsecs using d = 1/p?
2 Using H0 = 70 km/s/Mpc, estimate the recession speed of a galaxy 50 Mpc away.
3 A star has a surface temperature of 5800 K. Use lambda_max = 2.9 x 10^-3/T to estimate its peak wavelength in meters.
4 A distant galaxy shows spectral lines shifted toward longer wavelengths. Explain what this tells astronomers about the galaxy and the universe.