Hubble's law describes the relationship between a galaxy's distance from Earth and how fast it appears to be moving away. This cheat sheet helps students connect redshift observations to evidence for an expanding universe. It is useful for solving astronomy problems involving velocity, distance, and the Hubble constant.
It also supports big-picture reasoning about the Big Bang model and the scale of the universe.
The core formula is v = H0d, where v is recessional velocity, H0 is the Hubble constant, and d is distance. Redshift provides evidence of motion away from us because stretched light has longer wavelengths. A larger distance generally means a larger recessional velocity, which shows that space itself is expanding.
The inverse of the Hubble constant gives a rough estimate of the age of the universe when units are handled correctly.
Key Facts
- Hubble's law is v = H0d, where v is recessional velocity, H0 is the Hubble constant, and d is distance.
- A common classroom value for the Hubble constant is H0 = 70 km/s/Mpc, though measured values vary slightly.
- If H0 = 70 km/s/Mpc and d = 100 Mpc, then v = 70 x 100 = 7000 km/s.
- Cosmological redshift is calculated by z = (observed wavelength - rest wavelength) / rest wavelength.
- For small redshifts, recessional velocity can be approximated by v = cz, where c = 300,000 km/s.
- One megaparsec is 1 Mpc = 1,000,000 parsecs, which is about 3.26 million light-years.
- The expansion of the universe means distant galaxies separate because space stretches, not because galaxies fly through space from a single center.
- A rough Hubble time estimate is age ≈ 1 / H0 after converting H0 into units of 1/seconds.
Vocabulary
- Hubble's Law
- The rule that a galaxy's recessional velocity is proportional to its distance from us, written as v = H0d.
- Hubble Constant
- The proportionality value H0 that tells how fast recessional velocity increases with distance.
- Redshift
- The stretching of light to longer wavelengths, often observed when a galaxy is moving away or when space expands.
- Recessional Velocity
- The speed at which a distant galaxy appears to move away from an observer due to cosmic expansion.
- Megaparsec
- A distance unit used in astronomy equal to one million parsecs, or about 3.26 million light-years.
- Cosmic Expansion
- The increase in distances between widely separated galaxies as space itself stretches over time.
Common Mistakes to Avoid
- Treating Hubble's law as ordinary motion through space is wrong because it describes the expansion of space between distant galaxies.
- Forgetting units in v = H0d is wrong because H0 is usually in km/s/Mpc, so distance must be in Mpc to get velocity in km/s.
- Assuming every nearby galaxy follows Hubble's law perfectly is wrong because local gravitational motion can be larger than expansion effects at small distances.
- Using v = cz for very large redshifts without caution is wrong because the simple approximation works best only for small redshift values.
- Saying Earth is at the center of expansion is wrong because observers in any distant galaxy would see other faraway galaxies receding on average.
Practice Questions
- 1 Using H0 = 70 km/s/Mpc, find the recessional velocity of a galaxy that is 250 Mpc away.
- 2 A galaxy has a recessional velocity of 5600 km/s. Using H0 = 70 km/s/Mpc, calculate its distance in Mpc.
- 3 A spectral line has a rest wavelength of 500 nm and is observed at 525 nm. Calculate the redshift z.
- 4 Explain why Hubble's law supports an expanding universe but does not mean that Earth is at the center of the universe.