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.
Understanding Hubble's Law and the Expanding Universe
Astronomers do not usually watch a galaxy move across the sky to find its recession. The motion is far too slow to see directly over a human lifetime. Instead, they split the galaxy's light into a spectrum.
Dark or bright spectral lines come from particular atoms, so their laboratory wavelengths are known. When every identified line is shifted toward the red end by the same fraction, the shift can be measured reliably.
This method works even for galaxies too distant to resolve into individual stars. Redshift is therefore one of astronomy's most useful distance and motion clues.
Distance is the harder part of the measurement. Nearby galaxies can be measured using parallax, where a star's apparent position changes as Earth travels around the Sun. Farther away, astronomers use objects with known true brightness, especially certain exploding stars called Type Ia supernovae.
Comparing true brightness with observed brightness gives an estimate of distance. Each step outward depends on earlier measurements, forming a cosmic distance ladder.
Errors at one rung can affect later rungs. Students should remember that a graph of recession speed against distance is built from two separate kinds of evidence, spectral shifts and distance estimates.
Hubble's law is most accurate for galaxies that are very far away. Nearby galaxies have extra motions caused by gravity. For example, the Andromeda Galaxy has a blueshift because it is moving toward the Milky Way as the two galaxies attract each other.
Galaxy groups and clusters have similar local motions. These are called peculiar velocities. At small distances, a peculiar velocity can be a large fraction of the expansion speed, making the pattern look messy.
At greater distances, the overall expansion becomes much clearer. This is why scientists use many galaxies and look for a trend rather than treating one measurement as final proof.
The phrase expanding universe can create a misleading picture of an explosion into empty space. There is no observed central point that all galaxies are moving away from. From any sufficiently distant galaxy, other distant galaxies would appear to recede in the same general pattern.
A useful model is dots on the surface of an inflating balloon. The dots separate because the surface grows, though the balloon itself is not a complete model of the universe.
Gravity still holds solar systems, galaxies, and many galaxy clusters together. Expansion matters mainly across the immense spaces between unbound groups of galaxies.
Using the inverse of the Hubble constant to estimate cosmic age gives a timescale, not an exact birthday calculation. The expansion rate has changed during cosmic history. Matter's gravity slowed expansion for a long time, while dark energy now causes the expansion to speed up.
A fuller model includes these effects and gives an age close to 13.8 billion years. Current measurements of the Hubble constant made using nearby objects do not perfectly match values inferred from the early universe.
This difference is called the Hubble tension. It reminds students that scientific models are tested by measurement, and that even a well supported law has limits on where and how it should be used.