How do astronomers measure extreme cosmological distances?

Question

A: Cepheid variable stars.

B: Tully-Fisher correlation.

C: Geometric parallax.

D: Hubble’s Law.

Answer 1

All of these are ways that astronomers can measure distances but are effective at different distances--something they often refer to as "the distance ladder." Let's go over each one.

We'll start with geometric parallax. You can experience parallax yourself: hold your arm out and stick one finger up. Next, close one of your eyes, and then the other. You should see how the background of your room appears to shift, even though neither you or the background is moving. This is parallax--the difference in position of each of your eyes means that an object appears to shift some amount relative to the background. Mathematically, d = 1/p, where d is distance in parsecs ("parallax seconds") and p is the angle in arc-seconds, and the difference in position we take advantage of is the Earth on opposite sides of the Sun. Parallax is great for assessing relatively nearby objects' distance, such as other stars in our galaxy. However, as distance is inversely proportional to angle, it is extremely difficult to measure parallax distance of super-far objects.

Cepheid variable stars are useful because their period of variability--how long it takes for one cycle of their fluctuating brightness to occur--correlates to their overall magnitude. Astronomers can measure the received flux of a Cepheid variable, and use the luminosity-flux relationship to determine its distance. However, there is a limit to how far away we can view these Cepheids; while they might be visible in local galaxies, you won't be able to see them in galaxies on cosmological scales. (Note: Cepheids were discovered by Henrietta Swan Leavitt, one of astronomy's great female figures!)

The Tully-Fischer relationship is similar to Cepheid variables, except it relates brightness of a spiral galaxy to its rotation. This allows for greater distances to be measured than Cepheids, but not enough for extreme cosmological scales.

Finally, we have Hubble's law. Hubble's law says that there is a linear relationship v = H₀ d, where v is the velocity of a galaxy, d is the distance to that galaxy, and H₀ is the "Hubble Constant," a constant of proportionality that describes the expansion of the universe today. We can measure the velocity simply by measuring far-away galaxies' redshift. This simplified version of Hubble's law provided early evidence for the expansion of the universe--a cosmological phenomenon--and determining the Hubble constant remains a foremost goal of cosmological physics.

D is our answer!