# Hubble's Law

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Published 2022-10-09

# 7.2 Hubble's Law

Photographs of some galaxies and their spectra captured by Milton
Humason using the 100 inch Mount Wilson Telescope. As shown the fainter
the galaxy (thus further), the more red-shifted its spectrum is. — Photographs of some galaxies and their spectra captured by Milton Humason using the 100 inch Mount Wilson Telescope. As shown the fainter the galaxy (thus further), the more red-shifted its spectrum is.

In 1920s, Edwin Hubble and Milton Humason began to measure spectra of galaxies. Hubble found that the amount of redshift of a galaxy is not a random value, but directly proportional to the distance away from us. Using the observational data (see Sec. \ref{subsec:Hubble's-data}), he published in 1929 a relationship between distance and recession velocity of a galaxy, now known as the Hubble's law

\begin{equation}
v=H_{0}d
\end{equation}

The Hubble parameter H_{0} is an empirically fitted value. The subscript 0 is a convention that astronomers use to indicate that the value is as measured at current time t_{0}. (Theoretically the Hubble parameter can be a function of time, so it could be very different say 10 billion years ago.) Since Hubble's 1929 report, various groups have obtained different values of the Hubble's constant. Recent measurements narrows the value to be around 70 \text{kms}^{-1}\text{Mpc}^{-1}.¹

The redshift of galaxies that Hubble found follow a rule that is applicable to the entire Universe. For this reason, we call this redshift the cosmological redshift.

Try it Yourself!

Cosmology is the study of the Universe as a whole. How did Hubble's work impact the field of cosmology?

Try it Yourself!

See Pre-Lecture homework on Hubble's data and the Cosmological principle. Why do you think that Hubble proposed a linear relationship based on his seemingly scattered data?

Try it Yourself!

What is causing the galaxies to "move away" from us (and from each other)?

Try it Yourself!

Ex. What is the difference between Doppler redshift and Cosmological redshift?

See this article for an overview of recent techniques and results on the the measurement of Hubble's constant.↩