gen-define-redshift-and-hubble-s-law-and-give-one-short-worked-e-51d0

Define redshift and Hubble's law and give one short worked example.

# Redshift and Hubble's Law ## Redshift **Redshift** is the phenomenon where light from distant objects is shifted toward longer (redder) wavelengths. It occurs when objects move away from us due to the expansion of the universe. The redshift parameter *z* is defined as: $$z = \frac{\lambda_{observed} - \lambda_{emitted}}{\lambda_{emitted}} = \frac{\Delta \lambda}{\lambda_{emitted}}$$ ## Hubble's Law **Hubble's Law** states that galaxies recede from us at velocities proportional to their distance: $$v = H_0 \times d$$ where: - *v* = recession velocity (km/s) - *d* = distance to the galaxy (Megaparsecs, Mpc) - *H₀* = Hubble constant ≈ 70 km/s/Mpc ## Worked Example **Question:** A galaxy is measured to be 100 Mpc away. What is its recession velocity? **Solution:** Using Hubble's Law: *v = H₀ × d* $$v = 70 \text{ km/s/Mpc} \times 100 \text{ Mpc}$$ $$v = 7000 \text{ km/s}$$ The galaxy is receding from us at **7,000 km/s** (about 2.3% the speed of light). --- *Note: For small velocities, redshift z ≈ v/c, so this galaxy would have z ≈ 0.023*