057.1 The Red-shift Distance Relation

The red-shift or lengthening of wavelength means that the source of the waves is traveling away from us. We can calculate how fast it is moving away, the recession velocity.

For galaxies within 200 million parsecs (Mpc) we can measure how far away they are by using Cepheid variable stars, supernovas, and the Tully-Fisher relation.

A graph of recession velocity versus distance for a large number of galaxies reveals a simple relationship.

The constant H₀ is called Hubble's Constant.

Suppose that a galaxy is 200Mpc away. How fast is it moving away from us?

Velocity = (65km/s/Mpc) × 200Mpc
  = 65 ×200 km/s = 13,000km/s

Suppose that a galaxy is 400Mpc away. How fast is it moving away from us?

Velocity = (65km/s/Mpc) × 400Mpc
  = 65 ×400 km/s = 26,000km/s

Suppose that a galaxy is 4000Mpc away. How fast is it moving away from us?

Velocity = (65km/s/Mpc) × 4000Mpc
  = 65 ×4000 km/s = 260,000km/s
 = 260,000,000m/s = 2.6×10⁸m/s

Since the speed of light is 3×10⁸m/s, such a galaxy would be moving away from us at nearly the speed of light.