(g) Hubble’s law; v ≈ H 0 d for receding galaxies, where H 0 is the Hubble…

The idea

Hubble’s law states that the recessional speed v of a galaxy is approximately proportional to its distance d from the observer: v ≈ H₀ d, where H₀ is the Hubble constant. The constant has units of s⁻¹, often quoted as km s⁻¹ Mpc⁻¹. The law applies to galaxies that are receding, which is almost all galaxies beyond the Local Group. You should be able to use the equation to find v, d or H₀, and understand that the linear relationship is evidence for an expanding universe. The approximation sign indicates that the relationship is not exact for very large distances or very high speeds.

What earns the marks

• Hubble’s law is v ≈ H₀ d, where v is recessional speed, d is distance and H₀ is the Hubble constant.
• H₀ is the Hubble constant, with units of s⁻¹ (often km s⁻¹ Mpc⁻¹).
• The law applies to receding galaxies.
• The equation can be rearranged to find v, d or H₀.
• The linear relationship between v and d supports the expanding universe model.

Common mistakes and how to put them right

• Using the wrong units for H₀.

  Put it right: Convert H₀ to SI units (s⁻¹) before using v = H₀ d with v in m s⁻¹ and d in m.

• Thinking Hubble’s law applies to all galaxies.

  Put it right: It applies to galaxies that are receding, which is most galaxies outside our Local Group.

• Confusing the Hubble constant with the age of the universe.

  Put it right: 1/H₀ gives an estimate of the age of the universe, but they are not the same quantity.

• Assuming v is the speed of the galaxy through space rather than the recessional speed due to expansion.

  Put it right: v is the recessional speed.

Exam tips

• Check that the distance is in metres and speed in m s⁻¹ when using H₀ in s⁻¹.
• If H₀ is given in km s⁻¹ Mpc⁻¹, convert Mpc to km or m as needed.
• Remember that the equation is v ≈ H₀ d, so the graph of v against d is a straight line through the origin with gradient H₀.