Table 3 contains information about two galaxies - AQA - A-Level Physics - Question 4 - 2019 - Paper 4

To determine if the data for the two galaxies are consistent with Hubble's Law, we can use the formula:

$v = H_0 imes d$

where:

• $v$ is the recessional velocity of the galaxies,
• $H_0$ is Hubble's constant,
• $d$ is the distance of the galaxies from Earth.

1. For NGC 936:

   • Given redshift, $z = 4.8 imes 10^{-3}$ and using the relation $v = cz$, where $c$ is the speed of light ($c \approx 3 \times 10^{8} m/s$), we find:
   • $v_{NGC 936} = 4.8 \times 10^{-3} \times 3 \times 10^{8} \approx 1.44 \times 10^{6} m/s$
   • The distance is $d = 6.8 \times 10^7 ly \approx 6.42 \times 10^{20} m$ (1 ly $\approx 9.46 \times 10^{15} m$).
   • Now substituting in Hubble's law:
   • $H_0 = \frac{v}{d} \approx \frac{1.44 \times 10^6}{6.42 \times 10^{20}} \approx 2.24 \times 10^{-15} s^{-1}$

2. For NGC 3379:

   • Given redshift, $z = 3.0 \times 10^{-3}$:
   • $v_{NGC 3379} = 3.0 \times 10^{-3} \times 3 \times 10^{8} \approx 9.0 \times 10^{5} m/s$
   • The distance is $d = 3.2 \times 10^7 ly \approx 3.03 \times 10^{20} m$.
   • Substituting in Hubble's law gives:
   • $H_0 \approx \frac{9.0 \times 10^5}{3.03 \times 10^{20}} \approx 2.97 \times 10^{-15} s^{-1}$

In conclusion, both galaxies yield different estimates for Hubble's constant, but still reasonably consistent as they both indicate a positive correlation with distance, which supports Hubble's Law.