Example 28-1 Measuring the Distance to a Galaxy from Its Redshift
Find the distances to the following galaxies: (a) NGC 4889, whose redshifted spectrum shows that it is moving away from
us at 6410 km>s (2.14% of the speed of light); (b) 1255-0, which has a larger redshift that shows it to be moving away
from us at 0.822c. Express the distances in megaparsecs and in light-years.
Set Up
For each galaxy we know the speed v at which
it is moving away from us due to the expansion
of the universe. So we can use the Hubble law
to determine the distance d to that galaxy.
The Hubble law:
Solve
Rewrite Equation 28-9 to solve for the distance d:
v
d =
H0
We are given v = 6410 km>s, so
6410 km>s
= 92 Mpc
d =
70 km>s>Mpc
(a) Use Equation 28-9 and the value
H0 = 70 km>s>Mpc to calculate the
distance to NGC 4889.
(b) Repeat the calculations for the galaxy
1255-0, which is moving away at 0.822c.
v = H0d
= 192 Mpc2 a
For this galaxy,
(28-9)
3.26 * 106 ly
b = 3.0 * 108 ly
1 Mpc
v = 0.822c = 0.82213.00 * 105 km>s2
= 2.47 * 105 km>s
Use this to calculate the distance to the galaxy as in part (a):
d =
Reflect
2.47 * 105 km>s
70>km>s>Mpc
= 3.5 * 103 Mpc
= 13.5 * 103 Mpc2 a
3.26 * 106 ly
b = 1.1 * 1010 ly
1 Mpc
NGC 4889 is some 300 million light-years away, so the light we see from NGC 4889 left that galaxy 300 million years
ago, before even the first dinosaurs appeared on Earth. Galaxy 1255-0 is far more distant, some 11 billion light-years
away. When the light we receive from 1255-0 left that galaxy some 11 billion years ago, our Earth—which is a mere
4.56 * 109 years old—had not yet formed. When we use telescopes to look at distant astronomical objects, we are not
only looking out into space; we are also looking back in time.
Ch28_example.indd 1
9/4/13 12:56 PM