SOLUTIONS TO EXERCISE 13

 back to exercise motion: TOC for Knowledge Concepts, Exercises, and Solutions

```

We do exactly the same calculation as in Exercise 12 above.  Thus,

for NGC 4471,  H = (997 km/s) / (14.4 Mpc) = 69 km/s/Mpc
for NGC 3193,  H =  1399      /  21.0        67 km/s/Mpc
NGC 6824        3386         46.6        73
NGC 7619        3762         56.7        66
NGC  384        4287         57.2        75
NGC 2563        4900         75.5        65
NGC 1277        5066         68.3        74
NGC 4853        7660        115.0        67
Baade 24       12500        169.0        74
Leo 1          20200        302.0        67

In this case, if we do the same statistical analysis above, we get the values

H = 70.5 +/- 4.0 km/s/Mpc  (margin of error is 4/70.5 or about 6%)

Note that this distribution had a small cluster of data points around H =
67 km/s/Mpc, and another cluster around H = 74 km/s/Mpc.  If only there were
more galaxies in this measurement, we could determine if one is the "real"
peak of the distribution, or if these measurements just caught two sides of
a peak in the middle of the distribution, or if there are really two peaks!
This is a demonstration of why more data points is very important in reducing
the error of a measurement - in this case, random error.

The potential systematic errors in these modern measurements are exactly
the same as those faced by Hubble and Humason decades ago.  Larger telescopes
and better technology, however, have clearly reduced the random error; this
is demonstrated by the much smaller margin of error.

Hubble and Humason's result is clearly much larger - about 8 times larger -
than the modern result.  Note that the velocities they measured aren't that
far off - only 10-20% or so - from the modern; it was the distances that are
way, way off!  This is a telltale signature of systematic error, when one
entire column of numbers is consistently off by about the same amount.

```