| |||||||

SOLUTIONS TO EXERCISE 13
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. |