How Hubble Found a Constant
How do we know the value of the Hubble Constant? We can measure the distance to a galaxy by using standard candles, and we can tell how fast an object is receding by how redshifted it is. Of course, not every galaxy is receding at the Hubble expansion rate, but by averaging them out, we can get a pretty good estimate. Also, we know that gravity tends to accelerate closer galaxies towards us, so we can obtain better results by using more distant galaxies. Here are some galaxies, along with their distances and velocities:
| Distance (Mpc) | Speed (km/s) | |
|---|---|---|
| Whirlpool | 7.1 |
463 |
| 3C 273 | 749 |
47469 |
| M74 | 9.2 |
657 |
| M107 | 12.6 |
1048 |
| 0402+379 | 230 |
16500 |
We want to minimize the error by graphing the data and finding a trend. What is the Hubble Constant for these data?
Solution
To get the best approximation, let's find a line of best fit for our data. Our equation for Hubble expansion, v = H0D, is linear, just like the usual equation for a line: y = mx. We want to graph the following data with the distance on the x-axis and the recessional velocity on the y-axis. Then, using a calculator or MS Excel, we can graph the data and obtain a line of best fit for the Hubble Constant. Using Excel, we might come up with something like this:
Since the slope of a line is Δx/Δy, our slope must be the change in Distance (in Mpc) over the change in Speed (in km/s). This gives us our value for the Hubble Constant: H0=64 km/s/Mpc for this set of data.