Introduction:

In this activity you will determine the Hubble Constant or the Rate of Expansion of the Universe by simulating spectroscopic measurements of galaxies. Once you determine the distances to the galaxies and their velocity of recession by the Doppler Shift you can use Excell to estimate the slope of the line. This slope is the Hubble Constant. The inverse of this value is an estimate of the Age of the Universe.

Instrumentation:

You have already used the electronic observatory when you performed photoelectric photometry of the Pleiades galactic or open cluster. The controls are essentially the same but now you are using a different instrument. This instrument is a spectrometer. Basically you will be collecting photons from a galaxy and we'll see a plot of the spectrum. There are absorption lines (the H and K lines of Calcium) that are quite distinct. remember, absorption lines will bea definite "dip" in the continuous spectrum. In the lab for a stationary object these values are respectively 393.3 and 397.0 nanometres. What you'll notice is that if the galaxy is moving away (of course they are) the H and K lines will be shifted towards the longer wavelength. We call this redshifted. You must record the apparent magnitude as well as the H and K lines for each galaxy measured. You will need to measure one or two per cluster. Your instructor will make this clear to you.

Your instructor will explain the operation of the dome and telescope and how to slew from one galaxy to the next. He/She will also help you with the use of the spectrometer and how to identify which data to keep. basically, like you did with the photometer, a signal to noise ratio of 10 to 1 is sufficient for reliable results.

DATA Analysis:

We always don't have exact data to work with. Often we have to make some assumptions, which while reasonable are not necessarily exact. The first one we make is to assume that all the galaxies we observe are roughly the same brightness or the same absolute magnitude. This is an assumption. Ours here is M = -22 This is rather bright, but it tells us how it would look at a distance of 10 parsecs. (We note there is unceratinty in how much each varies from this value but it gives us a good start.) Additionally, we defined a parsec as the distance an object would extend a 1" parallax angle. This is roughly 3.26 LY. A Mega Parsec is a million parsecs, a very long distance away.

Using the equation for magnitudes we have

Basically, we measure m for a galaxy, assume M so we can calculate D which is in parsecs.

To get D we take the anti-log:

You can do this on your calculator or wait to do it in your Excel Spreadsheet. The latter is recommended (Flower's Law of Computers: No human should do work a machine can do)

You want the Velocity of recession for the galaxy which will be an average of the V_H and V_K calculated values. Basically:

Complete the Following Table: (better done on Excel than by hand with a calculator)

Plot the values of Distance (on the x-axis) and Velocity of Recession (on the y-axis.) Use the Chart Wizard to do this. Perform a linear regression process on these data sets to estimate the slope of the line. Your instructor will help.

Calculate the Age of the Universe. This is a simple process but the conversions of units can be tricky.

Discuss results.