Hubbles law lab

This is a big lab. Don't freak out!

Excel be calculating the math for you, and you will each only be doing a few galaxies. Calm down.

The data you are looking at is real. You will be doing the exact same calculations astronomers performed to determine the age of the universe.

Learning Objectives

Using analyses of images and spectra of selected galaxies, the students will

• measure angular sizes of galaxies and find their distances;
• measure the redshifts of spectral lines and find the recessional velocities;
• determine a value for Hubble's constant;
• estimate the age of the Universe from this constant and compare it to the age of the Sun and the Milky Way;
• discuss the effect that various uncertainties in measurements have on the Hubble constant ;
• summarize how our view of the Universe has changed as the value of the Hubble constant has improved.
  • Background and Theory
    • In the 1920's, Edwin P. Hubble discovered a relationship that is now known as Hubble's Law. It states that the recessional velocity of a galaxy is proportional to its distance from us:
    • ν = H_od [Eqn. (1)]
    • where v is the galaxy's velocity (in km/sec), d is the distance to the galaxy (in megaparsecs; 1 Mpc = 1 million parsecs), and H_o is the proportionality constant, called "The Hubble Constant." Hubble's Law states that a galaxy moving away from us twice as fast as another galaxy is twice as far away as that galaxy (or, three times faster is three times farther away than another galaxy, etc.). The Hubble constant is a hotly contested quantity in astrophysics. In order to precisely determine the value of H_o, we must determine the distances to and velocities of many galaxies, preferably those extremely far away so that we get beyond the Milky Way's gravitational interaction with "nearby" galaxies.

Recording on the spreadsheet:

You will only be adding things to the columns that say 1s. That is it. The columns for Z are redshift. Try to be as accurate as possible with your measurements, and SAVE OFTEN!

You Need These Links!!!!

Spectra and Galaxy pics

Instructions for reading wavelength- note that it is not the same for each!!!!

Notes on excel!!!

If using the Hubble's Law EXCEL spreadsheet, follow these directions:

1. Right-click Hubble's Law Spreadsheet and open it or choose to save the target on the computer you are using. Ignore all errors (#div by 0, NaN, *****, negative numbers, all values being the same, etc.) shown on the spreadsheet as they will all disappear once you start entering your data.
2. Enter the measured angular size, and the spreadsheet will calculate the distance to that galaxy in megaparsecs (millions of parsecs).
3. Once you enter your values of the redshifted wavelengths, the formulae in the worksheet should automatically calculate the redshift z for Ca II K, Ca II H and H-alpha lines for each galaxy, as well as average these 3 values AND find the velocity.
4. If the spreadsheet is working correctly on your computer, it should also automatically update the chart of the data as you enter your numbers. (This feature is actually pretty cool. Watch as you enter your last few data points.)
5. If the spreadsheet does not produce a plot automatically:
   1. After you have finished entering all of your data and your chart shows all of the data points, you need to add a trendline to the data and tell the program to display the fit of that line:
      • Activate the chart region in the spread sheet by left-clicking on an edge.
      • From the top menu, choose "Chart" and "Add Trendline."
      • From that menu, choose "Linear" for Trend/Regression type.
      • Click on "Options" and check all three options at the bottom: Set intercept = 0, Display equation on chart, and display R-squared value on chart.
      • Click "OK."
   2. The chart now shows the slope of the line in the form: y = mx + b (but here b = 0, so is not given). Round off the slope to 2 significant digits (e.g., 75.4839485 would be 75). The R-squared value is a measure of how well the fit represents the data; if the value was equal to 1, then the fit would be perfect. Anything close to 1 is good here. Be sure you OBVIOUSLY note how good the fit is to your data.

REMEMBER TO SAVE YOUR SPREADSHEET OFTEN! When finished, print your Excel or Google spreadsheet. Please format your spreadsheet so that the information reproduces on only 1 or 2 sheets of paper.

Procedure - PART II: Age of the Universe (all methods converge here)

If the universe has been expanding at a constant speed since its beginning, the Universe's age would simply be 1/H_o.