Step 5: Data Analysis

Determining the Hubble constant

1. Using the graph provided in the the student answer sheets), graph your data with distance in megaparsecs (Mpc) on the x-axis, and velocity in kilometers per second (km/s) on the y-axis. Draw a straight line that best fits the points on the graph; remember that this line must pass through the origin (the 0,0 point). Measure the slope of this line (rise/run), this is your value of the Hubble constant, in the units of km/sec/Mpc. Please show all calculations and record the slope (the Hubble constant) in the Table of Results (under Step 6).




Determining the uncertainty in the Hubble constant

2. Hubble's Law predicts that galaxies should lie on a straight line when plotted on a graph of distance vs. velocity. Your data probably do not make a perfectly straight line, and you most likely had to make a guess as to where to draw your line. One simple way to estimate the uncertainty in the value of H_o is to draw the steepest reasonable line and the shallowest reasonable line on the graph, and calculate their slopes. Half of the difference between these two slopes would be your uncertainty. Record this number in the table.
   

   Please show all calculations and results on your Table of Results (PDF) given with the answer sheets.

   Determining the Age of the Universe:

3. Maximum age of the Universe
   
   If the universe has been expanding since its beginning at a constant speed, the universe's age would simply be 1/H_o.
   1. Find the inverse of your value of H_o.
   2. Multiply the inverse by 3.09 x 10¹⁹ km/Mpc to cancel the distance units.
   3. Since you now have the age of the Universe in seconds, divide this number by the number of seconds in a year: 3.16 x 10⁷ sec/yr.
      
      

   EXAMPLE: Your Hubble constant is 75 km/sec/Mpc, then 1/75 = 0.0133 = 1.33 x 10-2 (1.33 x 10-2) x (3.09 x 1019) = 4.12 x 1017 (4.12 x 1017) divided by (3.16 x 107) = 1.3 x 1010 This is 1.3 x 1010 years, or 13 x 109 years, or 13 billion years.

   
   This age represents a very simple model for the expansion of the universe, and is the maximum age the universe can be.
   
   
4. The age of the Universe with gravity
   
   A better model would account for the deceleration caused by gravity. Models like this predict the age of the universe to be: t = (2/3)*(1/H_o), or 2/3 of the maximum age of the Universe. Re-calculate the age using this relation (don't forget to take care of the conversion of units!), and record in the table. Remember to show all calculations.