Name:____________________________  Lab Section: Online  Date: _____________

Exercise 

   Find Distances

1.      Measure the size of each galaxy in millimeters.  For elliptical galaxies, an average of the long and short axis will be give satisfactory results.

2.      Try to measure the small galaxies to a fraction of a millimeter if possible.  The Hydra galaxy is very close to another galaxy.  Be sure to measure the left one.

3.      Record your measurements in the data table.

4.      Use the equation below to calculate the distance to each galaxy.  Record the distance in the data table with the correct number of significant figures.

   Find Recessional Velocities

  1. Measure the distance L between the 388.8 nm and the 501.5 nm helium emission lines in millimeters.  L = _______________
  2. Measure the linear distance x from the 388.8 nm emission line to the H calcium absorption line for each galaxy (the H line is the rightmost absorption line of the pair).  Record these values in the data table.
  3. Calculate λobs and recessional velocity v for each galaxy.  Record both values in the data table with the correct number of significant figures.

              ,     (λo = 396.8 nm)

Data Table

 

 

 

 

Cluster

Average Galaxy  Diameter “S”

(mm)

Distance “d”

(Mpc)

H Line

Displacement “x” (mm)

λobs

(nm)

Recessional Velocity “v”

(km/s)

Virgo

49.4

15.6

 

 

 

Ursa Major

 

 

 

 

 

Corona Borealis

 

 

 

 

 

Bootes

 

 

 

 

 

Hydra

 

 

 

 

 

Now you are ready to make a Hubble Diagram.  Using the graph paper provided, make a plot of velocity (vertical axis) verses distance (horizontal axis) using the data in the table (circle each data point plotted).  There is one additional data point besides the five galaxies—the one for our home galaxy, the Milky Way.  Place an asterisk on the plot to mark the Milky Way.

 

  1. From your graph determine Hubble’s constant Ho.  First, draw a best fit line through the data points making sure the line begins at the origin (use a clear ruler).  Determine the value for Ho by measuring the slope of the line.  Show your work below and be sure to use the proper units.

 

 

 

Ho = __________________

 

  1. Once Hubble’s Law has been calibrated then it becomes a very useful tool for finding distances to other galaxies (any type or size).  To find distance astronomers measure the recessional velocity from the redshift of the galaxy’s spectrum and then apply Hubble’s Law.  What is the distance to a galaxy with a recessional velocity of 29,000 km/s (use the Hubble Diagram or v = Hod and your measured value of Ho from question 1.)?

 

 

 

d = __________________

 

  1. Calculate the age of the universe using your value of Hubble’s constant.  Your final answer should be in billions of years.

Useful Conversions:

1 Mpc = 3.1 X 1019 km

1 yr = 3.16 X 107 sec

1 billion yrs = 109 yrs

 

 

 

t = __________________

 

Name:____________________________  Lab Section: Online  Date: _____________