Lab Sheet: Determining the Extragalactic Distance Scale

Name:________________________________

ID number:____________________________

Course (circle one): A01 or A20

Lab Sheet: Determining the Extragalactic Distance Scale

I. Find the Cepheids!

A. Record all the grids you visited:

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B. Cepheid information

Find a minimum of 8 Cepheids.

Cepheid name   Grid #   Avg m_v   P(days)    M_v     m_v-M_v
____________   ______   ______   _______  ______  ______ 
____________   ______   ______   _______  ______  ______ 
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______ 
____________   ______   ______   _______  ______  ______

C. Other objects of interest:

Grid #   (x,y)coordinates                Comments
______   ________________   _______________________________________
______   ________________   _______________________________________
______   ________________   _______________________________________
______   ________________   _______________________________________
______   ________________   _______________________________________

II. The distance to M100

A. The P-L relation

Calculate the absolute magnitudes for each Cepheid in Part I, Section B using the equation

    M_v = - [2.76 (log₁₀(P) - 1.0)] - 4.16,

where P is the period of the Cepheid in days from column 4. Enter your results in column 5.

B. The average distance modulus

Calculate the distance modulus (m_v-M_v) for each Cepheid in Part I, Section B and write your results in column 6.

Sum all the distance moduli and divide by the number of Cepheids to get the average distance modulus.

    Average distance modulus: m_v-M_v =  __________

C. The distance to M100

Calculate the distance to M100, using the average distance modulus in the equation

    d(pc) = 10^{[0.2 (m_v - M_v + 5 - A_v + 0.05) ]}

    d = __________ pc,      or      d = __________ Mpc.

III. Estimate the Hubble Constant

Write the value of v (from the lab pages) here:

    v = ________  km/sec

Copy the average distance to M100 from Section II, Part C here:

      
    d = __________ Mpc.

Now calculate the current Hubble constant:

    H_o = v/d =___________  km/sec/Mpc

How does this compare to the value of H_o that you learned in class or from your text?

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IV. Estimate the Age of the Universe

A. Assume the universe has been expanding at a constant rate

Use the value of H_o from Part III to calculate the age of the universe for the case when H_o represents the expansion of the universe for all time:

                     1   sec Mpc (3.09 x 10¹⁹ km)     (1 year)
  Age of universe = ---- ------- ----------------- ----------------
                     Ho    km         1 Mpc        (3.15 x 10⁷ sec)
 

  Age of universe = ________________ years.   (Constant expansion.)

Does your answer seem reasonable? How does this compare to the presumed ages of the oldest globular clusters?

B. Assume the expansion has been slowing over time

Calculate the age of the universe taking into account the slowing of the expansion with time, assuming

_o = 1.

                        2   
    Age of universe  = ----.     (_o = 1)
                       3 Ho 

    Age of universe = ________________ years.   (_o = 1)

How does this compare to the presumed ages of the oldest globular clusters?

What can you infer about the actual value of _o by comparing the two ages you have calculated? How does your evaluation of _o compare to what you learned in class?

V. Feedback

A. Science

Do you feel that this lab improved your understanding of how the extragalactic distance scale and the Hubble constant is determined? If so, how? If not, why?

B. General Comments/Suggestions

Please let us know what you liked and/or disliked about this lab. If you have suggestions for improving the lab, please include them. Your feedback is important!

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