History of the Universe Lab, Hubble Law and the Age of the Universe
Table 1 – Data – Apparent Magnitude and Measured Wavelength of Calcium Lines
(Modified for remote class April 2020, LPP)
Galaxy ID 
Apparent
Magnitude (m) 
λ Measured
Calcium K line (Å) 
λ Measured
Calcium H line (Å) 
36747  15.60  4130.0  4165.0 
NGC 4889  12.50  4018.3  4055.0 
NGC 7499  14.10  4088.9  4123.3 
54875  16.90  4246.7  4283.3 
51976  17.90  4445.0  4485.0 
Table 2 – Calculated Velocity and Distance
Galaxy ID 
Distance
(Mly) 
Velocity from K line (km/s) 
Velocity from H
Line (km/s) 
Average V
(km/s) 
36747  818  14,912  14,854  14, 833 
NGC 4889  
NGC 7499  
54875  
51976 
(Show one calculation of velocity on next page)
History of the Universe Lab, Hubble Law and the Age of the Universe
Table 3 – Present Hubble Parameter ( H0 ) and Age of the Universe
Age of the Universe
(calculated) 

Hubble Parameter
(calculated) 
Calculations (show one calculation of velocity, and calculations for Table 3)
History of the Universe Lab, Hubble Law and the Age of the Universe
Calculations
Velocity: Use the Doppler Equation to calculate the velocity of each galaxy due to the expansion of the universe.
For each galaxy calculate the velocity from each of the H and K lines and take the average for a more accurate answer.
Δλ/λ = v/c so v = c (Δλ/λ)
where Δλ = Measured λ – Lab λ and c = 300,000 km/sec.
Lab Wavelengths: K line is at 3933.7 Å; H is at 3968.5 Å.
Distance: Use the following table to get the distance to the galaxies. This comes from comparing the apparent magnitude to the assumed absolute magnitude of 21.4. This calculation involves logarithms which you will probably never see again and is omitted for the remote lab.
Apparent Magnitude (m)  Distance (Mly) 
15.60  818 
12.50  196 
14.10  411 
16.90  1,490 
17.90  2,360 
Calculating the Hubble Parameter and age of the universe:
By definition, H0 ((km/s)/Mly) = v (km/s)/d (Mly); My calculations give answers between 16 and 33 km/s per Mly so don’t let that bother you. (The accepted value is about 22.2)
Calculate H0 for each galaxy using the average velocity from the H and K lines and then average your answers to get a better answer.
The age of the universe is just 1/H (ignoring changes in H over time)
But to do the calculation you must get the units consistent. Change Mly to Km to get the age in seconds and then convert that to a more reasonable unit (like Billions of years!)
See next sheet or your text.
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