Hubble Law and the Age of the Universe

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History of the Universe Lab, Hubble Law and the Age of the Universe

Hubble’s Law Lab Activity

Table 1 – Data – Apparent Magnitude and Measured Wavelength of Calcium Lines

More to Read:
Velocity

(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.

Last Updated on January 29, 2025

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