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.