Hubble's Law Lab
Background
Before the 20th century, it was believed that the universe was static and consisted only of the Milky Way. This is to say that it was believed that the Milky Way Galaxy was the universe and the universe was the Milky Way Galaxy. Therefore, the words "galaxy" and "universe" were used interchangeably. It was also believed that no other galaxies existed outside our own.
Strange spiral nebulae had been observed in telescopes, but it had not been discovered if these were objects within the Milky Way or if they could possibly be outside of it. Astronomers debated this in the beginning of the 20th century, with the most famous exchange occurring in 1920 when two well-known astronomers, Harlow Shapley and Heber Curtis, engaged in what today is often referred to as the "Great Debate."
In 1912, Vesto Slipher, an American astronomer,observed the shift in the spectrum of galaxies. Thus, he was the first to observe the redshift of galaxies. Few other astronomers from different observatories understood the significance of this discovery.
Between 1922 and 1923, Edwin Hubble observed Cepheid variable stars in many of the known spiral nebulae and found that they could not be objects within the Milky Way as they were too far away. It was thus understood that they were other galaxies, and became known as "island universes." He published his results in 1924 and 1925.
Then in 1927, Georges Lemaître, a Belgian Catholic priest, astronomer, and professor, published a paper describing mathematically a universe that was expanding. "In that paper, he showed that the data collected by Hubble and two other astronomers up to that time was enough to derive a linear velocity-distance relation between the galaxies, and that this supported a model of an expanding universe based on Einstein's equations for General Relativity." [https://en.wikipedia.org/wiki/Edwin_Hubble] Unfortunately, the journal he published his article in was one read by few astronomers outside of Belgium. In the same year, he also proposed what today is called the Big Bang Theory.
Hubble applied Henrietta Swan Leavitt's period-luminosity relationship for Cepheids to determine the distances to the spiral nebulae, and combined his data with redshift data from Slipher and Milton L. Humason. From this larger data set of 46 galaxies, he noticed a linear relationship between the distance to the objects and their redshifts. This came to be known as "Hubble's Law." It supported the Big Bang theory.
Hubble's Law Lab Data Sheets
I. Scale factor
1. Measure to the nearest millimeter the distance from the "a" line to the "g" line: ___________ mm
2. 5015.7 Å - 3888.7 Å = _________________ Å
3. #2 / #1 = ___________________ Å/mm (this is your scale factor for part II below ONLY)
II. Velocity Determinations
Fill-in the data table below
|
Galaxy
|
Distance on spectrum in mm (s)
|
λ = λa + (#3)(s)
(Å)
|
R = λ - λrest
(Å)
|
V = (R×c)/ λrest
in km/s
|
Average
V in km/s
|
|
in
|
K
|
H
|
K
|
H
|
K
|
H
|
K
|
H
|
K & H
|
|
Virgo
|
|
|
|
|
|
|
|
|
|
|
Ursa Major
|
|
|
|
|
|
|
|
|
|
|
Corona Borealis
|
|
|
|
|
|
|
|
|
|
|
Bootes
|
|
|
|
|
|
|
|
|
|
|
Hydra
|
|
|
|
|
|
|
|
|
|
III. Distance Determinations
4. Measure the line under the Hydra galaxy on the first page in millimeters: ___________________ mm
5. 150" / #4 = ____________________."/mm (arc seconds per millimeter) (this is your scale factor for part III data table below ONLY)
Fill-in the data table below
|
Galaxy in
|
Diameter on image
in mm
|
Diameter in arc seconds
|
Diameter in radians (d)
|
Distance in Mpc
D = 0.02/d
|
|
Virgo
|
|
|
|
|
|
Ursa Major
|
|
|
|
|
|
Corona Borealis
|
|
|
|
|
|
Bootes
|
|
|
|
|
|
Hydra
|
|
|
|
|
IV. Final Results
Fill-in the data table below using the last two columns of the above data tables
|
Galaxy in
|
Virgo
|
Ursa Major
|
Corona Borealis
|
Bootes
|
Hydra
|
|
Distance in Mpc (x)
|
|
|
|
|
|
|
Average
V in km/s (y)
|
|
|
|
|
|
Plot the above data table on page 2. Remember to (1) label your axes, (2) show grid lines, (3) plot the points, (4) insert a linear trendline that has an intercept set to the origin, and (5) display the equation on the graph. After plotting the points on the graph above, known as your Hubble diagram, copy-paste it into the graph placeholder above on page 3.
6. What is your Hubble constant? This is the slope of your best-fit line. Hint: the number in front of the "x" variable
7. How does your Hubble constant compare to the currently accepted value of 72 (km/s) / Mpc?
V. Age and size of the universe
8. Estimate the radius of the observable universe using c = H × D, where c = 3 × 105 km/s and H = your Hubble constant
9. Convert this from Mpc (megaparsecs) to light years by multiplying by 3.3 × 106.
10. Divide your Hubble constant by 1 × 1012 to convert it from (km/s) / Mpc to (km/yr) / km. Then take the inverse (1/H). This is your age of the universe.
11. How does this age compare with:
(a) the known age of the Earth? (~ 4.3 billion years)
(b) the known age off the Sun? (~ 4.5 billion years)
(c) the oldest stars? (~13 billion years)
Attachment:- law-lab.rar