LABORATORY EXERCISE  NUMBER V.Aa. TITLE: HUBBLE’S LAW (part I)  DATE PRINT NAME/S AND INITIAL BELOW: GROUP
DAY
LOCATION

OBJECTIVE:
Be able to:
Graph data, visually fit the data with a line, graphically evaluate errors.
Determine the dispersion of spectroscopic data.
Determine redshifts; infer cosmic distances using Hubble’s law.
DESCRIPTON:
Because of the Big Bang, spacetime is expanding. As a result, distant galaxies are receding from us. They are not truly moving away from us—it is space itself which expands between the galaxies. This is the origin of Hubble’s Law:
v = H r Equation 1
Where: v is the recessional velocity (in km/s),
H = Hubble’s constant (in km/s per Mpc),
r = distance to the galaxy (in Megaparsecs).
Graphing the recessional velocities of galaxies, as a function of distance, allows us to observe this linear relationship, and to determine the value of Hubble’s constant.
Once Hubble’s constant is determined, it can be used to determine the distances to other galaxies, after their recessional velocities are measured. These velocities are determined by measuring their redshifts (i.e., shifts in wavelength) and converting them via the Doppler equation:
v = c (Δ/_{o}) Equation 2
Where: v is the recessional velocity (in km/s),
c = the speed of light (3×10^{5} km/s),
Δ = the change in wavelength (the redshift)
_{o }= the wavelength of light being studied, when not redshifted.
PART I
Construct a plot of galaxies, graphing distance versus recessional velocity. From this, Hubble’s constant will be determined.
PROCEDURE:

Table IA lists distance estimates to a variety of galaxies, their recessional velocities, and the methods the distance estimates were obtained^{1}. These galaxies were studied by astronomers engaged in a number of separate research programs, and so many have strangesounding catalog names. Plot these data on the graph supplied. Use the scale of 2500 km/s for each major vertical tick and 50 Mpc for each major horizontal tick. Make sure each scale starts at 0.

Using a ruler, estimate a best fit with a straight line.

Draw two more lines to estimate an upper and lower boundary for data, as demonstrated in class.

Read a value of v and r from each of your three lines, to calculate three estimates for Hubble’s constant—a best fit value, an upper value, and a lower value. Record your results in Table IB.

Using the discrepancy formula, calculate uncertainties in your estimate for Hubble’s constant. Record your results in Table IB.
TABLE IA: GALAXY DISTANCES AND VELOCITIES
Galaxy name/catalog listing

r (Mpc)

v (km/s)

Method
 
NGC 0048

IC 1601

UGC 00646

UGC 03576

MH92d 074119.0622406

P96 J003618.17+112334.7

MH92b 1006432624.0

LSBG F119024

UGC 05691

2dFGRS S839Z607

MH93a 103235.1341103

MH93a 103235.1341103

MH93a 1001253513.1

MH92n 033422.3183104

MH93 014355.4562057

61
120
80
108
165
142
182
237
275
271
262
342
217
340
387

1972
3642
5474
5994
10377
10719
12977
12998
15968
17665
19760
19760
20310
22670
25108

Sosies (Milky Way lookalikes)
Sosies (Milky Way lookalikes)
SNIa
SNIa
SNIa
SNIa
SNIa
SNIa
SNIa
SNIa
SNIa
SNIa
SNIa
SNIa
SNIa

TABLE IB: CALCULATING HUBBLE’S CONSTANT
Estimate

v
(km/s)

r
(Mpc)

H
(km/s per Mpc)

Uncertainty
(% difference from “best fit value”)

Low value





Best fit value





High value





0
Distance (Mpc)
00
QUESTIONS

A research program is studying an object called “EXO 0706.1+5913”, with v = 35150 km/s. What do you calculate for the distance for this object, using your best fit value of Hubble’s constant?

The research program, using a new method to determine the distance to EXO 0706.1+5913, concludes the distance is 531 Mpc. Assuming your value is correct, does this new method seem to provide accurate results? (Use the discrepancy formula to determine how far off the team’s distance is from your value.)

The distances to the first two galaxies in your list were determined using a method called “sosies.” Draw a new Hubble line on your graph, but in drawing this new line, fit only those two galaxies. What is the value of Hubble's constant that you would calculate using this method?

Suppose a research team using the sosies method was studying EXO 0706.1+5913. What would they calculate the distance to this galaxy to be? Is this in agreement with your method from question 1? (Use the discrepancy formula to determine how far off the sosies team's distance is from your value.)
