Sierra college observational astronomy




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SIERRA COLLEGE OBSERVATIONAL ASTRONOMY

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 (3×105 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:

  1. Table IA lists distance estimates to a variety of galaxies, their recessional velocities, and the methods the distance estimates were obtained1. These galaxies were studied by astronomers engaged in a number of separate research programs, and so many have strange-sounding 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.

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

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

  4. 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.

  5. 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

  1. NGC 0048

  2. IC 1601

  3. UGC 00646

  4. UGC 03576

  5. MH92d 074119.0-622406

  6. P96 J003618.17+112334.7

  7. MH92b 100643-2624.0

  8. LSBG F119-024

  9. UGC 05691

  10. 2dFGRS S839Z607

  11. MH93a 103235.1-341103

  12. MH93a 103235.1-341103

  13. MH93a 100125-3513.1

  14. MH92n 033422.3-183104

  15. MH93 014355.4-562057

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 look-alikes)

Sosies (Milky Way look-alikes)

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

  1. 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?


  1. 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.)



  1. 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?



  1. 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.)


1 Data from NASA/IPAC catalog, http://nedwww.ipac.caltech.edu/level5/NED1D/


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