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During the early twentieth century, astronomers discovered that galaxies are rushing away from us at huge speeds. The Sombrero galaxy, for instance, was found to be moving away from the Earth at about 1000 km/s. These speeds can be found very accurately from the doppler red shift of spectral lines.

Hubble concluded that the speed of a galaxy is proportional to its distance – that is, that if one galaxy is three times further from us than another, then it will be moving away at a speed which is three times greater than the other. This result was a huge step forward for astronomers. It implied that in the beginning, the Universe was very much more dense than it is now, and that since the Big Bang all the matter in the Universe has been flying apart. http://www.aps.org/ publications/apsnews/200801/physicshistory.cfm

Using a subset of Edwin Hubble’s original data from the 1920’s, you will plot a graph by hand of velocity against distance and draw a straight line (by eye) to the points which “best fits” the data. Should the line should go through the origin? The slope of the line represents velocity/distance, and is known as the Hubble constant Ho. Use your value of Ho to deduce the age of the Universe.

As you prepare this assignment for submission. NOTE:

Marks will be deduced for incomplete and poorly presented work. Steps in the calculations need to be described or explained as required, terms in the equations defined. The graph (by hand) needs to be properly titled and axes labeled, i.e., “V versus D” is not a title, a title should be at least a complete sentence which describes what is being shown.

An estimate for the age of the Universe, 1/Ho is being derived by a “best fit line” through a set of data points. Ho is the Hubble Constant in Hubbles, Law: V = Ho*D.

V is the recessional velocity and D is the distance to far away galaxies. Note that nearby galaxies, our local group, are not necessarily moving away from us but are in mutual gravitation orbits.

Also keep in mind, that the data being plotted is from the 1920’s — Hubble’s original data. The age estimate derived has been vastly refined over the decades through more data, but primarily from a better understanding of stellar properties and assumptions made in distance estimates — Hubble’s distance estimates were flawed resulting in considerable activity in the scientific community — both Astronomy and Earth Science.

. Show your work, the answer alone is not sufficient!

1. (8 marks) Plot the data by hand (or with EXCEL if you Know how to make a graph) on a full page using sensible axes ticks. By convention, Hubble data is plotted with V on the vertical axis, and D on the horizontal. Draw a straight line, by eye that best fits the points. The slope of this line will lead to the age of the Universe. The line can go through (0,0). Excel can do this for you and return the value of the slope.

A subset of Edwin Hubble’s original data from 1929

i. title and caption: descriptive (2) ii. axes labes: ticks marks, use of page (2) iii. points: accurately plotted (2) iv. line of “best fit”, (2)

2. (7 marks) Estimate the age of Universe from the slope of the best fit line. On a two dimensional plot, a straight line means the vertical change is proportional to the horizontal change. Rise/Run is assumed to be consistent through the whole set of data.
Ho =(the change in velocity)/(change in distance) as determined by the line of best fit!

a. Calculate the slope of your best fit line. Ho = Rise/Run (3)

b. Convert Mpc to kilometers giving 1/Ho in seconds, (2) c. Then convert seconds to years. (2)

3. (3 marks) Uncertainty! Determine a reasonable estimate for the error in your value. There are mathematical means to do this, or you can use maximum and minimum slopes on the graph — “draw these by eye”. Convert the error in the slope to a relative error, then

ΔΗoΗ =ΔTT o

4. (2 mark) Summarize your work with a statement of your result. Round off your final values. The error should only have one, at most two significant digits, for instance if you find a value of 15%, leave it as such.)

Mpc is a distance measure of astronomical dimension: it needs to be converted to kilometers, information to do this is in the lecture slides.
1 Mpc = 3.26 Mly. “M” is an S.I. symbol for 106

ly is the distance light travels in one year: distance = speed * time Speed of all EM radiation: c= 3.00 * 105 km/s in free space.

Marks will be deducted for sloppy or incoherent presentation.