Question

The table below contains distance and recessional velocity data for ten galaxies.

Galaxy	Distance (Mpc)	Observed Velocity (km/s)
1	42.0	2546.0
2	92.3	5964.9
3	92.7	5490.1
4	92.9	6652.7
5	93.1	5115.3
6	150.0	9800.0
7	320.0	20260.0
8	450.0	28150.0
9	553.0	34889.0
10	642.0	40536.0

1. a) Plot the ‘Hubble Diagram’ for these galaxies. This is simply a plot of the observed velocity on the y-axis and the distance on the x-axis.

2. b) Fit a line to the data that goes through the origin of the plot (that is, where the dis- tanceandvelocityarebothzero). TheslopeofthislineistheHubbleconstant.What is the Hubble constant for these data? NOTE: The value is not the same as the Hubble constant we are adopting in the text.

3. c) Calculate the redshift, ? = ∆?/?& for each galaxy. HINT: Go back to the definition of the Doppler effect in Destination 6 to recall what = ∆?/?& is equal to (or just look at question 1c above). You will see that have the information you need in the table above to calculate the redshift (though, strictly speaking, only for redshifts that are significantly smaller than 1.0).

4. d) Notice that galaxies 2-5 in the table are all at about the same distance, but their ve- locities differ rather significantly. Explain what is likely happening to account for this behavior.

Answer 1

a) The Hubble Diagram is as below,

b)The Hubble constant is determined from the slope, here it is,

c)The redshift is related to the Hubble's constant as,

D is the distance to the galaxies, v is the observed velocity

Then the redshfts for each galaxy is given by,

d)The abrupt change is velocity lead to one of the most profound predictions in modern astronomy ie the existence of the Dark matter, ie, gravitationally massive matter that cannot be detected with any contemporary equipments.