ASTR 1040                                                                      Spring, 2005

ANSWERS - HOMEWORK NO. 5

ASTR 1040Spring, 2005

1. Here is a revised table of the galaxy data you were given, with calculated distances (from the distance modulus relation m - M = 5log(d/10), where M is always assumed to be -21.0), and with calculated recession velocities (in most cases requiring the use of the relativistic Doppler shift formula).

mV/Distance /Lambda/Velocity 

11.12/26.5 Mpc/3961.032/2087 km/sec 

13.32/73.1/4007.522/5633

10.70/21.9/3954.567/1594                

13.64 /84.7/4019.836/ 6572           

13.60/83.2/4023.457/6848                

12.79/57.3/ 3992.052/ 4453

13.40/75.9/4013.540/6092                  

8.60/8.3/3939.568/450

6.39/3.0/ 3936.418/210                

12.21/43.9/3983.942/3835

12.96/61.9/4004.984/5439                

13.82/92.0/4033.938/7647

13.20/69.2/4010.998/5898                

13.17/68.2/ 4005.251/5460

12.27/45.1/3979.163/3470                

10.55/20.4/3955.754/1685

11.94/38.7/3975.318/3177                  

9.19/10.9/ 3946.402/972

10.05/16.2/3951.800/1383                

13.82/92.0/ 4030.038/7350

13.25/70.8/ 4005.384/5470             

12.91/60.5/3997.113/4839

12.39/47.6 /3983.278/3784                

10.15/17.0/ 3949.429/1202

13.45/77.6/4018.496/6470                

11.83/36.8/3969.021/2697

11.64/33.7/3970.550/2813             

12.55/52.3/3993.383/4555

12.67/ 54.2/3987.264/4088                

13.49/79.1/ 4016.084/6286

When these values are plotted to show the correlation between recession speed and distance, you should get a slope around 80 km/sec/Mpc. You may have found different values, though you should be close to this (and note that this is NOT the currently accepted value! I made this stuff up!).

(a) Using a value of 80 km/sec/Mpc, from 1/Ho you should calculate an age of 3.8 X 10^17 sec = 1.2 X 10^10 = 12 billion years.  This is what the age would be for this value of Ho, IF the expansion rate had been constant over time.

(b) But it hasn't.  In the standard Einstein-De Sitter models, a correction factor for deceleration is applied, which is a factor of 2/3.  Multiplying the result above by 2/3 leads to an age of 8.1 billion years.

But that is not right either, because now we know that the expansion has been accelerating for the past few billion years.  A better adjustment factor is 0.9, which leads to a current age of the universe of 11 billion years.  This isn't right either, because the best value of Ho is 68 km/sec/Mpc instead of 80 km/sec/Mpc.

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