How Long to Observe a Galaxy's Redshift Change in a Flat Matter-Only Universe?

[matpo39]

I just finished a problem from ryden's intro to cosmology, but I am not sure the answer makes sense here is the problem and my work:

suppose you are in a flat, matter-only universe that has a Hubble constant H0=70 km/s Mpc. you abserve a galaxy with z=1. how long will you have to keep observing the galaxy to see its redshift change by one part in 10^6?

The equation to use is :

dz/dt0 = H0(1+z) - H0(1+z)^[3(1+w)/2]

we know:
H0=70km/s Mpc
z=1
w=0
dz=1/10^6
plugging into the equation we get dt=-7.28E-13 s*Mpc/km
multiplying (-7.28E-13 s*Mpc/km) * ( 3.1E19 km/Mpc) = -22.6E6 s.

this seems a bit large and is negative.
does this seem right?

thanks

 

[Jhero]

Thank you for sharing your problem and your work with us. I can understand your confusion about the answer and I would be happy to help clarify things for you.

First of all, your calculation is correct. The negative sign just indicates that the time is decreasing, which makes sense since we are looking for the time it takes for the redshift to change by 1 part in 10^6. This means that as time passes, the redshift is decreasing.

However, the value does seem large because we are dealing with a very small change in redshift. To put it into perspective, let's convert the time into years. -22.6E6 s is approximately -0.72 years. So, you would have to observe the galaxy for about 8.6 months to see a change in redshift by 1 part in 10^6.

I hope this helps clarify things for you. Keep up the good work in your studies of cosmology!