For example, Galaxy NGC 3689 has the right ascension of 11:28:11 and declination of +25:39:40.0. Using these values, how can we find the distance to the galaxy? If it helps, its radial velocity is 2727 km/s.
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3$\begingroup$ It is not possible to do this with only RA and DEC, even if you have radial velocity. You would need the redshift, RA, and DEC to do this. $\endgroup$– WarpPrimeMar 20, 2021 at 16:16
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$\begingroup$ Given the redshift is 0.009136, how can we calculate the distance to the galaxy? $\endgroup$– andiMar 20, 2021 at 16:39
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You can't use the RA and dec. These tell you the direction that the galaxy is in, relative to the stars. It is possible and normal for two galaxies to have the same (or very similar) RA and dec and be at completely different distance.
You can estimate the distance using the Hubble law $v= H_0 d$, if $v$ is measured in km/s and d is in mega-parsecs the value of H_0 is approximately 70 (measuring this value accurately is a major problem in cosmology)
So $D= 2727/70 \approx 39$ So we estimate the distance to the galaxy to be 39 million parsecs (multiply by 3.26 to convert to millions of lightyears). This can only be an estimate, as the actual value of $H_0$ is not know with certainty, and the galaxy can have particular motion relative to the Hubble flow (for example, Andromeda is actually blue shifted, but it isn't a negative distance from us, as this value would suggest!)
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$\begingroup$ So if the redshift was 0.009136, how can we use those values to calculate the distance to the galaxy?? Because I read in another answer that we can use RA, dec, and redshift to measure the distance to a galaxy. $\endgroup$– andiMar 21, 2021 at 13:58
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$\begingroup$ You can convert redshift to resession velocity (v = cz is a good approximation for small values of z where relativity isn't needed.) and convert to distance by D = v/70. This gives an estimate for the distance . You don't use RA and dec at all. These give direction not distance $\endgroup$– James KMar 21, 2021 at 16:07
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1$\begingroup$ For example, if I say "London is due north" Can you tell me how far away it is? No! But if I also say "It takes me an hour to drive there" Now you can estimate the distance of London from me. Because you have a model of how fast cars travel. Similarly we have a model of how fast galaxies move away from us at different distances, so if we can measure this (using redshift) we can estimate their distance. $\endgroup$– James KMar 21, 2021 at 16:10