Problem #1: Suppose a supernova goes off in Galaxy M245 and ejects a spherical shell of material into the surrounding interstellar medium.
a) Spectra of the ejected gas shell indicate that Hydrogen-alpha emission (rest wavelength = 656nm) is doppler-shifted to a wavelength of 652.4 nm. Calculate the expansion speed of the ejected shell.
b) Ten years after the supernova appears, radio astronomers measure the size of the ejected shell to be 78 micro-arcseconds in diameter (1 micro-arcsecond = 10-6 arcseconds). Assuming that the shell has been expanding at the same rate for ten years, calculate the distance to the supernova (and therefore, the galaxy it's in).
Problem #2:a)If astronomers measure the redshift of a galaxy which is receding at a speed equal to 90% of the speed of light, what redshift will they measure? (Remember to use the relativistic redshift formula!)
b) The Lyman-alpha spectral line from atomic hydrogen (i.e., the transition from the first excited state to the ground state) is noramlly found in the ultraviolet region of the spectrum, and has a rest wavelength of 121.6 nm. At what wavelength would you expect to measure emission from this transition for atoms in the galaxy receding at 90% of the speed of light?
Problem #3:a) What is the speed of a galaxy which has a measured redshift of 5.0?
b) How far away is this galaxy if we live in an open universe and Ho = 75 km/s/Mpc?