Another commonly calculated velocity in galactic dynamics is the escape velocity Vesc, that is the minimum velocity a star must have in order to escape the gravitational field of the galaxy. (a) Starting from the work required to move a body over a distance dr against f show that the escape velocity from a point mass galaxy is vesc = 2GM/r where r is your initial distance. (b) Since we know galaxies aren't actually point-masses, also show that vese from r for a galaxy with a p(r) x r2 density profile is vesc = 2v²(1 + ln(R/r)). Here you must assume that R is a cutoff radius at which the mass density is zero. (c) The largest velocity measured for any star in the solar neighbourhood at r-8 knc

Another commonly calculated velocity in galactic dynamics is the escape velocity Vesc, that is the minimum velocity a star must have in order to escape the gravitational field of the galaxy. (a) Starting from the work required to move a body over a distance dr against f show that the escape velocity from a point mass galaxy is vesc = 2GM/r where r is your initial distance. (b) Since we know galaxies aren't actually point-masses, also show that vese from r for a galaxy with a p(r) x r2 density profile is vesc = 2v²(1 + ln(R/r)). Here you must assume that R is a cutoff radius at which the mass density is zero. (c) The largest velocity measured for any star in the solar neighbourhood at r-8 knc