Day 8.13Dark Matter(6.2)1) Astronomers have analyzed the stars in the galaxy UGC 11748. They found that most of the stars lie within a radius r = 1.64 x 1020m and that the total mass within this radius is 1.54 x 1041kg. a)At what speed are the stars at the outer radius moving? GMm/r2= mv2/rv = sqrt(GM/r) = 2.58 x 105m/sb)There are a few stars that lie further out. They should be moving A) fasterB) slowerC) about the same speed D) not enough informationv = sqrt(GM/r) means that a greater orbital radius will result in a slower speed.c)What speed would you expect for a star at a radius of 6.48 x 1020m?The simplest way is to take 2.58 x 105m/s and multiply by sqrt (1.54/6.48) = 1.26 x 105m/s d)The speed turns out to be 2.47 x 105m/s. This means that either the equations are wrong or that thereis a lot of mass that was not seen. How much mass was missed? What percentage is ‘invisible’? GMm/ r2= mv2/rM = v2r/G = 5.93 x 1041kg.(5.93-1.54)100 /5.93 = 74%Watch the video: The Mystery of Dark Matter.