1. The problem statement, all variables and given/known data The Andromeda galaxy is at a distance of 2.1 X 1022 m from our Galaxy. The mass of Andromeda is 6 X 1041 kg and the mass of our Galaxy is 4 X 1041 kg. (a) Gravity accelerates the galaxies toward each other. As reckoned in an inertial reference frame, what is the acceleration of Andromeda? What is the acceleration of our Galaxy? Treat both galaxies as point particles. (b) The speed of Andromeda relative to our Galaxy is 266 km/s. What is the speed of Andromeda and what is the speed of our Galaxy relative to the center of mass of the two galaxies? (c)What is the kinetic energy of each galaxy relative to the center of mass? What is the total energy (kinetic and potential) of the system of the two galaxies? Will the two galaxies eventually escape from each other? 2. Relevant equations G=6.67X10-11 T2= 4* PI2/GMGalaxy 3. The attempt at a solution I've been stumped on this question for a while now. Usually, I try and come back to it the next day (in this case the past few days) and try anew, but it didn't work.\ a.) I got the answers for this part pretty easily. I used F= GMm/r2 and solved for F, and then acceleration. I got 9.07X10-14 m/s2 for the Milky Way, and 6.05X10-14 m/s2 for Andromeda. b.) Here is where I the trouble starts..... I first came up with the center of mass of 1.26X1022 meters and 8.4X1021 meters, with the larger one being the distance between the Milky Way and the center of mass (since Andromeda has more mass, the center of mass is closer to it). From there, I've tried using v2=GMCOM/r and KE/PE for the system, but I haven't come up with the book answers of 1.1X105 m/s (speed of Andromeda) and 1.6X105 m/s (speed of the Milky Way). c.) I've tried to do this part, using the answers from part b. I managed to sum up the KE somewhat correctly, but I failed to sum the total energy correctly. Is there only one gravitational potential energy calculation, or two (one for each radius from the center of mass)? KEAndromeda= 1/2mv2 = 1/2 * 6X1041 * (1.1X105)2 = 3.63 X 10 51 J ---> Answer in back= 3.4X1051 J KEMilky Way= 1/2mv2 = 1/2 * 4X1041 * (1.6X105)2 = 5.1X1051 ---> Answer in back = 5.1X1051 J For the summation I have: 3.6X1051 + 5.1X1051 - (6.67X10-11*6X1041*4X1041) / 1.26X1022 - (6.67X10-11*6X1041*4X1041) / 8.4X1021 Total Energy = 8.75X1051 - 1.27 X 1051 - 1.9057X1051 = 5.574X1051 ---> Answer in back = 7.7X1051 The book I have is Ohanian Physics 2nd edition which doesn't have many examples that deal with this type of problem. Any help would be greatly appreciated. Thanks.