I haven't seen the twin problem configured this way before. But it seems to me it should lay to rest the argument that SR can't account for the age difference. Instead of going from the earth to the star and back, the traveler goes from the earth in a big circle around the star and back. The star is the center of the circle and the earth is a point on the circle. The traveler then experiences a continuous acceleration throughout his trip. If the star is 100LY from earth and the traveler's speed is .99c then his acceleration (v^2/r) works out to about 8m/sec/sec. That's less than the 9.8m/sec/sec that his twin experiences staying on the earth! So, when he returns (2pi*100 years later), if he has aged any less than his twin, it can't be because of acceleration. Now all you have to do is a relativistic doppler calculation for an object moving in a big circle. I haven't done it, but it shouldn't be hard. The distance between the twins is r*sin(theta/2) where theta is the angle at the star. So their relative speed is just 1/2*r*cos(theta/2), or about 50*cos(t/200), where t is in years. The total number of ticks on the traveler's clock should be an integral of his tick rate doppler adjusted for this speed.