So, I am having trouble understanding how time dilation and length contraction in special relativity merge together and describe space-time. I guess the best way to ask this question is to pose a question, which i know how to answer mathematically, but I would like to discuss some thoughts about it. Question: Jack boards a spaceship and travels away from Earth at a constant velocity 0.45c toward Betelgeuse. One year later on Earths clocks, Jack's twin, Jim, boards a second spaceship and follows him at a constant velocity of 0.95c in the same direction. Would the people on earth measure the spaceship to be in the same position as the people in the spaceship or would both of the observers measure the spaceship to be at different locations? From my current knowledge I would think that the earth observers would view the spaceship to be closer than it actually appears because of the time it takes for light to travel back. Is this correct? I asked my physics professor and he said that I have to factor in Lorenz contraction at the same time and he said both observers would see the spaceship at the same position, which I found to be extremely confusing. Which would be the case. Can anyone explain how to understand time dilation and length contraction together in and mathematical or even intuitive sense? Thanks ahead of time.