Interstellar Travel

Chapter 9, another chapter unique to this book, applies four-momentum conservation of Chapter 8 to rocket propulsion. The motion of fuel-carrying spacecraft is analyzed for massive as well as photon exhaust cases and their impracticality demonstrated. The alternative ground-based laser propulsion is covered in lengthy detail in light of the recent interest in such projects. The peculiarity of one-dimensional photon collisions is investigated and it is shown that both energy and momentum conservation are needed to come up with an equation that holds in all reference frames, unlike the equations in the existing literature. A manifestly relativistic differential equation of one-dimensional motion involving photons is derived and applied to the motion of a spacecraft equipped with a light sail from which laser photons can reflect. The position of the spacecraft as a function of speed is derived. The explicit time dependence of velocity is presented for the beginning of the voyage. It is shown that the craft has a terminal velocity determined by the characteristics of the ground-based lasers and the light sail. Nonrelativistic limits are obtained and shown to agree with those in the literature.