equations

Journeys to the stars, however, will be much more difficult. The key to tomorrow’s space propulsion systems will be hydrogen fusion and, later, matter-antimatter annihilation. The fusion of hydrogen into helium provides energy E = 0.008 mc2 . This may not seem like much energy, but when today’s technological hurdles are overcome, fusion reactors will produce far more energy in a manner far safer than today’s fission reactors. Matter-antimatter annihilation, on the other hand, completely converts mass into energy in the amount given by Einstein’s famous equation E = mc2 . You cannot get any more energy than this out of any conceivable power, or propulsion, system. Of course, no system is perfect, so there will be some losses that will reduce the efficiency of even the best fusion or matter-antimatter propulsion systems by a few percent. How long would it take to travel from Earth to the Moon or any of the planets in our solar system under constant 1g acceleration for the first half of the journey and constant 1g deceleration during the second half of the journey?

Using the equations you can calculate this easily. Keep in mind that under a constant 1g acceleration, your velocity quickly becomes so great that you can assume a straight-line trajectory from point a to point b anywhere in our solar system.

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