## Traveling At Relativistic Speeds

Conceptual planning of long QI or interstellar precursor missions must eventually include relativistic effects. In Chapter 7 exploration of the Solar System was proposed using constant acceleration (a) for a sizeable portion of the trip. One may think this strategy could work also for interstellar missions. Consider, for instance, a trip to Proxima Centauri at constant 1 ''g'' acceleration (a = 1g = 9.807 m/s2) until half-way, Sj/2, followed by deceleration with a = —1g till final destination, Newtonian mechanics predicts a trip time

Here S1=2 is the half distance from Earth to Proxima Centauri, or about 2 light-years (a 1 "g"-trip is often proposed because this acceleration results in spacecraft living conditions equal to those due to Earth's gravity). Mid-course speed, Vj/2, is then:

and in this example its actual value is 6.3 x 108m/s, or 2.1 times the speed of light! According to the Theory of Special Relativity, this is impossible, and so is the acceleration a = 1g chosen for this trip. Beyond the issue of the power needed to keep accelerating for long times, this example shows there are also issues associated to the type of physics and math needed when spacecraft speed starts approaching the speed of light. Relativistic speeds need a completely different suite of physical and mathematical tools. Newtonian mechanics is insufficient to calculate or plan, even conceptually, trips over such distances when the spacecraft speed starts approaching the speed of light.

Note also that in the 1916 version of the Theory of Special Relativity [Einstein, 1916] mass ''at rest'', mo (that is, when its velocity V = 0) is different from the same mass, m, in motion:

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