The first two of these Interstellar posting explained how immense the distances involved are, and as a consequence how fast one would have to travel to get to even the nearest star system in a reasonable length of time, and finally how dangerous even a tiny dust particle could be at those high speeds. But another consequence is the immense amount of energy required to get even our little miniaturized spacecraft up to those speeds, and double that to slow it down again at the other end, unless we are satisfied to just flash through the system in a fraction of a second.
Lots of propulsion methods have been proposed for our little interstellar probe, from ion engines to light sails to laser “pushes” from the earth. All are constrained by the same basic physics equation for kinetic energy. Since we are travelling at an appreciable fraction of the speed of light, this time we will use the relativistic equation for kinetic energy, which is given as K.E. = ( γ - 1) m c2, where γ (gamma) is a function of the speed that accounts for the increasing mass as we approach the speed of light (though at 10% the speed of light, the mass increase is very small still, so we could have used the Newtonian equation and gotten pretty close to the same answer).
We already know we have to be going a reasonable fraction of the speed of light in order to complete the trip in a reasonable time, say a century or less. So let’s assume our target average speed is 10% the speed of light. For simplicity (just to get ball-park figures), let’s ignore the acceleration and deceleration phases and assume instead a steady 10% speed the whole way.
Now the mass of the probe matters, so how heavy a probe shall we assume? We already know from the previous post that it has to carry a substantial shield in front of it. And of course it has to carry instruments (else why send it), communications equipment powerful enough to report back to earth (else why send it), a propulsion system and fuel (for most proposed forms of propulsion), and an energy source to power everything. So let’s assume a miracle of miniaturization, still well beyond us technically, gets us a 100 kg (220 pound) interstellar probe.
So how much energy does it take to accelerate a 100 kg object from a standing start (in our earth-oriented frame of reference) to 10% the speed of light? From the equation above, it turns out to take 4.5278 x 1016 Joules of energy to accelerate it to that speed, and as much again to slow it down at the other end.
Again, let’s put that into perspective for those who don’t normally think in terms of Joules. 4.5278 x 1016 Joules is about 4.5 times the estimated impact energy that created the Arizona Meteor Crater, or roughly 1000 times the amount of energy released by the Hiroshima atomic bomb. It’s a LOT of energy!
And of course realistically a probe is likely to have to weigh a lot more than our wildly optimistic assumption of 100kg, once we have added the shield, a large enough communication system to send data back from 4.4 light years away, a propulsion system, a long-term energy source, etc, etc. So the energy to accelerate it to cruising speed will likely be immense, several orders of magnitude greater. That is our third problem.
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