Escape from Proxima b

By Abraham Loeb

Almost all space missions launched so far by our civilization have been based on chemical propulsion. The fundamental limitation here is easy to understand: a rocket is pushed forward by ejecting burnt fuel gases backwards through its exhaust. The characteristic composition and temperature of the burnt fuel set the exhaust speed to a typical value of a few kilometers per second. Momentum conservation implies that the terminal speed of the rocket is given by this exhaust speed times the natural logarithm of the ratio between the initial and final mass of the rocket.

To exceed the exhaust speed by some large factor requires an initial fuel mass that exceeds the final payload mass by the exponential of this factor. Since the required fuel mass grows exponentially with terminal speed, it is not practical for chemical rockets to exceed a terminal speed that is more than an order of magnitude larger than the exhaust speed, namely a few tens of kilometers per second. Indeed, this has been the speed limit of all spacecraft launched so far by NASA or other space agencies.

By a fortunate coincidence, the escape speed from the surface of the Earth, 11 kilometers per second, and the escape speed from the location of the Earth around the sun, 42 kilometers per second, are close to the speed limit attainable by chemical propulsion. This miracle allowed our civilization to design missions, such as Voyager 1 and 2 or New Horizons, that could escape from the solar system into interstellar space. But is this fortune shared by other civilizations on habitable planets outside the solar system?

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