Answer to the Question 02/99
INTERSTELLAR TRAVELThe question was:
In 1960 Bussard proposed an interstellar vehicle that would collect its fuel from interstellar medium. A large scoop would pick up protons present in space, and the protons would be fed into a fusion reactor where part of their mass would be converted into kinetic energy. How big would the scoop have to be in order to produce a constant 1g acceleration for a 3500-ton vehicle?
(02/2000) The problem has been solved correctly by Lenny Eusebi, Physics student at Wesleyan University in Middletown, Connecticut (e-mail leusebi@mail.wesleyan.edu). A detailed discussion of the problem can be found in the article by R.W. Bussard, Astronautica Acta 6, 179 (1960). Short solution of the problem is presented below.
The answer: The radius of the scoop should be of order of 10,000 km.
The solution:
The acceleration a (=10 m/sec2) of a vehicle of mass M=3500 ton will be
a=nmc2Afk / M
where n is the density of protons in the interstellar space (=0.1 cm-3, or slightly above that value), m is the mass of the proton, c is the speed of light, A is the area of the scoop, f fraction of mass converted into energy (it can be estimated by comparing, say, binding energy of He or deuterium with its mass; this number is smaller than 0.01). k efficiency with which the fusion energy is converted into thrust. (Of order 1(?).) This equation is obtained by equating the required force Ma with energy which can be released by protons in space in a volume which is multiplication of the area of the scoop and unit length. From this expression we can extract the area (and, thus, the radius) of the scoop.
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