## Times and distance

With this "distance" caveat in mind, 1 light year will be a yardstick for stellar space trips. Moving final destination from Solar System planets to nearby stars, or even to the Oort Cloud, crossing times become huge traveling at constant speed. In the hypothetical trip to Neptune at 1 ''g'' acceleration, used as an example in Chapter 7, the top speed reached near Neptune was 6,700 km/s. Assume the engine turned off there: coasting to Proxima Centauri at the same speed would take 188 years. Such an engine would have to produce sufficient thrust to keep constant 1 ''g'' acceleration for 74 days, consuming a propellant mass that depends exponentially on Isp. Using the Tsiolkovski's rocket equation, the propellant mass consumed, Mppl, assuming an Isp = 1000 s typical of a nuclear thermal rocket, would be a truly astronomical number:

Mppl = exp( — ) = exp(683.2) = 5.131 x 10296 (8.3)

Unless the Isp of the propulsion system can be drastically raised (say, from the 103 s typical of nuclear thermal or current ion electric propulsion), the initial mass of the ship would be completely dominated by propellant mass, and the thrust to ensure 1 ''g'' acceleration would, accordingly, be just as immense. Thus, mass-frugal means to power such acceleration must be found. Alternatively, any such propulsion system must have a much higher Isp than discussed so far. Stellar or quasi-interstellar missions using Newton's Third Law are doubly constrained: at constant speed, they take too long; at constant acceleration, they need large thrust and propellant mass. They may become feasible only for Isp much larger than those seen in Chapter 7.

Bypassing the second constraint is possible, in principle, by collecting mass to utilize for propulsion while traveling, just as the airbreathing engines in Chapter 4 do in the Earth atmosphere. Interstellar space is not a mathematical void: in the disc of our Galaxy the mass density, pH, of interstellar hydrogen is of order 10~27 kg/m3 [Sciama, 1971, p. 25] (since a hydrogen atom weighs about 1.67 x 10~27kg, this density corresponds to about one hydrogen atom per cubic meter). At ''sufficient speed'', this density can be exploited, i.e., atoms can be captured by an appropriately designed inlet. This strategy leads to the concept of ''interstellar ramjet'' [Bussard, 1960; Cassenti and Coreano, 2004]. For instance, the hydrogen collected could be fused to provide power and thrust. The power, P, collected is a function of speed, V, and inlet area, A, since pH AV is the mass of H atoms collected while flying:

where a is the fraction of H captured actually fused, of order 3 to 4 x 10 ~3 (see Figure 8.3). Hence the minimum inlet area to ensure a given P, for instance 1 GW, is

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