From Clive K. Semmens
Elon Musk says that “with a nuclear thermal rocket, you could definitely reach a tenth of the speed of light” (1 December, p 27). Nonsense.
The speed of light is 300,000 kilometres per second. The most heat-resistant material known (for the combustion chamber of such an engine) has a melting temperature of about 4300 kelvin. The mean velocity of hydrogen ions at about 4300 K is about 10 km/s – so that’s the highest possible exhaust velocity for a thermal rocket, whatever its energy source.
This implies that the initial mass of a thermal rocket must be at least 2(v/10) where v is the final velocity in km/s. This is an inescapable lower bound, and in practice it would be much higher. To reach one-tenth of the speed of light (30,000 km/s), the initial mass of a thermal rocket is therefore at least 23000 times its final mass, or 10900 if you prefer. You could do a lot better, in theory, with a rocket with an ion drive, with its much higher exhaust velocity – but one-tenth of the speed of light would still be cloud cuckoo land.
Ely, Cambridgeshire, UK
