David Shaw wrote:
> I am currently reading John Ringo's 'Gust Front' in which a ground based
> anti-starship weapon is described as firing bars of depleted uranium,
> 100mm in diameter and two metres long at a muzzle velocity of 0.3c.
volume bar: pi x (0.05)^2 x 2 = 0.0157 cubic metres
density uranium: 19.1 tonnes/cubic metre
mass bar: 300kg
relativistic kinetic energy: (m x c^2 x gamma) - (m x c^2), where
gamma (aka Lorentz factor) = 1/sqrt(1-(v^2/c^2))
at 0.3c, gamma equals 1.048 so the kinetic energy is equal to 4.8% of the rest mass:
0.048 x 300 x c^2, or 1.296 x 10^18J using c = 3 x 10^8 m/s - 1.296 exajoules.
Your maths are fine.
As Craig Berry pointed out you can use Newtonian mechanics with minimal loss of accuracy out to almost 0.5c (gamma 1.155)
This is a nonsensical weapon in an atmosphere - unless it's a glorified land mine.
How is the bar meant to be accelerated up to muzzle velocity?
Rob O'Connor