The crossover point, t, in hours is found by equating the nuclear power plant mass and that of the fuel cell with its associated fuel. The equation is
1000 = 50 + 25 + ½t t = 1850 hours = 77 days
E = ½ mv² = (10⁶(0.9 × 3 × 10⁸)²)/2 = 3.6 × 10²² joules
The ship will use the same amount of energy to decelerate at its destination. Note that this calculation assumes a perfect efficiency in converting the energy of matter annihilation into the kinetic energy of the space ship. The mass consumed is
m = E/c² = (3.6 × 10²²)/(9 × 10¹⁶) = 4.0 × 10⁵ kg
almost half the spaceship mass.
Footnotes
[1]Systems for Nuclear Auxiliary Power.
[2]Described in this booklet.