III. Method of attack (opportunity)
a) build up to speed in same system as target
b) build up to speed in different system than target
III is really the one that most influences defense.
a) A ship taking a month to accelerate will be noticed by a TL8+ world or any patrolling IN ships. The ship will be dealt with well before it can reach it's target. The few systems that are potentially vulnerable are unlikely to have anything worth targeting.
I'm not yet convinced a ship could intercept and redirect an incoming threat.
Also, every brachistochrone trajectory looks like a normal approach until the halfway point, if the ship fails to flip and burn. By that time, you could have a ship accelerating at 1G for 20 AU (about 2 billion miles or 3 billion km) without anyone really caring.
vfinal^2 = vinitial^2 + 2*a*d
vfinal^2 = 0 + 2 * 9.8 m/s^2 * [1km/1000m unit conversion] * 3*10^9 km
Let's just round acceleration to 10 m/s^2.
vfinal^2 = 2 * 10/1000 * 3 * 10^9 = 6 * 10^6 km^2/s^2 = 6 million (km/s)^2
Taking the square root of both sides:
vfinal = about 2500 km/s (0.0083 c) for 1G acceleration for 20AU.
Compare to
Asteroid 2010 NY65, which has a mass of 1.5e+10 kg but is moving "only" around 20-22 km/s.
I found a cool "
Asteroid Impact Calculator," in case someone who understands the sizes and densities of starships better than I do, wants to play with it.
Kinetic energy (K) is:
K = (1/2) m * v^2
For K in joules, you need m in kg and v in m/s. Checking a 1000 kg ship at 2500 kps:
K joules = 1/2 * 1000 kg * (2500 * 1000)^2 m/s = 3.125 x 10^15 Joules
1 Joule = 2.39006e-10 Ton TNT, so:
747 kTon explosion per 1000 kg of ship, if I did all my math right. And that's if you accept that the explosion is exactly like a nuclear bomb, which it isn't, because at that speed it's more like a bullet, punching into the crust, creating liquefaction and plasma effects, and so on.