Physics/Help regarding writing scifi
Hi! I am in the process of starting to write a scifi story. In my story the space ships for the time being use railguns as main weaponry. The space ships will be powered by multiple fusion reactors. Back to the railguns. I've been thinking of 50 metric ton projectiles fired at 1% lightspeed impacting with energy equivalent to the energy released by Tsar bomba in tons of TNT. The railgun will be 500 meters long and the ship will be 600 meters long, 200 meters wide and 100 meters high and it has a two meter thick titanium armor. The ship will have a shape similiar to an aircraft carrier except with a little bit of the shape of a fighter mixed to round the corners up. So does this sound impossible to you and if it does what kind of velocities and projectile masses would be more realistic?
There is one issue that may be a problem. The force required to give the projectile the speed you mention in 500 m would be significant. The reaction force (Newton's 3rd Law) would be equally significant in the opposite direction. I don't know the mass of the ship, but that reaction force could give it a significant kick in the opposite direction.
You can use conservation of momentum to predict the change in speed of the ship:
In a reference system in which the ship's original velocity is zero, the ship's recoil momentum would be equal and opposite the projectile's momentum
Ms*Vs + Mp*0.01*c = 0
where Ms is your estimate of the ship's mass, Vs is the ship's velocity due to recoil, Mp is the projectile's mass and c = 3*10^8 m/s. If you solve for Vs, that would be the ship's recoil velocity. That change in velocity would occur in the time it takes for the projectile to be ejected from the gun. At an average velocity of 0.005*c that velocity change would take place in a time of
t = 500 m / (0.005*3*10^8 m/s) = 0.33 millisec
Everything on the ship would need to be able to secured such that it also can change speed that quickly.
I hope this helps,