How would a rail gun affect the trajectory of a spacecraft?

What sort of force would a railgun need to produce to have a measurable affect on the trajectory of a large spacecraft?

In the scifi book I am working on the primary craft of the story is a military ship classed as a heavy destroyer and equipped with 3 massive railguns that extend along the central spine of the ship. As none of them can be directly in the center, I am mainly wondering if firing them one at a time would have enough force to cause the trajectory of the ship under power to alter slightly, or if the ship not under power might start to rotate along its length (like a helicopter, not a bullet).

Obviously, that would depend on the mass and velocity of the projectile, but when trying to determine a feasible mass the math got a little beyond me. Therefore, I have settled for determining minimum force, as that should allow me to come up with possible weight and speed of the payload. Likewise, if it turns out that the difference would be negligible or impractical/impossible, then I can just move on with the story and completely ignore the possibility all together.

For a clearer analogy of my concern: If I shoot a gun and it pushes my right shoulder back so that I end up turning slightly to the right, how much force would I need to make a spaceship do the same thing?

I'm not sure what values might be necessary, but I have some rough numbers that I imagine might be helpful:

Ship Length: 330 m

Ship Width: 60 m

Mass: 35,000 t

Railgun offset from ship center axis: 8 m

If it matters, assume ship center of mass is equal to geometric center. Please let me know if there is anything else I'm not considering.

posted almost 5 years ago

TitaniumTurtle‭

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