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A problem in space is a lot of the time heat dissipation. Another big problem is if you are set off course by the forces that the gun shooting inflicts on your spaceship.

For the same speed and stability of bullet, which is preferable in terms of amount of heat and forces transmitted to the spaceship and reusability, a railgun or a big cannon?

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In terms of heat, the cannon will leave less heat in the ship, as the extreme greater part of the heat will leave with the combustion gasses of the propellant. The only heat that remains is the tiny amount that transferred from the propellant to the mechanism (breech, barrel) of the cannon in the very brief fraction of a moment that it is actually firing.
By contrast, the railgun consumes an enormous amount of electrical energy, which needs to be generated, somewhere on your ship. This makes heat. It then uses this energy to propel the projectile, with significant losses, imparting more heat.

In terms of recoil, the cannon imparts a LOT more force.
You are accelerating not just the projectile, but also all of the gas behind it, all in the same direction.
Here is a typical lowvelocity practice cannon round.
enter image description here That bit on the right is what you throw at the enemy. That long tube on the left is the propellant charge that provides the push, and is also thrown in the general direction of the enemy. Every gram of mass, both in the projectile and the propellant, imparts recoil on your firing cannon and thus on the cannon's ship.

However, this whole discussion is moot.
The whole reason one would use a railgun in a space battle, is because such battles will be fought at much greater ranges, and much greater relative speeds, than any land or naval battle. Your projectiles need to get to the enemy at high speed, to have any chance of actually hitting the target.
A chemical propellant cannot accelerate a projectile faster than the speed of sound in the propellant. This limits maximum projectile speed to about 2km/s, in practice actually less.
A railgun is limited only by the energy density your materials can withstand, and even current primitive examples can reach speeds of 6.5 km/s, the theoretical limit is , well... unlimited.

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    $\begingroup$ Also for a gun guy has to carry additional mass of gunporwder, while energy may be stored in much denser form of nuclear or fusion or whatever. $\endgroup$
    – MolbOrg
    Jun 5, 2021 at 10:03
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    $\begingroup$ "...the theoretical limit is , well... unlimited." -- I don't know about unlimited... it probably tops out around 186,000 miles per second.... $\endgroup$ Jun 5, 2021 at 19:06
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Coilguns

Instead of railguns I would recommend coilguns. One uses contact and magnetic forces (more or less), while the other is fully magnetic. On Earth they sometimes try to make the barrel a vacuum, letting the bullet pierce something as it shoots out the barrel. This'll reduce drag to the bullet and damage to the barrel. But you're in space. There is a vacuum already. Coilguns can fire without touching the bullet, so the only problem to solve are the direct magnetic forces that interact with the magnets as well as the bullet.

The coilgun is more efficient per energy, especially at higher and higher velocities. High velocities are paramount in the long distances in space. As well as that a cannon will damage the barrels much more from certain velocities thabks the the greater inefficiencies. Inefficient also means more heat and physical firces you jeed to deal with.

As you can control electromagnetic forces to minute detail, you can even use any leeway between the magnetic coils and the bullet to fire just offset or straight, making it the more accurate option. A cannon can only use a big explosion and you need to hope it's as homogeneous as possible when it exits the barrel, as any timy offset will be catastrophic on long ranges.

Finally you have space, which is very cool. You can use this for easy supercooling of cannons and coilguns alike. It shouldn't pose a huge problem, except if the initial heat exchange is simply too much.

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  • $\begingroup$ Good answer, but not to this question. $\endgroup$
    – PcMan
    Jun 5, 2021 at 9:22
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    $\begingroup$ Space isn't super cool (cold), it's just a vacuum (it's not like "the artic"-cold, there is no cold air in space). The only way to cool (make cooler) something in space is through radiation. The most efficient way of radiating heat is with radiators (like solar panels but these do the opposite, they emit IR radiation to space). $\endgroup$ Jun 5, 2021 at 13:59
  • $\begingroup$ @PcMan thank you for your constructive criticism. $\endgroup$
    – Trioxidane
    Jun 6, 2021 at 5:52
  • $\begingroup$ @4.12.22.4.18.0. My apologies about making light of cooling. Although space is undeniably cold, it is too little to use in mainstream cooling. Still, as you say, radiating heat is the way to go, together with liquid cooling of the guns. I would cool magnets with liquid helium, just like an MRI. Just above 0°K the magnets can work generally better. Depending on the length of the barrel this can be a stable solution for very powerful magnetic forces. With further cooling with IR radiators it should be stable. Keep in mind that coil and railguns can just extend further to exert more force. $\endgroup$
    – Trioxidane
    Jun 6, 2021 at 6:02
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Rockets.

Not the question asked, which was answered by PCMan.

  • Rockets impart no thrust to your ship if they are not attached when the rocket motor starts up.

  • Propellant is used more efficiently than with a cannon.

  • The top speed of a rocket is the speed of light. Rockets can accelerate as long as they have propellant.

  • Rockets can steer.

The reason for railguns or cannons would be battles fought at close quarters where the rocket does not have time to get up to speed. Close quarters battles are exciting. Also exciting is a damaged ship set spinning after firing its mighty cannon so for CGI excitement I pick the cannon. If you just want to get the job done I pick railguns because explosions on impact are not as effective in space and so kinetic impactors make more sense.

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