Following this question, in the exact same setting
I'm making a world where sub-FTL interstellar travel is a thing, and so is interstellar war, but for the purpose of this question we'll assume the scale to be of a single system.
Spaceships have evolved quite a bit since our current era, and they range in size from several meters (something like 2 times larger than your average air superiority fighter, having a space-worthy manned vessel can't get any smaller than this in my universe) to up to 20 kilometers in the shape of a scaled-up space submarine.
Weapons comes in varying shape and size (proportional to the ship that bear them) and can be split in 3 categories:
Missiles : Just your everyday payload carrying self propelled firestick, you could also call them torpedoes at this point, it doesn't really makes a difference as far a I know. They won't get bigger in size than an ICBM and the tech didn't evolve much aside from targeting and space-worthiness.
Lasers: They are mainly used as a countermeasure and/or to mess with enemy targeting systems at close range (and occasionally to blind the enemy commander trough the window as a prank).
Railguns: This is where R&D was the most successful, since those guns can get pretty big (remember the 20km ships?) and the biggest projectile to date is a whopping 100m long and can travel at 30Km/s. Picture throwing Saturn V at the enemy vessel). Please note that for smaller projectiles the speed can get up to 150km/s, but that is a very specialized gun and the average is less that 100km/s for a decent gun.
Concerning energy requirements, capacitors went a long way and are now extremely efficient, as well as cooling, even in space (firing a railgun more than once won't melt it for the first couple consecutive shots) and fusion is the go-to mean of energy production across the civilization. Dyson sphere project started in some systems, and the question of the access to the host star sparked the wars in the systems.
This time I want to ask you guys about the feasibility of a 3 stage relativistic projectile that would work as follow:
- The first stage is a railgun that get the payload up to 150km/s over a 18km distance (hoping the acceleration doesn't destroy too much my payload)
- Second stage comes when the projectile is at safe distance for ablative laser propulsion, the ship firing directly at the rear of the shell, further accelerating it to [calculations needed] km/s
- Third and last stage is a mix of a HEAT charge and a casaba howitzer, and this is the last and only chance for the firing ship to make any trajectory correction by turning the shell around using tiny thrusters and detonating the nuclear charge, at a safe distance of course (maybe 1 A.U. or less, I don't exactly know what a safe distance is when 10,000km is considered point blank range in space).
Such a weapon isn't stealth-friendly in an already non stealth-friendry environment, so i'm looking to go really fast, really fast. Energy expenditure is out for simplicity's sake, and we shall consider the shell after the third stage to be going at relativistic speed (more than 1% of C), be hardly detectable and a pain to deflect (you don't want to create a relativistic could heading your way by destroying it... or do you?)
And now for the (somewhat) concise question: Would such a weapon system be realistically possible?
Please note the tech level to be several centuries ahead of today, so extrapolating current tech to the limit of physics is acceptable. Feel free to comment below for any missing info on the context if needs be (also feel free to edit for spelling, my previous question highlighted the fact that I utterly suck at it).