Short answer: as mentioned before, missile speeds & ranges are doubled in space, but to keep it simple just focus on the missile range & speed.
Long answer: unless your tech is using some sort of reactionless drive that acts like Star Trek impulse/warp drives or Star Wars drive systems, there isn't a "maximum speed" in space. However, then you have to start worrying about acceleration rates, fuel consumption, etc., which is extremely cumbersome & complex. Otherwise, you run into the problem of your launch platform running into its own missile volley.
Mid-sized answer:
- the listed ranges & speeds for missiles, whether in atmosphere or in space, assume that the missile is being launched from a (mostly) stationary platform.
- To find the modified speed/range for the missile, multiply the normal range by the sum of the normal missile speed & the launch platform's speed, & divide by the normal missile speed. The equation is R2 = R1 x V2 / V1, V2 is the speed of the missile plus the launch platform, V1 is the speed of the missile by itself
- Unless we are talking about missiles that have ranges measured in the tens to hundreds of thousands of miles, the space speed & range for a missile should reallybe x10....as should the sublight speeds of all fighters & starships. But if you're not comfortable with that, stick with the x2 multiplier.
- To make it simpler, if the launch platform's speed is less than 10% that of the missile's base speed, don't even bother adjusting the missile range, at least not for Medium-range missiles & smaller. Since you're adding at most 10% more range to the missiles, it won't really make that much of a difference (maybe 1/2 a mile for MMs & SRMs, 4-8 miles for MRMs).
So, from your example, a Rapier fires off some LRMs. Let's assume Nuclear/Multi-Warhead (Mach 3, 1800 miles range base). We double for space (Mach 6, 3600 miles range). We plug them into the formula: V
2 = V
1 (Mach 6) + launcher speed (Mach 16) = Mach 22, so R
2 = 3600 miles (R
1) x Mach 22 / Mach 6, or 13,200 miles. It'll take your missiles 54 minutes to get to the target, but your Rapiers will still be about 20 minutes out...or, to put it another way, your Rapiers will still be about 3,600 miles from their targets, well outside of sensor or visual range (although the missiles probably gave the target a warning that
something is out there).
Just to blow your mind...consider instead a volley of HE/Medium SRMs (5 miles, 500MPH in atmostphere; 10 miles, 1,000MPH in space). The calculation gives them a speed of 11,720MPH (Mach 17.49) & a range of 117.2 miles in space. They'll reach their target in 36 seconds...in which time the range to the target from the Rapier will shrink from 117.2 miles to 10 miles...still far enough out that the enemy has a -4 penalty to shoot back at you if using visual sensors (or half normal bonuses & -30% to Read Sensory Instruments if using radar & other non-visual sensors)
Also consider the Armor Piercing MRMs (base of 60 miles/1600MPH, increased to 120 miles/3200MPH in space). Factoring in the Rapier's speed, the MRMs have a range of 522 miles & a speed of 13,920MPH (flight time is 135 seconds). By the time they hit the target, the Rapier is still 120 miles out from the target -- -30% to be detected on non-visual sensors (half normal bonuses) & completely invisible to visual sensors (so unable to fire if only visual sensors are available or if they fail their Read Sensory Instruments skill role).