The fins are there to keep the rocket stable and ensure the pointy end is pointing forward. The fins might also have rudders on them which are movable surfaces used to control the direction. But the fins do create some drag and slow down the rocket. Another way to keep the rocket stable and to control it is to use thrust vectoring. However this only works when the engine is running. When the engine stops the rocket may end up out of control. For a missile this tends to be a problem as the rocket often burns out of fuel before it hits the target. However for a space rocket it is far more common to detatch the spent stage and ignite the next stage before it goes too far out of control. Of course there are plenty of situations where missiles do not have finns as they drag too much or where launch rockets have fins as they are much simpler then thrust vectoring.
Fins are worthless in space because there is no air they can work on. Their effectiveness decrease when pressure drop at high altitude. The result is you need to have a rocket engine you can turn a bit to control the rocket, this is a gimbaled rocket engine.
The rocket had fins because it was a simple way to add extra stability close to the ground where the engine gimbal was not enough. But as technology improved the gimbaled engine was enough and the fins were removed because they result in drag and extra weight.
A gimbaled rocket engine is quite complete, so it adds weight and cost. If you only fly in the dense lower part of the atmosphere using fins is the cheap and light option so that is what missiles are used.
So space rockets add an engine gimbal system because they need a higher up and can skip the fins. Missiles that are quite close to the ground all the time so gimbaled engines are not required and fins are enough.
So both use the control methods most appropriate for the environment they operate in.
Because space rockets are powered until they are out of the atmosphere, and use other methods for controlling their attitude such as thrust vectoring, reaction control thrusters, and gyros. Fins won’t do you any good in the vacuum of space.
Missiles, on the other hand, stay in the atmosphere for the duration of their flight and (with the exception of cruise missiles) burn themselves out within a few seconds of launch. They are required to steer themselves to their target *without* the benefit of those other methods a space rocket uses.
Fins are only effective at low altitude where the air is thick. A guided missile will usually stay down in those low altitudes, while a space rocket only spends the first 3 or 4 minutes of flight in thick air, after that the air is getting so thin that fins wouldn’t help much.
Space Rockets usually steer by “engine gimbal” which means the exhaust nozzle can deflect. This is steering similar to a boat with an outboard motor where you steer by angling the motor rather than by rudder. While fins *would* work for the first stage of a rocket for those few minutes that it’s still in thick air, the engine gimbal also works both in and out of thick air, so you may as well just engineer one system and use it for both.
Space rockets also tend to do gentler steering. The entire point is to get it aimed the right way at the start so you don’t have to make large turns later and you’re mostly just going straight the way you’re already pointed with steering deflections of only a few degrees. In fact, having to steer too much in a space rocket is a source of inefficiency. The goal is to get the software to predict as early as possible how the rest of the flight will get shaped so you can do small corrections now so you don’t have to perform large corrections later.
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