Some of the answers here are wrong. We know that fins are only effective with airflow, but some answers ignore that big rockets have stages and they even have different engines for atmospheric flight and another for vacuum.
Another problematic assumption is that “modern rockets don’t have fins”. Some of them still have, and some of the older designs didn’t have it. SpaceX Starship and the Chinese Changzheng 5 still have fins.
But if I had to guess, I would say that the trend of using fewer fins for rockets would be to how gimbal engines become more reliable and stable.
(And I don’t know about missiles, lol)
Fins are useful in atmosphere, but a space rocket quickly leaves it so fins become useless and it has to steer without anyway. If it can steer without anyway, then why bother with fins to begin with? It’s dead weight.
Still, some space launchers do have fins, Chinese launchers for example, aerodynamic stability is necessary and small fins can ease the engineering constraints in other parts of the design.
Missiles operate either partially or entirely in atmosphere (depends on the missile) and in the atmosphere fins are very cheap and effective ways to maintain stabilization. You don’t need any fancy technology to dramatically improve the missiles, just slap on some fins and boom, a much more accurate missile.
Space craft, however, operate almost entirely out of atmosphere in a vacuum. Since vacuums have no air in them fins are literally useless. So if you add fins to a spacecraft you are just wasting money (even more so than you might think, because it’s not the fins themselves that would cost much, it’s the extra weight they would add that would mean having to use more fuel which is expensive.)
That said, there have been spacecraft that have had fins, most notably the space shuttle, but the only time that ever happens is if the spacecraft is planned to spend a decent amount of time in the atmosphere, like the space shuttle did when it would land for reuse.
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