This was brought up in a discussion about sci-fi weapons, where people were discussing simply using kinetic projectiles from orbit to hit with tremendous force. That's obviously a theoretically possible thing. Where I'm being unsure is that some posters were claiming that you could get substantially more energy by launching a kinetic projectile just slightly slower than orbital speed, which would cause it to loop repeatedly around the planet (we'll say the Earth here) gaining speed on each pass until eventually it reaches the ground with enormous kinetic energy.
At a glance, "OK, it keeps falling toward the planet being accelerated by Earth's gravity so it goes faster and faster" makes sense, but...I'm pretty sure it doesn't work actually work that way. But my knowledge of physics and orbit dynamics is minimal and I've forgotten most of it. So I figured I'd crowdsource to a place with experts.
Some things that bother me about this:
* "It keeps gaining speed over a prolonged period of time" is possible with gravity involved, but always kind of a general physics red flag. Things go slower over time, not faster.
* Orbits degrade over time; they get slower, not faster. This isn't an orbit, but...it is very similar.
* As far as I know, satellites and things HAVE degraded and dropped out of of orbit unintentionally, which should follow pretty much the same path as an object fired just below the speed of a stable orbit. They didn't cause massive city-destroying damage when they fell.

* If an object every got going faster than escape speed, it would just fly away from the planet and no longer be orbiting, so it appears to me that the absolute fastest a projectile that looped the planet could ever go would be just below escape speed for whatever altitude started at.
* I have no idea how air resistance would factor in. Would a direct path have less air resistance than a looping one?
Any thoughts on this?