Actually, it seems to me that there is only acceleration (speeding up over time), and deceleration (slowing down over time) and either can happen on either side of the illustrated curve. But I am just winging it - it's been a long time since I've been in a classroom.
No, deceleration is going slower. He wants a term for accelerating (going faster) at a declining rate. So the term I offer is accelerate at a declining rate.
I think this tungsten pole idea is somewhat related to the idea of super fast missiles. At some point, such missiles don't need an actual warhead, as the kinetic energy of the missile itself (plus maybe some blob of mass) is high enough to make folks happy about the destructive power of the missile. Plus, the missile can supply guidance. Like that missile, I think a "rod from god" weapon would have to have a power supply and guidance capability. All spacecraft returning to Earth to land safely in some location have power and guidance systems. And, that's even when all you want to do is hit some broad area in the Pacific Ocean. At geosynchronous orbit, unpowered objects would coast along in orbit for centuries. When Earth sends objects to such orbits, they have on board enough power so that at the end of their functional life they leave leave orbit and fall to Earth, undoubtedly burning up due to friction well before reaching the surface.
Modernpaladin mentions nothing about a guidance system, which would, of course, entail the use of rockets. And to be able to significantly change the trajectory of something with so much momentum, in the relatively brief, available timespan, they would have to be some pretty serious "boosters." I think this is contrary to his original concept, of a "natural" weapon of mass destruction. I think it is more appropriate to think of this as being analogous to the rock that one uses in a "dead-fall," animal trap. All that said, Modernpaladin had responded to my post, saying that the amount that the factors I suggest here would affect the point of impact, would be minimal. As I do not have the requisite knowledge of these things (as I'd noted) I have no basis for disputing that. But, later in the thread, I point to a much bigger problem with this type of weapons' system: if it's just sitting up in orbit, undefended, there's every reason to think that those who are targets, will simply tow the missile to a different, geosynchronous orbit, probably over the country which had initially targeted them.
I like your last point, as it does show a serious weakness. But, if I were the one being targeted, I think I wouldn't bother towing it! Also, if a geosynchronous satellite were to be used to drop tungsten on someone, it certainly would NOT be someone directly below. First of all, the tungsten rock would need to be decelerated. If all that happens is that it gets unhooked, it's just going to stay there. If it is pushed directly toward Earth, it's forward velocity is still present, and the result will not be that the tungsten rod just goes down. That velocity is NOT going to keep the rod in geosynchronous orbit. Beyond that, the rod will start falling through the atmosphere. And, the friction experienced will have to do with the atmospheric density encountered at various elevations. So, the rod's orbital velocity will be slowed by varying degrees and that will change the trajectory. In the end, the very idea that the rod would need no targeting capability is ridiculous. The density of the rod may be an issue. But, it is still a rod (not an orb). It might even tumble. And, even slight effects will make a real difference in the impact location.
@WillReadmore You should add @modernpaladin to your post, above, as these all apply to his assumptions, about this weapon; so I imagine that he would be interested in discussing these things. You are presenting the arguments that I did not feel competent to further argue, and more! Even if you didn't think the aiming of this would not be accurate enough, had your nation been targeted, to be worth towing it to drop on your adversary, wouldn't you at least tow it out of orbit & try to send it out into space (assuming you could calculate a trajectory that would not bring it back to Earth, in the future)?
I agree with you on this. In fact, I'd suggest there is only acceleration. Acceleration is a vector, not a scalar. That is, acceleration comes with a direction and a magnitude, not just a magnitude. So, one can accelerate in any direction, including in the direction opposite to ones direction of travel. From there, we have various terms, often poorly defined, that people use day to day without caring about physics.
