Of course it wouldn’t matter. But neither would any other factors, since there’s no such thing as terminal velocity in a vacuum.
Other than c. 
No, scr4 isn’t talking about a conventional black hole. He’s talking about small ones, which are speculated to exist. A small black hole with enough mass to survive long enough to reach the earth’s surface might weigh only a few grams, and so there’s no question about the earth falling “toward” the black hole, the black hole’s not heavy enough. The black hole wouldn’t gobble the earth up, either, because small black holes decay very quickly.
Back to the original question, what’s wrong with neutrons? Unless they happened to hit an atmospheric nucleus, they won’t be slowed down by the atmosphere. They have a half life of around 15 minutes, which is enough time for a 4,000 km fall, and a terminal velocity of around 9,000 m/s (32,000 km/h, 20,000 mph). That’s pretty close to the 11,000 m/s escape velocity of the earth.
A longer lived object could achieve a higher terminal velocity, and it’s shape and size wouldn’t really matter much. A big rock dropped from way outside the atmosphere would achieve most of the 11,000 m/s escape velocity while it was still outside the atmosphere, but once it did hit the atmosphere, it would start to burn up and slow down, so it might impact at say, 10,000 m/s.
But a big rock dropped from higher again, say from the orbit of Pluto, would approach the escape velocity of the earth/sun system, which is around 44,000 m/s (160,000 km/h, 100,000 mph).
Well some bombs are certainly designed for maximum terminal velocity. See Tallboy for example. This bomb fell at up to 750 mph. And it is exactly the shape that many contributors to this thread have anticipated.
In addition to atmospheric friction, you have to take into account lithospheric friction, is all.
But you see, we are not talking about impact velocity, but about terminal velocity, which is where the object has zero acceleration. The BIG ROCKS are still decelerating when they hit.
I don’t think this question has an answer unless some constraints are added. For a sphere, just use more material and the terminal velocity will increase. If you specify the mass, make the sphere denser (and hence smaller) and the terminal velocity will increase. If you specify a mass and maximum density, Sam Stone’s needle shape can always be made longer and narrower and I suspect its terminal velocity will increase.
I also like a needle shape… and another way to keep it straight up and down is to have it be spinning very fast around its axis.
Note that the lifespan of a particle is not a hard-and-fast thing. The average lifespan of a neutron is about fifteen minutes, but a very lucky neutron could, in principle, live for any length of time. However, if it doesn’t chance to interact with any nucleus, then it’s effectively falling through vacuum, so I don’t think that one can meaningfully talk about terminal velocity. If one had a uniform atmosphere of sufficient thickness in a uniform gravitational field and a sufficiently long-lived neutron, then the assumption of no interactions would eventually break down, and eventually one would be able to define an average interaction rate and therefore a terminal velocity. While that terminal velocity would no doubt be very large, I don’t know offhand what it would be.
Also incidentally, neutrinos are an even better candidate here. They’re only about a billionth the mass of the neutron, but they more than make up for that with their low cross-section for interaction with other matter, and they apparently have an infinite lifespan.
Ok so two things are still unclear to me:
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Does density affect the speed of the object? With and without the presense of air.
F=MA but is “A” not fixed at 9.8g (or whatever it is).? -
If we fix mass and density (ie the contraints talked about earlier), can it be calculated say computationally, what the most efficient free fall shape is?
There are two forces acting on a falling object. The first is the force of gravity acting on the mass of object. The second is wind resistance. As an object falls it will start out with a wind resistance of zero, so it will accelerate. As it picks up speed, the force from wind resistance increases. When the two forces balance out, the object has reached terminal velocity and will no longer increase in velocity.
So, if two items have identical wind resistance, the heavier one will fall faster. You can try this by taking two ping-pong balls and injecting one with water. Then drop both of them and see what happens.
There might be several shapes that are equally efficient. The two most critical parameters are going to be frontal area, and wetted area. Frontal area determines how much air must be ‘pushed aside’ as the object falls, and wetted area is the total surface area of the object. Air is viscous, and tends to stick to things. So the bigger the object, the more drag created by air sticking to the surface.
I assume you mean the density of the object (as opposed to density of the atmosphere). But yes, in general a denser object will have a higher terminal velocity – I’m reasonably sure all the posters above would abree on that.
Now, let’s take a look at the definition of terminal velocity; one such is “the constant maximum velocity reached by a body falling through the atmosphere under the attraction of gravity. [my italics]” The point is, the definition of terminal velocity requires the presence of an atmosphere; the “terminal velocity” without air is a meaningless concept (or… maybe not meaningless, but you probably shouldn’t be calling it terminal velocity).
Wouldn’t that burn incredibly fast? Or am I just crazy?