Damage of a high mass object falling at terminal velocity

[Agemegos]

Originally Posted by Kfireblade

Not without doing a lot of other work. I straight up admit I don't know much about the physics involved, if you let an object fall from high orbit gravity would in fact pull it down and it would accelerate to terminal velocity right?

No, not really. The key to this is to know that orbit isn't a place or zone, it is a ballistic condition. If something is in high orbit (or any orbit) and you literally drop it what will happen is that it stays in orbit. When people say "drop from orbit" they mean and are understood to mean that the thing is de-orbited by changing its trajectory to one that impacts the surface.

The other thing to understand is that things don't have a terminal velocity in the vacuum of space, because terminal velocity is the condition where the drag force acting on a thing is equal in magnitude and opposite in direction to the force of gravity on it, and there are no drag forces in vacuum. When an object falling from space first enters the atmosphere its terminal velocity is very high because the air is thin. As the object moves down into thicker air its terminal velocity diminishes, and at some point it equals the falling object's velocity. From then on the object is slowed by drag forces more than it is accelerated by gravity, so its velocity will tend to diminish. But it won't diminish rapidly. And as the object continues to move down at a great speed it gets into ever thicker air where its terminal velocity is ever slower, but it doesn't necessarily slow down to match. It ends up going faster than terminal velocity, not because it got faster, but because terminal velocity got slower. And it will likely hit the ground before it can slow down to terminal velocity.

Drag depends on shape and size and weight (mass times gravity), so terminal velocity does too. A small object with an unstreamlined shape and small mass has a low terminal velocity and it adjusts to its terminal velocity rapidly. A 640-ton iron bar has a high terminal velocity and adjusts to terminal velocity very gradually.

I mean, things in orbit have to keep a certain speed to stay in orbit right?

Well, they have to have at least a minimum speed to be in orbit. If they lack it they are in space on what we call a "sub-orbital trajectory", they are not in orbit.

so if something was just created and had no velocity it would get pulled in by the planets gravity yes?

Correct. All motion is relative, so there is no such thing as objectively having no velocity, but a thing that had no velocity relative to the centre-of-mass of the planet would fall straight down, and a thing that had no velocity relative to a wizard standing at some point on the surface of the planet would fall into a narrow elliptical trajectory that would intersect the surface (unless it were a very, very long way away).

The thing is that an object that is created in space lacking orbital velocity is in space, but it isn't in orbit, so it's being dropped from space, not dropped from orbit.

So, if we consider something dropped from space, everything depends on from how high it drops. The limit is Earth's escape velocity: 11.2 km/s. It certainly won't be going any faster than that when it hits the atmosphere. 11.2 km/s is faster than the terminal velocity I calculated for your rod a few posts back (which was about 1.7 km/s) so the rod will be slowed by air resistance faster than it is accelerated by gravity, and it will slow a little bit. But it will hit the surface about nine seconds after hitting the atmosphere, and will barely slow down at all. At the other extreme, an object that falls from less than 147 km altitude will never get up to the terminal velocity of that rod in air at the surface.

I think terminal velocity is a distraction. The thing is falling mostly through vacuum and the thin upper atmosphere, and its very high cross-sectional density means that it will decelerate only very slowly if it is faster than terminal velocity (which it is likely to be). Basically, the drag forces on this object aren't very significant. It is so massive, and has such a small frontal area, that you can just ignore drag.

So we have orbit and terminal velocity out of the way, this is just the physics of dropping a weight from a great height.

[Bicorn]

Some of this also depends on what means you are using to get up there and how magic in the campaign interacts with laws of physics.
Normally when you move into orbit you will achieve the correct orbital velocity for staying there in the process; if you're doing it by teleportation or the like, it's largely a GM call what happens to your motion or potential energy, since teleportation breaks standard laws of physics - do you retain the velocity equal to the planet's rotation you had when you were on the surface, gain orbital velocity fitting your current altitude, or something else?
Similarly, because in reality you can't just create matter out of nowhere, it's again a GM call what happens to magically created matter in such an environment - does it match velocities with the caster, the planet, or something else?

[Kfireblade]

Originally Posted by Bicorn

Some of this also depends on what means you are using to get up there and how magic in the campaign interacts with laws of physics.
Normally when you move into orbit you will achieve the correct orbital velocity for staying there in the process; if you're doing it by teleportation or the like, it's largely a GM call what happens to your motion or potential energy, since teleportation breaks standard laws of physics - do you retain the velocity equal to the planet's rotation you had when you were on the surface, gain orbital velocity fitting your current altitude, or something else?
Similarly, because in reality you can't just create matter out of nowhere, it's again a GM call what happens to magically created matter in such an environment - does it match velocities with the caster, the planet, or something else?

Well, I'm not relying on teleportation or anything like that. (Although if I did teleport I know I would retain velocity.) I'm flying up in a craft capable of doing so. I also know that when I create matter Its not moving (Well, technically EVERYTHING is moving, but its not moving relative to me.)

[Kfireblade]

So say I fly about, 200 miles up, come to a complete stop, create a platform with force wall, stand on it, and drop the rod. What kind of damage would that do? Of course it would be impossibly hard to hit any specific given general area like that, though with ETS and Intuitive Mathematician I *might* be able to eventually figure out when I needed to drop it and from where to hit near a given target.

[Agemegos]

Originally Posted by Kfireblade

So say I fly about, 200 miles up, come to a complete stop, create a platform with force wall, stand on it, and drop the rod.

You'll need an oxygen supply and pressure protection, of course.

What kind of damage would that do?

I have a feeling that I'm doing something wrong because this figure is higher than I expected, but I reckon that your rod will land doing about 2.3–2.4 kilometres per second, and explode like about 400 tons of TNT. Roughly speaking you get a crater 165 m across and 35m deep, and masonry buildings are levelled by the air blast out to about 390 metres.

Of course it would be impossibly hard to hit any specific given general area like that, though with ETS and Intuitive Mathematician I *might* be able to eventually figure out when I needed to drop it and from where to hit near a given target.

If you're operating over a small range of latitudes and are reasonably careful to keep the same altitude and speed each time it ought to be fairly easy to learn from experience how far and what way it drifts when you drop it.

[Anthony]

Originally Posted by Agemegos

I have a feeling that I'm doing something wrong because this figure is higher than I expected, but I reckon that your rod will land doing about 2.3–2.4 kilometres per second, and explode like about 400 tons of TNT.

Energy sounds about right. However, it's a dense enough object and moving slow enough that it won't generate an air explosion, it will bury itself and come to a stop a significant distance underground.

[Bicorn]

Originally Posted by Kfireblade

I also know that when I create matter Its not moving (Well, technically EVERYTHING is moving, but its not moving relative to me.)

In other words, it matches velocities with the caster - as you noted, there's not really such a thing as an unmoving object. The distinction is usually academic but pretty important when talking about orbital mechanics.

[whswhs]

Originally Posted by Bicorn

In other words, it matches velocities with the caster - as you noted, there's not really such a thing as an unmoving object. The distinction is usually academic but pretty important when talking about orbital mechanics.

Right. If, for example, you're standing on the equator, you're moving due east at about 1000 mph (Move 500). The mass that appears above you is moving due east at the same speed. You'd need to work out the shape of its orbit based on its initial altitude and velocity. I expect it would intersect the surface of the Earth, but it wouldn't fall straight down; at any altitude above you it would trace out a smaller angle of longitude than you would, and would thus appear to be moving westward.

[Kfireblade]

Originally Posted by Anthony

Energy sounds about right. However, it's a dense enough object and moving slow enough that it won't generate an air explosion, it will bury itself and come to a stop a significant distance underground.

so what would the effects be in the area around where it hit?