"orbiting" iron pulling

[campino]

I can't believe that no one else has theorized about this yet, but I can't find it anywhere on the forum. So, I apologize if this thread already exists.

I am wondering if it would be possible for a Lurcher to pull an object in a circular path using the same straight-line-only physics that is used to create orbital paths. For this discussion, I am assuming you have a basic understanding of physics (which is all I have). And as with all good physics discussions, I will discuss things in a frictionless vacuum to simplify my life.

First, brush up on orbital mechanics. http://en.wikipedia.org/wiki/Orbital_mechanics is a good place to do that. Basically, an orbit is a circular path created by the combination of a constant momentum moving "forward" in a straight line (tangential to the circular orbital path) and a force drawing the object toward a larger object at the center (like a satelite being drawn slowly toward a planet by gravity).

So, assume that a metal ball is thrown in a straight line on a trajectory 5 feet to the left of a Lurcher. When the ball is directly to his left, he subtly pulls on it. The ball would continue with its forward momentum, but would feel a slight pull towards him, angling its trajectory slightly. If he keeps pulling (very gently) as it continues moving on this new slightly-angled path, it should continue moving forward and changing its trajectory to create a circular path around him. Using this, couldn't a (very skilled) Lurcher create an orbiting shield of bullets, kind of like Magneto in X-men II?

I just feel like Lurchers are under-utilized because they can "only" draw things in a straight line from mass-center to mass-center, but that's a pretty powerful ability.

[thanners]

Hmm, I don't see why a Lurcher would not be able to make something orbit him by constantly pulling it towards him if it's already got momentum perpendicular to that pull.. But I think it would take some insane amount of skill to be able to make one thing remain in orbit around you, let alone keeping up enough to provide some sort of shield. Also you'd have to deal with gravity pulling down and air resistance slowing them..

Hmmm. But now you have put into my mind pictures of Lurchers hurling things around in a similar way to an olympic hammer thrower. Redirecting projectiles by Pulling the projectiles around themselves, rather than directly to themselves. Have any Lurchers done this already? I can't remember.

[campino]

Hmmm. But now you have put into my mind pictures of Lurchers hurling things around in a similar way to an olympic hammer thrower. Redirecting projectiles by Pulling the projectiles around themselves, rather than directly to themselves.

Yeah, I think that would be super-awesome. Slingshoting any bullets that aren't directly aimed at them back at the assailant. But, as you said, it would be really, really hard. Maybe some sort of Iron-savant?

Have any Lurchers done this already? I can't remember.

I'm pretty sure no Lurchers have done anything like this

Edited December 9, 2011 by campino

[Kurkistan]

I can't believe that no one else has theorized about this yet, but I can't find it anywhere on the forum. So, I apologize if this thread already exists.

I am wondering if it would be possible for a Lurcher to pull an object in a circular path using the same straight-line-only physics that is used to create orbital paths. For this discussion, I am assuming you have a basic understanding of physics (which is all I have). And as with all good physics discussions, I will discuss things in a frictionless vacuum to simplify my life.

First, brush up on orbital mechanics. http://en.wikipedia.org/wiki/Orbital_mechanics is a good place to do that. Basically, an orbit is a circular path created by the combination of a constant momentum moving "forward" in a straight line (tangential to the circular orbital path) and a force drawing the object toward a larger object at the center (like a satelite being drawn slowly toward a planet by gravity).

So, assume that a metal ball is thrown in a straight line on a trajectory 5 feet to the left of a Lurcher. When the ball is directly to his left, he subtly pulls on it. The ball would continue with its forward momentum, but would feel a slight pull towards him, angling its trajectory slightly. If he keeps pulling (very gently) as it continues moving on this new slightly-angled path, it should continue moving forward and changing its trajectory to create a circular path around him. Using this, couldn't a (very skilled) Lurcher create an orbiting shield of bullets, kind of like Magneto in X-men II?

I just feel like Lurchers are under-utilized because they can "only" draw things in a straight line from mass-center to mass-center, but that's a pretty powerful ability.

An interesting theory. I see no reason why it wouldn't be possible, although it would probably take an Iron/Zinc twinborn to pull it off with bullets. There are two obvious problems with maintaining an "orbit" for any real length of time, though: friction with the air and that evil gravity applying downward acceleration on "satellites." Both of these would be non-issues in space, so I image we could possibly see something like this 50 years from now in the third trilogy.

A more realistic use of this technique would be for a particularly adept Lurcher to alter the course of an object without trying to create a stable orbit, such as deflecting a passing bullet and/or slingshotting projectiles around him/her-self.

Welcome to the forums, by the way.

EDIT: So what that ninja Thanners said, essentially.

Edited December 9, 2011 by Kurkistan

[campino]

There are two obvious problems with maintaining an "orbit" for any real length of time, though: friction with the air and that evil gravity applying downward acceleration on "satellites."

Yeah, that first one would be a serious problem for sustained "orbits", but I don't think that gravity would be. When I first thought about this, I was also thinking that the orbit would slowly decay as the "satellite" fell due to gravity, but IIRC, pushes and pulls draw the center of the metal's mass toward the center of the allomancer's mass. This means that the satellite would be in an orbit somewhere around the chest of the allomancer, because whenever it falls below his center of mass, it is pulled up by his iron.

That said, I do recognize that there are serious limitations on this, and it would be impractical to actually do. I just like to theorize about what is on the margins of possibility.

[Kurkistan]

Yeah, that first one would be a serious problem for sustained "orbits", but I don't think that gravity would be. When I first thought about this, I was also thinking that the orbit would slowly decay as the "satellite" fell due to gravity, but IIRC, pushes and pulls draw the center of the metal's mass toward the center of the allomancer's mass. This means that the satellite would be in an orbit somewhere around the chest of the allomancer, because whenever it falls below his center of mass, it is pulled up by his iron.

That said, I do recognize that there are serious limitations on this, and it would be impractical to actually do. I just like to theorize about what is on the margins of possibility.

Ah, good point about gravity. I suppose that we ought to picturing this Lurcher like someone holding a string to spin a tennis ball around, only not applying any lateral force.

Actually, wouldn't an "Orbiter" be able to walk while Pulling on these satellites, adding lateral momentum to counteract friction and increasing the amount of time that they satellites can keep orbiting, perhaps indefinitely?

Edited December 9, 2011 by Kurkistan

[Arcanist Lupus]

Isn't this kind of what Kelsier did when he fought the Inquisitor? True, he used both Pushes and Pulls, but the overall idea was similar.

[Kurkistan]

Isn't this kind of what Kelsier did when he fought the Inquisitor? True, he used both Pushes and Pulls, but the overall idea was similar.

Why yes, yes it is.

Although not in the sense of long-lasting orbits, and not with boolets!

Edited December 9, 2011 by Kurkistan

[happyman]

Possible? Theoretically yes. In practice, though, like others have noted, on the surface of a planet, friction and gravity would make it difficult. Also, we have to take the size of the resulting orbit into account. My guess is that for anything that it would be possible to make orbit you, the orbit would be really, really big, and least compared to human size scales.

[Kurkistan]

Possible? Theoretically yes. In practice, though, like others have noted, on the surface of a planet, friction and gravity would make it difficult. Also, we have to take the size of the resulting orbit into account. My guess is that for anything that it would be possible to make orbit you, the orbit would be really, really big, and least compared to human size scales.

Actually, size shouldn't be an issue. The size of an orbit is normally entirely a function of mass, distance, and relative velocity for the bodies in question: The higher the mass of the satellite, the higher its inertia, but also the higher the gravitational attraction. Plug in the masses, positions, and relative velocities of all of the bodies and you get an orbit.

We don't have to worry about any of that rigamorale for a Lurcher, though, since the Lurcher essentially chooses how strong the attraction of "gravity" is between him/her-self and the satellite. This is equivalent to fiddling with the gravitational constant if we abstract this out to Newtonian physics in space.

The Lurcher can increase "gravity" for a tighter orbit and decrease "gravity" for a larger orbit. As long as the satellite doesn't actually impact the Lurcher or get out of range of a Pull, he/she has complete control.

EDIT: He/she could also vary the strength of the Pull at different points during the orbit to adjust its path, i.e. regularizing an eliptical orbit by increasing the strength of the Pull as the satellite's orbit begins to approach it's apoapsis, or decreasing the strength as it heads towards the periapsis.

P.S. English really needs a gender-neutral pronoun that isn't equally applicable to a toaster.

Edited December 9, 2011 by Kurkistan

[campino]

Actually, wouldn't an "Orbiter" be able to walk while Pulling on these satellites, adding lateral momentum to counteract friction and increasing the amount of time that they satellites can keep orbiting, perhaps indefinitely?

That is a pretty awesome idea. As long as he keeps moving, he could (I think) keep the projectile moving.

[EHyde]

Yeah, that first one would be a serious problem for sustained "orbits", but I don't think that gravity would be. When I first thought about this, I was also thinking that the orbit would slowly decay as the "satellite" fell due to gravity, but IIRC, pushes and pulls draw the center of the metal's mass toward the center of the allomancer's mass. This means that the satellite would be in an orbit somewhere around the chest of the allomancer, because whenever it falls below his center of mass, it is pulled up by his iron.

Sort of like how someone who knows what they're doing can keep a hula hoop going?

I had visions of epic allomantic poi-spinning until I realized that having to pull towards your center of mass would keep that from working. However--if the allomancer was standing on a platform or otherwise suspended midair, would she be able to keep an object in orbit beneath her?

[campino]

if the allomancer was standing on a platform or otherwise suspended midair, would she be able to keep an object in orbit beneath her?

I would think so. It's all about equalizing forces. So, if she were to pull up with the force to accelerate the object 9.8m/s/s, that would hold it at the same distance from the ground. I'm not sure exactly how that would affect the size of the orbital though. I feel like I would need a real physicist (or someone who took physics 101 less than 8 years ago) to give that one some thought.

[Pechvarry]

I do think gravity and orbit size are both large obstacles. You could really only do this with fast-moving objects, as slow-movers would require less Pull (and therefore larger orbits) and eventually, the required pull wouldn't overcome gravity and it would drop to the floor. So the less velocity the object has, the larger the orbit, until finally, you lose it completely. No amount of varying the strength of your Pull will overcome this. Though the vacuum of space would.

[Thor]

I would think so. It's all about equalizing forces. So, if she were to pull up with the force to accelerate the object 9.8m/s/s, that would hold it at the same distance from the ground. I'm not sure exactly how that would affect the size of the orbital though. I feel like I would need a real physicist (or someone who took physics 101 less than 8 years ago) to give that one some thought.

I have a physics final on Friday, though it isn't on mechanics (not baseline, anyway) so I feel like taking a "refresher" by doing this.

Alright. Conditions. *takes deep breath* So we have some Allomancer standing on a platform and he/she is trying to get a moving spherical object (we will treat it as a point, its easier this way. Oh, and we ignore friction. ) to move in orbit around him/her. His/her center of mass (which is what I will be using to determine the force exerted by his/her pull) is some number of meters above the platform. (Irrelevant to the physics, it is just some variable number that will be accounted for in the math.) The total height above the plane of orbit (assuming the orbit traces out a circle in the plane perpendicular to the surface of the Earth. And we are assuming that the Earth, or at least this section, is flat. ) that the Allomancer's center of mass is at will be shown by 'h'. The angle of declination/inclination from the Allomancer's CoM to the object is 'theta', the radius from the object of mass, 'm', to a vertical line from the ACoM along the plane of orbit is 'r'. The force of the Allomancer's pull is the vector "T", as it is similar to a tension force, and the components of this vector are 'Tx' and 'Ty' for the horizontal and vertical components, respectively. The vector 'T' travels in the direction of the line that connects the mass, 'm', to the ACoM. The force due to gravity is the vector 'Fg' and its magnitude is in the negative y direction. 'v' is the tangential speed of the object, as it is moving in a circle, we do not need to use a vector. When vectors are not bolded, treat the value as the magnitude of the vector. Having defined all variables, we will proceed to the math:

The radius 'r' can be solved to be r=h/tan(theta) using trig identities.

The total force on the system: sum(Force)=Fg + T, rewritten in component form: sum(Force)x=Tx, sum(Force)y=Fg + Ty

The components of the vector T can be solved to be: Tx=T*cos(theta) and Ty=T*sin(theta)

The force due to gravity is defined: Fg=m*g, where 'g' is the acceleration due to gravity, -9.8 m/s^2. We will leave 'g' as a symbol for clarity.

Because the object is not moving vertically, the forces of Ty and Fg must be equal, with opposite signs, so that the sum(Force)y=0. Thus T*sin(theta)=m*g and solving for T we get: T=m*g/sin(theta)

As the only net force acting on the object, Tx can be said to fit the centripetal acceleration definition. Therefore Tx=m*v^2/r Substituting for Tx yields: T*cos(theta)=m*v^2/r

If we wish to find the horizontal speed of the object, v, we must solve the equation for v.

After substituting some variables and solving, we get the lovely result of:

v=sqrt(g*h*[cos(theta)/sin(theta)]^2), take the positive root and use a positive value for 'g.' Can also be rewritten as: v=cot(theta)*sqrt(g*h)

Hurrah! Now all you need to do is plug in a mass 'm', (for the object you wish to sling in a circle), a height 'h', (the height that the Allomancer's center of mass is above the orbiting plane) and an angle 'theta' (the angle of declination from the Allomancer's CoM to the object) and you can figure out how fast the object is traveling, 'v', and the force the Allomancer's pull is exerting on the object, T. And all of that weak stuff, like friction...ignore it!!!

Your math/physics fix for the day has been given. It is also interesting to note that holding an object in an orbit plane perpendicular to your body (or parallel to the surface) at the same height as your center of mass is impossible (with only a pulling force) when gravity is present. As soon as the object drops any fraction of distance from that height, you can put it into a stable orbit at that height, using the formulas above. (And of course, ignoring friction. )

Edit: Oh, if you want to find out exactly how far away from your body the object is, just use the following equation:

distance to body=sqrt(h^2+h^2/tan[(theta)]^2) or =sqrt(h^2+r^2)

Edited December 12, 2011 by Thor

[happyman]

The key element of such orbits is the radius of curvature of the resulting orbit. My calculations are made assuming the orbit is circular, but any reasonable elliptical/other orbits will have similar curvature, which is what matters most.

First, we start with Newton's first law, which says that for any object at any time, ignoring relativity, we have that the acceleration on it is the Force applied to it divided by the mass of the object. Thus

(1) a = F/m.

In circular motion, the magnitude of the acceleration is constant, and is related to the circumference of the motion by

(2) a = v^2/R

where, v is the velocity of the orbiting object and R is the radius of the circle. This can be generalized to other orbits by calling 1/R the local curvature of the orbit. Since we are just doing a rough approximation in any case, any value we find for R will give us a reasonable scale on which such orbits could exist.

Thus the radius of curvature is given by

R = m*v^2/F.

For simplicity, lets assume that a reasonable size for something that can orbit is 1 kg and a typical velocity is order 30 mph = 13.4 m/s (this is actually pretty fast). Let the force be on the scale of a typical human push, lifting 100 lbs at the surface of the Earth, which requires 444.520523 newtons of force. Then the radius of curvature would be 0.4 meters.

This sounds entirely reasonable, although I'd be pretty scared to have a 30 mph piece of metal going around me at half a meter away. Fiddling with the parameters would probably result in something more useful if you spent some time with it; this calculation was just intended to find the scale of plausibility, which I think I've established.

[Deus Ex Biotica]

Also, since you could control the parameters pretty completely, you could have a bunch of objects orbiting you at the same speed (so they don't collide). Happyman may be nervous about having a 1kg ball spinning around him at 30 kn/h, but ow will people want to get close to you is you had six of them doing that? This could be a potent personal armament!

Also interesting: with the right equipment, this might be yet another means to generate infinite power, though I admit it is far less practical than an Iron Ferring and a level.

-- Deus Ex Biotica

[Arcanist Lupus]

Also, since you could control the parameters pretty completely, you could have a bunch of objects orbiting you at the same speed (so they don't collide). Happyman may be nervous about having a 1kg ball spinning around him at 30 kn/h, but ow will people want to get close to you is you had six of them doing that? This could be a potent personal armament!

Also interesting: with the right equipment, this might be yet another means to generate infinite power, though I admit it is far less practical than an Iron Ferring and a level.

-- Deus Ex Biotica

I don't see how this would generate infinite power. It doesn't seem much different (to me) from attaching an object to a string.

Also, I don't think infinite power is possible. Arbitrarily large power, on the other hand, is possibly possible.

Edited December 12, 2011 by Sir Read-a-Lot

[Kurkistan]

Well this was alot more science than I was prepared for. I stand humbled and agree that yes, you need wider orbits once Earth's gravity is accounted for.

I don't see how this would generate infinite power. It doesn't seem much different (to me) from attaching an object to a string.

Also, I don't think infinite power is possible. Arbitrarily large power, on the other hand, is possibly possible.

Actually, as far as I can tell (though my theories aren't holding much water lately) you can't generate any power using Iron/Steel Allomancy.

Link to Hopefully not Crazy Theory

Looking at this again, you can actually generate power for all intents and purposes as long as you consider changes in Scadrial's inertia to be externalities, and simply look at the Allomancer-target system. You can simply dump the inertia from the opposite reaction into the planet and have what looks like a perpetual motion machine going fairly easily.

Edited December 12, 2011 by Kurkistan

[Deus Ex Biotica]

(This post will have some Alloy of Law spoilers, which it would break the flow too much to mark individually. You have been warned.)

I agree with that theory as far as motion is concerned, but not energy. Allomancy is explicitly drawing energy from a Shard, thereby bringing energy into the system that could not have been accessed otherwise - that's the whole meaning of being an end-Positive Art, and the reason why, say, a Thug is suddenly able to exert more force, even though their muscles to not change structure.

And it has to be a lot of energy: Wax is able to collapse an entire building with a Steelpush. And it's not just gravity doing all the work: he's still moving up when the Push ends¹. This means that a strong Coinshot is able to, temporarily at least, arrest the motion of a body which weights enough to crush the supstructure of a skyscraper into the ground - tens or hundreds of tons, at the least. There is just no way human biology could provide that many calories.

And, yes Sir Read-A-Lot, you are technically correct about how one cannot have a literally "limitless" source of energy, I just meant a system which can produce energy without meaningful costs, with the only limiting factors being wear on the components and time. As it happens, I was mistaken about Iron Orbiting ever quite reaching that level (it also needs Iron as a catalyst), so unlike the Ironmind trick, this one cannot quite become a "perpetual" motion machine (where "perpetual" is read to be a factor of the lifespans of your Feruchemists), but it could probably be hacked to generate power in a pinch.

-- Deus Ex Biotica

¹: Alloy of Law, page 296: gravity specifically starts pulling him down after the building is pulverized.

[Cuaiir]

I think it's notable here that we've determined that holding a stable orbit anywhere above a Lurcher's Center of Mass is untenable, assuming you want a horizontal plane of orbit.

Now what if those of you that are closer to the physics of it played with 'skewed angle' planes of orbit? Ex: over the Lurcher's head, in front of him/her, under him/her, behind him/her, then back over the head again. Could a Pull-only shield of flying objects be viable? I think that's the burning question here.

[Deus Ex Biotica]

I think it's notable here that we've determined that holding a stable orbit anywhere above a Lurcher's Center of Mass is untenable, assuming you want a horizontal plane of orbit.

Have we? I thought it was still possible, assuming that the Lurcher remains moving at a constant velocity.

[Kurkistan]

(This post will have some Alloy of Law spoilers, which it would break the flow too much to mark individually. You have been warned.)

I agree with that theory as far as motion is concerned, but not energy. Allomancy is explicitly drawing energy from a Shard, thereby bringing energy into the system that could not have been accessed otherwise - that's the whole meaning of being an end-Positive Art, and the reason why, say, a Thug is suddenly able to exert more force, even though their muscles to not change structure.

And it has to be a lot of energy: Wax is able to collapse an entire building with a Steelpush. And it's not just gravity doing all the work: he's still moving up when the Push ends¹. This means that a strong Coinshot is able to, temporarily at least, arrest the motion of a body which weights enough to crush the supstructure of a skyscraper into the ground - tens or hundreds of tons, at the least. There is just no way human biology could provide that many calories.

And, yes Sir Read-A-Lot, you are technically correct about how one cannot have a literally "limitless" source of energy, I just meant a system which can produce energy without meaningful costs, with the only limiting factors being wear on the components and time. As it happens, I was mistaken about Iron Orbiting ever quite reaching that level (it also needs Iron as a catalyst), so unlike the Ironmind trick, this one cannot quite become a "perpetual" motion machine (where "perpetual" is read to be a factor of the lifespans of your Feruchemists), but it could probably be hacked to generate power in a pinch.

-- Deus Ex Biotica

¹: Alloy of Law, page 296: gravity specifically starts pulling him down after the building is pulverized.

Allomancy may be broadly end-positive, but Iron/Steel are not. They provide a cheat by letting you bypass the entropy normally introduced when you transfer inertia in the real world, but they do not create any energy that I have seen.

We really have sketchy evidence about how much energy a Push/Pull can transfer in any given moment of time, and how distance affects that. Assuming that the maximum energy at range X is constant for a given Allomancer, we could simply assume that normal-mass-Wax would have been shot into the stratosphere by a Push of that strength, with the building quickly falling out of range of his Push.

Wax gets to cheat using Iron Feruchemy (the most game-breaking system out there, as it seems to be becoming), and adds on ridiculous amounts of inertia to himself, only needing to impart some small fraction of it to crush the building while remaining essentially in place.

Edited December 13, 2011 by Kurkistan

[Thor]

Have we? I thought it was still possible, assuming that the Lurcher remains moving at a constant velocity.

Cuaiir is correct. A Lurcher cannot keep an orbit at or above his/her center of mass (on a plane parallel to the planet's surface). If the object is above the CoM, the Pull causes the orbit to decay faster and drop towards the ground but if it passes the plane that bisects the CoM it can be Pulled into a stable orbit. And, in case you are wondering, a Coinshot cannot create any stable orbit, all of them decay and spiral outward from the Coinshot.

Now what if those of you that are closer to the physics of it played with 'skewed angle' planes of orbit? Ex: over the Lurcher's head, in front of him/her, under him/her, behind him/her, then back over the head again. Could a Pull-only shield of flying objects be viable? I think that's the burning question here.

Hmmm, I think that specific one is possible. (And other slanted orbits may also work.) It may take me a little longer to get the proper calculations done as the Pull's force equations will be time-dependent... Time to get crackin'!

Edited December 13, 2011 by Thor

[Cuaiir]

Have we? I thought it was still possible, assuming that the Lurcher remains moving at a constant velocity.

No word on if making the Lurcher move changes the math (it probably would), but here's what I was basing my statement on, bolded for emphasis.

[snip]

Hurrah! Now all you need to do is plug in a mass 'm', (for the object you wish to sling in a circle), a height 'h', (the height that the Allomancer's center of mass is above the orbiting plane) and an angle 'theta' (the angle of declination from the Allomancer's CoM to the object) and you can figure out how fast the object is traveling, 'v', and the force the Allomancer's pull is exerting on the object, T. And all of that weak stuff, like friction...ignore it!!!

Your math/physics fix for the day has been given. It is also interesting to note that holding an object in an orbit plane perpendicular to your body (or parallel to the surface) at the same height as your center of mass is impossible (with only a pulling force) when gravity is present. As soon as the object drops any fraction of distance from that height, you can put it into a stable orbit at that height, using the formulas above. (And of course, ignoring friction. )

The bolded and italicized part i took to mean you couldn't hold an object above your center of mass, either. Correct me if I'm wrong.

Edited December 13, 2011 by Cuaiir