Newton’s Shell Theorem in an Infinite Solid Universe.

August 15, 2018

Despite the ominous title, you will find no math in this entry. You’re welcome.

Some of you will be familiar with Newton’s shell theorem. Basically, it says this; if you are inside a sphere, or a thin shell, of homogeneous mass, then the gravitational forces of the mass around you will cancel out, and you will float freely no matter where you are inside that sphere; you will not be attracted to the center of the cavity, and you will not be attracted to the inside edge of the sphere.  See Figure 1 below.

I’ve done the math for the basic shell theorem (Fig. 1). It works. This is a fairly common undergrad physics problem. 

newton1

Since you can add additional shells of mass ad infinitum, then you can fill an infinite volume, a universe, with these shells, and the object in the spherical cavity will still be floating freely, since all the forces will balance out. See Figure 2 below.

newton2

This works great if you have a spherical universe.

A while back, while working on an SF story, I speculated on how a universe that was completely solid might work, especially if you had an Earth-sized cavity in it. My conclusion was that you would be attracted to the side of the cavity, which at first seems to contradict Newton’s shell theorem. But let’s take a look a that.

newton3

So the big rectangular gray area in Figure 3 represents the infinite, solid universe of whatever density you like. Marshmallows, quartz, whatever. We’ve carved out two Earth-sized spheres of whatever this stuff is, and discovered that if you stand where the little guy is standing, then the mass is completely symmetric around him, pulling with equal force in all directions. There is no gravitational gradient there.

Now, we fill in one of those spheres.

newton4

In Figure 4, on your LEFT, there’s a volume the size of the Earth, but it’s full of the aforementioned universal solid. On your RIGHT, there is an empty hole the size of the Earth. Since, as we’ve seen in Figure 3, all the rest of the mass in the universe balances out, not pulling you any direction at all, then the only mass pulling on you is that sphere to the left. If the average density of the universal ‘stuff’ is the same as the Earth, then you would feel a force of 1 gravity no matter where you stood on the inside of that hollow sphere. Feel free to imagine Figure 4 without the extra circle on the left. It’s not really necessary except to help with the explanation.

This is an issue when trying to solve problems involving an infinite universe. In this example, the universe would have to either be infinite and eternal, or closed in such a way that the distribution of mass was the same everywhere, such that if you went in a straight line forever, you would end up back where you started (though digging that hole would be very time consuming).

This is an interesting SF universe to play in, however. Pockets of air scattered around would create their own gravity, as described above, little bubbles in an unknowable solid universe. What if gravity in a large pocket became so great that it overcame the structural integrity of the matter that made up the universe? Would it propagate outward, consuming the universe with a growing ball of vacuum?

If you like this speculation, be sure to check out my short stories listed at my website.

 

 

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Zero Gradient Gravity Fields, Dark Matter, and the Formation of Stars

May 17, 2018

We’ve mentioned in the past (to ourselves) that the formula for the Schwarzschild radius for a black hole, c2=2GM/rs tells us that no matter how thinly distributed a mass is, (such as 1 atom per cubic centimeter), if you have a large enough sphere of it, it will have a Schwarzschild radius when viewed from outside that volume. You can see this just by shuffling the equation around a little, so that c2/2G, which is a constant, equals M/r, the mass over the radius. For any given density, the mass, M increases with the cube of the radius, so for any given density, you can always find a radius that contains enough mass to equal the value c2/2G. Cute, huh?

I struggled for awhile wondering if an infinite 3D field of particles (which would appear to be flat gravitationally, that is, not have a gradient), would allow for overlapping apparent black hole horizons; everywhere you looked, there would be large, overlapping, spherical volumes that had enough mass to become black holes. Could this be our apparent cosmological horizon? But today (5/12/18) it occurred to me that the key feature of a black hole is that it has a gravitational gradient. You have to work to get out of the gravity well, or the idea of an event horizon is meaningless. But an infinite field of equally distributed mass has no gradient. It appears flat. Ergo, no event horizon, no matter the density.

Cruising along in deep space, there is, in essence, the same amount of mass pulling on you from all sides, that tenuous 1 atom per cm3. It could just as well be 10 atoms, or 100, or a million, with no noticeable effect. Once we attained a velocity, we would maintain that velocity – an object in motion remaining in motion. The interstellar gas would eventually slow you down, but it would take a very ong time.

Working with the 1 atom/cm3 extending to infinity, let’s say we superimpose another huge sphere of 1 atom/cm3 gas on top of that, so huge that it provides you with an event horizon (if I’ve done my math right, it would amount to roughly 1.5×105 light years in radius, or a ball 0.3 million light years in diameter). Now there is a mass and a very small gravity gradient. Is the event horizon based on the 2 atoms/cm3, or the 1 atom/cm3 density? We’ve already seen that the original 1 atom/cm3 field provides no gradient, so it would make sense that the only effect to the observer is to see the event horizon created by the new 1 atom/cm3 superimposed on the existing field; the other previously existing field is completely flat and cancels out.

However, the new field created by the new mass is going to affect both the old mass (1 atom of hydrogen per cm3 everywhere) and the new mass (1 atom per cm3 in the giant sphere). The object will form with twice the mass (in this case) predicted by the theory. When it’s first put in front of us, we will measure a mass represented by the 1 atom/cm3 in that volume. As it collapses and takes the background mass with it, it will finally produce a mass that accounts for the 2 atoms/cm3 that we actually started with. While it’s doing this, it will also be backfilling the area that it vacated with more interstellar gas, as that gas is also being pulled in by the gravity of the developing black hole, so the overall density of the universe will appear mostly unchanged, even around the black hole.

Practically speaking, this would be more likely to happen in a nebula, where the density is much higher.

One of the most interesting things about this process is that if there is an undetectable mass-type in the universe (like dark matter) that only interacts with regular matter through gravitation, and it’s distributed equally everywhere, then objects that form (planets, Suns, black holes) will also pull in this other mystery mass. As described above, the tenuous gas (1 particle per cc) that we currently measure may actually mass 2 or 10 or 100 particles per cc. We wouldn’t know since the field is flat. Since this new mass doesn’t react with normal matter, it will clump in the center of the object (although it may have its own chemistry and volume that prevent excessive density). Small objects existing on a larger mass (like humans), would have the dark matter pulled out of them, and when we performed tests like The Cavendish experiment to measure the gravitational constant, it would give us a good value for G for normal matter, and would give us erroneous results for the masses of the planets and the Sun. We would think the core is made of denser matter than it really is, both in the Sun and Earth. We know the mass of the Earth, but a substantial chunk could be dark matter and we’d never know it. Perhaps the iron core is made of silicon at half the molecular weight (which is interesting, because magma is 50% silicon dioxide, and only 9% ferrous oxide).

However, most objects that have formed in the last few million years are going to have some dark matter as part of their core. They have gravity, and any dark matter out there will be attracted to it just like regular matter, until an object forms which is part dark and light matter. This includes asteroids. Eventually, we’re going to move an asteroid, and when we do, the acceleration is going to leave the dark core behind. We may not notice it unless we’re looking for it, or if it’s a substantial enough part of the mass that we detect a mass-change in the object as it’s propelled. We would end up with two objects; the obvious light-matter asteroid, and the invisible dark-matter asteroid that could only be detected with a gravitational gradiometer. It would change the way we thought about the universe.

Black Hole Evaporation versus CMBR

May 5, 2018

Black holes evaporate. At least, that’s what most physicists tell us.

What I stumbled into recently was a conjecture that they can’t evaporate beyond a certain point if the input is greater or equal to their output. This was mentioned on Quora by some physicist as a response to a related question. I thought it was interesting enough to mention it here.

Really large black holes are colder than the cosmic microwave background radiation (CMBR), which is about 2.73 degrees. The radiation going into a black hole is actually greater than the radiation leaving the black hole. The only way a black hole could radiate is if it’s very small and already radiating hotter than the CMBR (plus whatever particles fall into it, adding to its mass).

The limit where the size/mass of the black hole is equal to CMBR input is about 1% Earth mass, about 4×10^22 kilograms, based on Susskind’s formula and Hawking’s formula. This would create a black hole smaller than a millimeter. But black holes can’t even form without at least three or more Solar masses to begin with.

So, any black hole larger than a millimeter is going to keep growing. Presumably, primordial black holes smaller than 10^11 kg, created during the Big Bang, would have evaporated by now. This leaves a range of possible primordial black holes from 10^11 to 10^22 kg as possible existing evaporators, since they would be hotter than the background radiation.

However….

Primordial black holes would form because of high density and radiation. It would be crazy to think that their mass wouldn’t quickly grow far beyond Earth mass when surrounded by a buffet of dense gas and radiation. Just the nature of the formative process suggests that they will never radiate faster than mass/energy is added to them from their environment, and will always grow larger in size.

I really WANT them to exist, however. My next SF story kind of depends on it.

The Spacetime Diet: Redistributing the Fat of the Universe

October 29, 2017

If you’ve had your nose in spacetime physics at all, you’re familiar with the idea that when you move really fast, other objects look thinner. Or, relatively, you look thinner from the viewpoint of someone else’s reference frame.

This is called the Lorentz-FitzGerald contraction. When you observe a moving object, it appears shorter, or thinner, along the axis of its motion relative to you. Likewise, you appear thinner relative to the moving object (who does not feel thin at all). There’s a formula for this, but it’s irrelevant for the discussion below.

You also appear to gain mass (using a similar formula). This is also irrelevant for the following discussion, but I thought I’d toss it out there.

So here’s the rub. You will often hear someone say or write, “When an object nears the speed of light, the universe flattens to a thin sheet from the viewpoint of an observer on that object.”

Just to clarify, this is bullshit. If you are cruising along at near-light speed, then all matter, relative to your frame of reference, is moving in the opposite direction at near-lightspeed. That’s okay so far. Except, the universe is expanding. And the farther out you go, the faster it’s expanding, such that there are regions of space expanding away faster than the speed of light (the expansion of “space” is apparently able to ignore the whole “speed of light” limit thing; go figure).

So when you attain a certain velocity, you become stationary relative to another part of the universe that is moving away from Earth at the same speed. There is no shortening of length or thickness for that object, that part of the universe.

Take the Andromeda Galaxy for example, moving toward us at 110 kilometers per second. When we measure the galaxy in the direction of its travel, along its axis of motion, it’s foreshortened in that direction. Now, fire up your rockets so you’re traveling at 100 kilometers per second in the same direction, and Shazam! The entire galaxy poofs back out to its real shape in its own frame of reference that happens to coincide with your own. Relative to you, the Andromeda Galaxy is no longer moving.

So, back to the expanding universe; as your spaceship speeds up more and more, there’s always a part of the universe that’s moving at the same speed at which you are traveling (a comoving reference frame). It won’t look compressed or thinner or foreshortened at all. In fact, if we take the viewpoint that all parts of the universe are essentially equal, (that is, there is no “center” of the universe) then the universe doesn’t compress into a pancake at all as you near the speed of light; it’s just that the non-foreshortened part of it, the part that matches your current velocity, is farther and farther away from you. But the overall volume will appear unchanged.

 

Black Holes and Those Pesky Event Horizons

October 8, 2017

In Leonard Susskind’s book, The Black Hole War, page 240, he states, “To a freely falling observer, the horizon appears to be absolutely empty space. Those falling observers detect nothing special at the horizon…” In Amanda Gefter’s book, she points out that the distant observer sees the event horizon, while the falling observer detects no event horizon at all. Of course, she took a lot of her ideas from Susskind. In the meantime, Hawking treats the event horizon as a fixed boundary where virtual particles can split apart (Hawking radiation).

black_hole_2013_0

I think none of these is right. The idea between the “escape velocity being faster than the speed of light” is relative to the delta between the gravitation potential of the observer and the potential at the event horizon. From an infinite distance, we observe an event horizon at a certain radius. Should the event horizon suddenly disappear if we are in an inertial frame starting our fall into the black hole? Starting at what distance? A thousand miles? A light year?

The more likely result is that the event horizon moves inward as you approach it. You are in a deeper gravity well as you approach the black hole, thus the difference between your local gravity potential and that of the event horizon, to maintain a high enough value for the escape velocity to equal the speed of light, requires that the event horizon continuously move away from you (toward the singularity) as you move toward the singularity. You never quite catch up with it. There’s a Wikipedia article that says this explicitly, but then, it’s a Wikipedia reference (Event Horizon). Sometimes they’re wrong, but usually they’re dead-on.

An interesting consequence of this is that if you maintain a certain orbit near the event horizon, and your version of the event horizon is closer to the singularity than that of a more distant observer, then a photon just outside your observed event horizon could reach you just fine, even though it cannot reach the more distant observer. Having received that photon, you could transmit the data from it outward, (boosting the frequency) as the distance from your gravity well to the distant observer requires an escape velocity somewhat less than the speed of light. Is this a loophole?

Why, then, do we think that a photon below the event horizon (for the observer at infinity) can’t escape the confines of the black hole? Is it only because it would be red-shifted to a zero frequency? Or is that false?

Escape velocity is merely a calculation of the velocity required to go from one gravity potential to another. If you are already in a gravitational well (like the outer edge of the Milky-Way galaxy) with an escape velocity of 300km/s, this has no effect on the escape velocity from Earth (11km/s), or the velocity needed to orbit Earth (7.5km/s). Likewise, consider a photon trapped just beyond the event horizon as viewed from an observer at infinity. To the guy in orbit around the black hole, the difference in potential is much smaller, and his relative event horizon is closer to the singularity. Won’t he see that photon? Can’t he receive it from the domain outside his apparent event horizon, but inside the event horizon of the observer-at-infinity? And then capture the photon and retransmit it?

So, even though a photon by itself can’t escape the event horizon of the observer-at-infinity, an intermediate process (natural or human) could conceivably pass a photon up through overlapping light cones, even though the light-cones at either end don’t overlap. This might eliminate the question of whether information can escape a black hole or not. The infalling observer can see what’s happening beyond the outer event horizon, and pass the information on, since his own event horizon is even closer to the event horizon.

A Variant Geometry for Spacetime

September 18, 2017

There are a lot of odd characteristics of existing spacetime physics, creating a lot of questions that are difficult or impossible to answer, such as, “Why is the speed of light approximately 300,000 km/s?” or “Why can’t you go faster than the speed of light?” or “Is there such a thing as a tachyon?” Or, “If you can’t go faster than the speed of light, how is it possible to age only 4 months due to time dilation while traveling 4 light years?” I hope to offer an alternate geometry to provide some reasonable answers to these questions.

Let’s start with some fundamental concepts about photons. It’s generally believed that photons are their own antiparticles, and also that the speed of light is the ultimate speed past which nothing can travel. Also, in a photon’s frame of reference, the distance from source to destination appears to be zero, and it takes zero time to travel that distance. This led me to speculate that light might, in fact, travel at an infinite speed, and that somewhere out there, there is a geometry in 4D space-time where that makes sense, where, when we try to measure it, we see light ambling along at a tedious 300,000 km/s. It would also explain why you can’t travel faster than the speed of light; the speed is, in fact, infinite. It’s really hard to go faster than that. The difficulty lies in finding that geometry. My second supposition regarding photons is that they are always emitted perpendicular to the path of travel (through time) of the originating particle. In a standard space-time diagram, assuming a velocity of c, this leads to the light cone diagram. In the new geometry, assuming an infinite photon speed, the picture is a little different, but still leads to the well-known equations we are used to.

Figure1

Looking at Figure 1, the vertical line A represents the source of photons a and b, which travel instantaneously to the observer on line B. Line B observes the two events a and b separated by time ct2, and from B’s perspective, the object has moved away a distance x, which equals a-b. In A’s proper time, the time between the two events is merely c time t, and the distance is zero, so the interval is s=ct1. From B’s proper time, the duration is ct2 and the distance A has traveled away from him is x, so the measured interval between the two events is s=√(ct22-x2), which should be familiar to everyone.

Figure2

In Figure 2, we see what happens as B gets closer to the X axis. But it still produces the common formula for the interval. What the diagram does not explain is why the speed of light appears to be roughly 300,000 km/s.

However, what Figure 1 can do is allow us to derive the standard time dilation formula:

∆t1=∆t2/√(1-v2/c2)

How do we get there?

Note the velocity of B away from A is

v=x/t2

 So x2=(vt2)2

From before, we had s=ct1 in A’s reference frame and s=√(ct22-x2) from B’s perspective. Set the two equations equal, and we get

(ct1)2=(ct2)2-x2

Substituting for x2 we get

(ct1)2=(ct2)2-(vt2)2

 Divide it all by c2 and pull the t2 out of the two terms on the right gives us

(t1)2=(t2)2•(1-v2/c2)

Or, ∆t1=∆t2•√(1-v2/c2), which should be familiar to a lot of you out there. It’s the standard formula for time dilation due to relative velocity.

So Figure 1 works out that if the line is at a 45 degree angle, then v=c/√2, which shouldn’t be a surprise. And as v gets closer and closer to c, then the graph gets flatter and flatter. But this graph is based on the idea that c is infinite. Why is it that when we measure it, it’s always 300,000 km/s? Clearly, if you set up an experiment that bounces light back and forth between mountain tops, and c=∞, then your test should show that light moves instantaneously. Not 300,000 km/s. And yet, we always measure c at the same boring 300,000 km/s (yeah, I know this isn’t exact value-it’s 299792.458 km/s. Get over it-this is easier to type).

So what is it that makes an infinitely fast photon measure as a finite number in all frames of reference? Is it the expansion of spacetime? Is it the curvature of spacetime due to gravity affecting the value of c that we measure? Is it that this theory is just wrong? I don’t know yet – this would obviously have to be resolved before this model made any sense, and may or may not appear in a later entry. Any speculations about this are welcome.

 

A Fool’s Physics

September 18, 2017

I’ve read a lot of physics in my life and have a lot more to read, a lot more to learn. It’s hard to read any general physics text without stumbling across some interesting tidbit that makes me sit back and ponder how that tidbit fits in with my mental model of the universe. Some things make sense, some don’t. When I heard of the Unruh effect, I was dumbfounded (to my understanding, this is the emergence of energy out of a vacuum relative to an accelerating object). When I learned that photons are their own antiparticles, I was confused. When I realized that the time component in the spacetime interval produces a hyperbolic curve in the formula, it was an enlightenment years in the coming. When I read that antiparticles are just regular particles going backward in time (Feynman, I think), that, too, messed with my mental models of the universe. To say nothing of dark matter, the accelerating expanding universe, and so on. So, I try to organize all this hodge-podge of apparently related information into a single model that makes sense. As most physicists will tell you, it is an insurmountable task. But, I am not a physicist, really. I have a Masters in Astronautical Engineering, and as Sheldon Cooper would tell you, I’m really just an engineer. I create mental models that make sense to me, but may not have any practical use or truth in the larger sense of things. But we all have to start somewhere. I’ll keep reading, and revise the incorrect bits as I go along.

In this log of ramblings, I’ll offer up a bunch of foolish ideas on physical reality. I’m a big fan of determinism, so be forewarned. I also think of time as an actual, physical dimension. If you happen to join me on this warped (!) journey of speculation, I’d love for you to tear my arguments apart, tell me what’s wrong, and perhaps help shape the speculations into something that makes a coherent sense of reality, or assure their demise.

Causality Paradox? What causality paradox?

September 11, 2017

I can’t call this real physics, this is just pure and wild speculation. I had a funny idea today about whether or not you can go back in time and shoot your grandfather, thus keeping yourself from ever being born. Ethical questions aside, I thought of a possible solution to the whole “paradox” issue.

First, if you aren’t familiar with the Grandfather Paradox, you can read up on the subject at Wikipedia at https://en.wikipedia.org/wiki/Grandfather_paradox.

Start with the idea that we are always travelling at the speed of light. You, the Sun, the Earth, your brother Bob, everything is travelling at the speed of light through the time dimension, all going the same direction so your relative speed is zero. This is a pretty common concept in modern physics, so I’m not going to expand on that here. Just more physics weirdness.

So, let’s say I get the dubious urge to go murder my grandfather at some time in the past, before I was born. Using some fantastic time machine, I go back in time to when Grandpa was just a young fella and shoot him. What happens then?

Well, imagine that space and time are a 4-dimensional matrix, but that changes made in the matrix can only propagate forward at the speed of light. Remember, that’s how fast we move through time. Eventually, the change (where I no longer exist) reaches the point where I would have gone back in time, but the particles that would have made up my body go shooting forward past that point and never go back. Well, they aren’t “shooting forward” so much as redirecting the world line of their old path at the speed of light. Now, instead of making a U-turn and heading toward their fate with my grandfather, the bullet-magnet, they continue forward in time. The old worldline going backwards collapses/disappears at the speed of light and eventually catches up to where Granddad is, and lets him live. I’m born again! And I foolishly decide, again, to go back in time and kill my granddad.

What does this result in? An oscillation. The world line shifts back and forth between the two realities, carrying the data from both possible realities, like a sine wave on a current. Just as a single electrical sine-wave can contain positive and negative values as it propagates through a wire, so can events toggle on a worldline as that worldline propagates through time. Even past the point where I made my fateful decision, the world line is toggling back and forth; both realities are true, taking their turn as the decision I made causes both of them to be real. The duration of this toggling or oscillation would be twice the duration of the time from when I went back in time to when I snuffed Gramps; the duration of the whole loop.

It’s my belief (not necessarily shared by many others) that we live in a four-dimensional space time that exists perpetually as a 4D matrix, and that what we perceive as our consciousness exists at each point along that worldline. There is the version of you that you perceive now, and the version that existed when you kissed your wife for the first time, savoring the moment you’ve forgotten. Kind of a repetitive immortality.

But what I’m suggesting above is that multiple realities can exist on a single worldline; you don’t need multiple universes dividing every time a critical decision is made or a quantum observation collapses a wave function, or a bit of antimatter goes back in time and changes an existing chemical configuration. Both events occur and exist on a changing, fluctuating, dynamic 4D worldline. There’s the version of you that remembers killing your Grandfather, and the version that never existed, propagating through time, one behind the other forever on the oscillating world line.

The normal view of a 4D worldline is of a static deterministic universe, bound by the future and past configuration of an unchanging worldline. Another view is that every decision, human or quantum, splits the universe into a multiverse, a crowded infinity of infinities. This version allows us to stick with one universe, but to modulate our worldline to allow multiple realities to exist along a single timeline.

Possibly, an outside observer could interface with either version of your reality, based on where he encounters your worldline from his own worldline. Could that be the “collapse of the wavefunction” we talk about? Good grief, that would make the Schroedinger’s Cat conundrum actually possible. Dead and alive! I always thought of it as complete nonsense.

One issue with this model is that each worldline, as it moves from one reality to another, may have to move instantaneously from the collapsed worldline to the new worldline. I think. No real way to test it, that I can imagine. Mmm…maybe pick a subatomic decay process that can have multiple durations, then have someone record the decay time data, then take off (with that data) somewhere at high-speed so your worldline is no longer in sync with the experiment’s original timeline, fast enough that the time separation is greater than the decay time variance. Then, come back and see if the recorded time is the same as it was before; you’ll have two sets of readings of the duration of a single decay, and they might not agree. Wouldn’t that be something?

 

Conservation of Linear and Angular Momentum

September 11, 2017

Some Simple Physics; Conservation of Momentum

There are no strange ideas in this entry. In fact, I might call this a boring entry. If you want to read the weird stuff, read one of my other entries.

I was sitting around reading a primer on particle physics (L.B. Okun) today, and got thinking about the conservation of linear and angular momentum.

Conservation of linear momentum means that, when you chuck something out the rear end of your spaceship, then your spaceship moves the opposite direction, so m1v1 = m2v2 . So, if you toss out a small mass of propellant from one end at a really high velocity, then you move the much larger mass the opposite direction at a much slower velocity (along with your remaining propellant). This is an exponential relationship, but that’s not what this blog is about today, so you can forget learning about that useful tidbit of knowledge.

Anyway, to increase your velocity, you have to chuck part of your mass the opposite direction. Pretty basic. If you just move stuff around inside your ship, the ship won’t move at all (except incrementally for the duration that you move around in the ship, but you won’t acquire a continuous velocity). Anyone who’s been on one of those playground spinners and tried to throw your body one way or the other knows how that works. You throw your body forward a foot, and the disk rotates a foot and stops.

So you can’t change the momentum of an object by moving stuff around inside. Not even if you have the rocket inside an enclosed sphere. The sphere won’t move.

I was recently (foolishly) wondering if that was true of angular momentum, too, if you had a rotating planet or moon, is there some way you can get energy out of the rotation by diddling around with the insides, somehow tapping the angular momentum of the planetoid for energy. Ultimately I realized you cannot in a closed system, but it should have been obvious to me all along. However, as with a rocket, you can change the angular momentum by ejecting part of the object. You can even speed up the spin a lot or slow it down.

Satellites do this sort of thing all the time. Usually they have spin they want to get rid of, and they call the technique “momentum dumping”. Two methods known to me involve extending tethers (like ballerina arms) to slow down the satellite’s spin, then releasing the tethers, or spinning up a high-speed gyro in the opposite direction of your spin (potentially dumping the core of the gyro, though I’m not certain any spacecraft does that – usually they use the gyros to turn the spacecraft both ways, hoping the overall effect will cancel out, and when the spin in one direction gets to be too much, they finally use propellant to dump the angular momentum). These are called Control Moment Gyros, or CMGs, and they usually have a minimum of three on board to cover the 3 axes.

Carrying this concept one step further, since you can eject propellant from a ship to make it go faster in a straight line, you can similarly spin up a chunk of mass from your planetoid in the opposite direction of your planetoid’s spin to make the planetoid spin faster, then eject that spinning mass into space. What amused me about the idea is that it’s essentially the same as a rocket ejecting propellant linearly to increase linear momentum, but here you are ejecting an object with accelerated angular momentum to increase the angular momentum of your planetoid. The difference being, you don’t ever have to eject the mass; it’s rotating in place, like a CMG.

That’s it. Not really that interesting, I guess. The equivalency of the two systems and the idea of “rotational rocketry” just struck me as amusing.

Trying to Accelerate an Infinite Mass

August 29, 2017

Short entry today; an easily digestible bit of physics.

A number of times in physics books and articles, I’ve come across people stating that “as an object approaches the speed of light, its relativistic mass increases, so it’s harder and harder to accelerate the steadily increasing mass, thus, you can’t speed up.”

I’d like to call bullshit on this argument. As your ship’s mass increases, so does the mass of your propellant in equal parts. If your mass doubles, so does the propellant mass being ejected out of your rockets, and you’re still obeying the law that for every action there’s an opposite and equal reaction. It’s just as easy to accelerate as it was before. You still can’t measurably reach the speed of light, but that’s for another entry I’m working on.

See? Easy peasy.