People assume there is no gravity 100Mi up but there is where does gravity "stop - Page 1
Forum section: electronics / general

author: Beamin
author_rank: Super Contributor
timestamp: March 16, 2019, 03:07:00 pm
content: A physics question: At 100 miles up around the ISS people assume there is no gravity because you are in space; no air, and when you look up you see black. Really there just happens to be no air up there because the atmosphere is not thick enough. There is almost as much gravity as the surface (995?), but since you are traveling away from the earth at a speed to balance the curve of the earth falling under you, you "float". So if the earth was a 8,000mi per side cube or flat, you couldn't orbit it 100 miles up like this?How does geosynchronous orbits work at 25k miles up? The curve falling under you wouldn't work or does that not depend on distance? Is the gravity really low, but it can't be too low because the moon is far above that. If you were standing still what are the gravity potentials? At some point around the sun you would be at 1 g since the surface is 8g; is this far out like half way to mercury or close like a few thousand miles away? At some point the earth's gravity wouldn't have much impact, but how far out does it go? A good way to put size in perspective is the codys lab youtube video where he takes the sun as the size of a pea and shows you the huge distance of the solar system to scale on a football field. America always uses the football system scale vs metric and maybe that's why we are so far behind in science. Its like having a pea influence you 20 feet away. Crazy it goes this far, but how much gravity is there at how far?

author: NiHaoMike
author_rank: Super Contributor
timestamp: March 16, 2019, 03:12:06 pm
content: https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation

author: coppercone2
author_rank: Super Contributor
timestamp: March 16, 2019, 03:21:33 pm
content: draw force vectors at various test points to get idea of how it looks like

author: ebastler
author_rank: Super Contributor
timestamp: March 16, 2019, 04:04:36 pm
content: Quote from: Beamin on March 16, 2019, 03:07:00 pmIn the time it took you to type that post, couldn't you simply have entered "Gravity" into Wikipedia's search field, and started reading to get some grounding? Or you could try the same with "geostationary orbit" as your search term, if that is your particular interest. Try it, it works!

author: apis
author_rank: Super Contributor
timestamp: March 16, 2019, 04:10:46 pm
content: \$ F = G \frac{m M}{r^2} \$F is the gravitational force pulling objects together, G a constant, m and M are mass of objects, r distance between them (gravitational centers). I.e. the gravitational force decrease with the square of the distance, but it never reaches zero.At a stable orbit the gravitational force is equal to the centrifugal force. At geosynchronous orbit the speed you need to generate the right amount of centrifugal force is such that it matches the speed at which the earth rotates, so the satellite will remain over the same spot on earth.

author: ebastler
author_rank: Super Contributor
timestamp: March 16, 2019, 04:44:48 pm
content: Quote from: 3roomlab on March 16, 2019, 04:34:29 pmCount for what? I don't think this concept is required to answer any of Beamin's questions.

author: coppercone2
author_rank: Super Contributor
timestamp: March 16, 2019, 06:01:07 pm
content: if you draw the vectors at various points with a reasonable total distance the points will be assumedor at least that one exists.i think there is a shoelace string method of approximating themif you like, zoom out various force vectors with arrows pointing to points between a crossline, it might be better then other methods of getting an idea of how the field looks like (compared to color density grading). by transforming& the coordinate system from spherical to a linear vector at fixed points you can get a linear scale idea of how you would feel the forces

author: T3sl4co1l
author_rank: Super Contributor
timestamp: March 16, 2019, 10:56:10 pm
content: You have to be multiples of Earth's radius away to see gravitational acceleration drop significantly.LEO is very close indeed, so the velocity is high, and the gravity similar.Gravity is inverse square with distance, so there is no point where gravity "stops". It stops at infinity, but space itself is finite (for all intents and purposes).Lagrange points, in a 3-body system with three very different masses (like the Sun, Earth and a satellite), are 1:1 resonant orbits that follow the middle-mass object. But that's not cancelling out gravity, that's still an orbit.Tim

author: Mr. Scram
author_rank: Super Contributor
timestamp: March 16, 2019, 11:10:11 pm
content: Quote from: Beamin on March 16, 2019, 03:07:00 pmGravity never ends. It just drops off according to the inverse-square law, which means it can effectively be ignored at large distances for most things. At larger distances it ever decreases, but shouldn't ever reach zero. As far as we understand all parts of the entire universe are interacting gravitationally with all other parts, but there seem to be some forces in the mix we don't quite understand yet. Geosynchronous orbits work because that's the altitude where the orbital speed matches up with the rotational speed of the Earth. This means that from the viewpoint of the Earth, satellites appear stationary. They're most definitely not truly stationary, as they would plummet towards the Earth if they were. It's simply that Goldilocks zone where the two speeds match up and produce a useful effect. Any planet should have a similar zone at a different altitude, except for those spinning so fast the required orbital velocity exceeds the escape velocity.

author: coppercone2
author_rank: Super Contributor
timestamp: March 16, 2019, 11:11:30 pm
content: according to models. imagine if forces had fixed bounds (maybe shows up when the universe gets big enough and stuff gets far away enough)if someone can figure out the ramifications/math behind this idea it would be interesting. its very contrary to everything though.

author: Rerouter
author_rank: Super Contributor
timestamp: March 16, 2019, 11:24:49 pm
content: Gravity never stops, If mass is in our observable universe, its imparting some influence on you right now, even if that force is so small that black holes would burn out before it made a measurable change,However like any other force, you can find ways to cancel it out, or at least reduce it close enough to 0 that for most practical purposes its irreverent, the ISS actually has a small force biasing dust and similar to the leading edge of the space craft, as the trace atmosphere of earth is constantly decelerating it, even if its a tiny amount the force is still there,So when your on a space craft, don't think gravity = 0, think the rate of turn of the orbit is enough that I'm constantly falling towards the earth at the same amount that its tugging me down, even if your in a highly eccentric orbit, as your zooming by getting furthur away from earth, your orbit is still being curved by the gravity, so even as you move away from the earth, its still being accelerated towards it.

author: Circlotron
author_rank: Super Contributor
timestamp: March 16, 2019, 11:35:00 pm
content: As the sun burns it gradually loses mass, so presumably it’s gravity would get weaker. Say you are several light years away monitoring this gravity. Do you see this change instantly or does it travel to you at the SOL? (if you’ll pardon the pun...)

author: Mr. Scram
author_rank: Super Contributor
timestamp: March 16, 2019, 11:37:55 pm
content: Quote from: Rerouter on March 16, 2019, 11:24:49 pmThat's actually why it's preferably called microgravity, rather than zero gravity.

author: apis
author_rank: Super Contributor
timestamp: March 16, 2019, 11:49:33 pm
content: Quote from: Circlotron on March 16, 2019, 11:35:00 pmIt travels to you with the SOL. (In classical mechanics it would have been instant).Quote from: T3sl4co1l on March 16, 2019, 10:56:10 pmWell, at e.g. L1moon and earths gravity are equal but working in opposite directions. Gravity is really just curvature of space and space would be flatter there. So in some sense, calling it cancelling might be appropriate.

author: Rerouter
author_rank: Super Contributor
timestamp: March 17, 2019, 12:00:58 am
content: The gravity of distant objects and where they are visually so far always line up, so its speed of light, If it was not, all the black hole mergers we have been recording from hundreds of light years away should show a bias in the direction they where travelling relative to us.

author: Nominal Animal
author_rank: Super Contributor
timestamp: March 17, 2019, 04:14:51 am
content: Quote from: Beamin on March 16, 2019, 03:07:00 pmYou don't travel away from the Earth; youorbitEarth. When the orbit is circular, you stay at a constant distance from Earths center of mass. "Float" is not a good term for describing the situation in an orbiting object;micro-g environment, orfree fallare much more precise.To get to orbit, you need to get to the altitude of that orbit, but also sufficient velocity to remain in that orbit. As an example, theISSorbits at an altitude between 330 km and 435 km, or about 6700 to 6800 km from Earths center of mass, at a velocity of 27,600 km/h or 7.66 km/s. So, to get to the International Space Station, you not only have to "climb up" 330 km, but also accelerate to 27,600 km/h (17,150 mph).You do have the right idea, I think. Essentially, at a circular orbit, your tangential velocity is such that even though you are in free fall -- the main force acting on you being Earths gravity, "falling towards Earth", you continually miss Earth.To escape Earth orbit, you need a velocity --escape velocity-- of about 40,000 km/h, or 25,000 mph. It does not matter in which direction you start, as long as it is not towards Earths center of mass (because you cannot tunnel through).Quote from: Beamin on March 16, 2019, 03:07:00 pmThe orbital velocity is such that each orbit takes 24 hours. If the orbit is around the equator (the same axis Earth rotates around), then the orbit is roughly stationary above a point on the equator. Technically, these aregeostationary orbits.If the orbit is tilted, the object stays above the same latitude, but its longitude changes sinusoidally, so that at the same time of day, it is always over the same point. In general, such orbits aregeosynchronous(but not necessarily geostationary) orbits.Quote from: Beamin on March 16, 2019, 03:07:00 pmThe mean radius of Earth is about 6371 km, and the standard acceleration due to gravity (at that distance) is 1 g = 9.80665 m/s2=g0. (Note that on equator, if you measure it, you'll get about 9.78 m/s2; the difference is due to rotation of Earth around its axis.)You can estimate the acceleration due to Earths gravity at altitudehusingg0(6371 km / (h+ 6371 km))2. Thus, at an altitude of about 2,650 km, the acceleration is halved; at an altitude of about 13,780 km, the acceleration is one tenth of what it is on sea level. At a circular geosynchronous orbit 35,786 km above the equator, the acceleration due to Earths gravity is just one 44th, or about 0.224 m/s2. Near the moon, Earths pull is one 3640th, or only about 0.0027 m/s2.While there is no limit to how far gravity reaches, its effects are swamped by other local objects pretty fast. Remember, even interstellar space is not truly empty, but has an occasional hydrogen atom, dust, and so on.Interestingly, even though space seems to be expanding, theShapley Superclusterabout 650 million light years away, in the direction our own Galaxy is headed, is a gravitationally interacting supercluster of galaxies: it is pulling itself together rather than expanding with the universe. (The Great Attractor is in the same direction, about 250 million light years away.) So, if you or your kids ever get that existential fear of the expansion of space pulling everything away, leaving just Earth and our Sun alone, look up the Great Attractor and the Shapley Supercluster.(I mean, just thinking/saying that it will all happen millions to trillions of my lifetimes later, while true, does not really help with such fears. Showing that the universe is not that simple and straightforward, and that although space itself is expanding there are unimaginably large structures that are not just spreading apart. Replace fear with wonder.)Quote from: coppercone2 on March 16, 2019, 11:11:30 pmIn moleculary dynamics, when you use non-quantum models (i.e., interatomic potential models), that is exactly what you do: you ignore the contribution of atoms further than a fixed distance. This is called thecut-off distance.It works pretty well in practice, when the ignored interactions are tiny. For a solar system simulation, it means that Sun's gravity dominates, unless you are very close to another object; "close" depending on the mass of said other object.In larger simulations -- galaxies, with hundreds of millions to trillions of stars --, you can combine the gravitational effects of a group/cluster/region of stars with just one point (as if their entire mass was at their center of mass) for calculations sufficiently far away. Again, you can only do that at sufficient distance without too much error, the distance depending on the size and density of the region considered. (To simplify, if you try to model how two galaxies collide, and you start say the galaxies being separated by ten times the sum of their diameters, you can certainly just use their centers of masses to calculate the attraction. This simply gives the same answer, to several significant digits, as you'd get by calculating the pairwise attraction of each unique star pair in the two galaxies. The difference (error!) increases as the distances decrease, of course.)It all boils down to relative significance. If you have a force acting on an object at magnitudeF, and you know that because of the size of your numerical integration time step, it has error bounds of about ±0.001F. If the sum of other forces are of magnitude ±0.0001For less, they can be ignored, because their contribution is within noise of the simulation or measurement.

author: orin
author_rank: Frequent Contributor
timestamp: March 17, 2019, 05:10:05 am
content: Quote from: apis on March 16, 2019, 04:10:46 pmEr, that would be centripetalforce. Which would have to be\$ \frac{m v^2}{r} \$for a circular orbit where v would be the magnitude of the velocity of the satellite.My physics teacher would bust a gut if anyone ever mentioned 'centrifugal' force.

author: TheNewLab
author_rank: Frequent Contributor
timestamp: March 17, 2019, 05:30:07 am
content: I was going to explain but everyone else has done an excellent job, so I'll be obnoxiousCENTIGRADE!! means strictly "angular velocity" regarding satellites .I want to scream whenever someone say the temp is xy centigrade.. it's CELSIUS, CELSIUS, CELSIUS !!It amazes me when so many physicists make this error, respected Engineers, climatologistsPlease oh please just remember Celsius and whenever someone says centigrade. think "angular velocity" what satellites do, and what the mariner and other space craft to loop around the sun and accelerate further into deep space.How obnoxious is that?

author: Monkeh
author_rank: Super Contributor
timestamp: March 17, 2019, 05:45:24 am
content: Quote from: TheNewLab on March 17, 2019, 05:30:07 amIt was centigrade for a couple centuries, history dies hard.

author: Rerouter
author_rank: Super Contributor
timestamp: March 17, 2019, 05:46:16 am
content: I applaud an american using Celsius to begin with,Work with enough cold stuff, so I just use kelvin

author: GeorgeOfTheJungle
author_rank: Super Contributor
timestamp: March 17, 2019, 06:44:40 am
content: If the ISS is traveling at 27,600 km/h, I, sitting in my sofa, am traveling at 6371*2*pi/24= 1668 km/h.

author: Mr. Scram
author_rank: Super Contributor
timestamp: March 17, 2019, 07:07:58 am
content: Quote from: GeorgeOfTheJungle on March 17, 2019, 06:44:40 amDid you take into account that the ISS isn't in a geostionary orbit?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: March 17, 2019, 07:18:53 am
content: Quote from: Rerouter on March 16, 2019, 11:24:49 pmOr even if it's not -- there could be matter outside of our horizon, which doesn't have an effect on us directly, but is nonetheless observable based on its interaction with the matter over there (matter which has a horizon that includes both the observer and the distant mass).Tim

author: T3sl4co1l
author_rank: Super Contributor
timestamp: March 17, 2019, 07:41:07 am
content: Quote from: apis on March 16, 2019, 11:49:33 pmNot only that, but where does the massgo?It flows away from the star into the surrounding interstellar medium. Say this is an impulsive event like blowing off a shell of material in a nova. If material is emitted in all directions uniformly, then its gravity still seems to be coming from the same center of mass. Any bodies orbiting the star, don't know any better until the material passes their orbit -- as long as all the material lies within a Gaussian surface of lesser radius than the orbit in question, nothing has changed.As the material expands, slows and cools, and collides with the greater interstellar medium, the apparent mass of the star finally drops.Which will be a very gradual process. So, even for an impulsive initial event, you can expect the observation (at a distance) to be very well filtered indeed, when observed in this way (i.e., extremely low frequency (sub-nHz) g-wave astronomy).QuoteYeah. It's still an orbit though -- you have nonzero angular momentum around the Earth. It's cancelling in relative motion (which, really, is the only important metric that matters), but it's also still an orbit, or at least what I would call one.A somewhat more contrived, but as far as we know, entirely possible, case, would be sitting in the center of a torus world: the planet can be sitting at rest in an otherwise perfectly empty universe, no forces acting on it (thus it isn't a special case orbit). The planet spins to maintain its shape, but the object floating in the center doesn't rotate along with it (at least, classically speaking).Catch though, it's still an orbit, just one that has a (unstable) fixed point. It's part of a family of orbits where the satellite bobs through the center of the torus (AFAIK).Tim

author: Rerouter
author_rank: Super Contributor
timestamp: March 17, 2019, 07:51:29 am
content: Nope, that is a step too far, again, the observable universe is literally based on light speed vs the expansion of space-time since the big bang, If light could not cover the gap, then neither has the gravity, so if you can "see" the reaction to mass, you are also affected by the gravity from it,As even if it was in a straight line behind what we where observing, the gravity of those objects reached what we where observing at the speed of light, then both the light of the observed object and the gravity of the objects behind as it was interacting at that particular second both continued our way to be observed. independent of how space time has stretched since then.

author: GeorgeOfTheJungle
author_rank: Super Contributor
timestamp: March 17, 2019, 08:48:39 am
content: Quote from: T3sl4co1l on March 17, 2019, 07:41:07 amI think what flows away is energy not mass, at a rate of 9e16 Joules per kg of mass lost (E=mc2). No?

author: GeorgeOfTheJungle
author_rank: Super Contributor
timestamp: March 17, 2019, 08:53:07 am
content: Quote from: Mr. Scram on March 17, 2019, 07:07:58 amIDK, I just copy-pasted the speed from reply #15...

author: Beamin
author_rank: Super Contributor
timestamp: March 17, 2019, 09:11:30 am
content: Quote from: T3sl4co1l on March 17, 2019, 07:41:07 amSo if you had a donut planet and were in the center would frame dragging cause you to spin? That energy has to go some where or would it cancel out since you are in the center?At some point you are so far away that gravity would pull you or the wave of gravity would be less then 1/2 a plank length if this happens gravity would have no effect since you can't move 1/2 a plank anything. So a limit to things after all?

author: Rerouter
author_rank: Super Contributor
timestamp: March 17, 2019, 09:30:48 am
content: The planet would not be what spins you, but rather the atmosphere, if the torus was not sufficiently wide,Frame dragging essentially twists space time, it doesn't actually constantly keep that local bit of space time spinning.Also gravity is one of those fun macroscopic things based on our current math, it doesn't really work for singular atoms, you can think of it like a friction-less slope, any mass tugs it down on a certain point, accelerating you towards it, however there reaches a point where its hard to tell it apart from flat, your still being accelerated, but our current technology cannot really measure it, also while the smallest distance may be a plank length, under what time scale, if I say its accelerating at a plank length per year, is it truly not moving, or just so slow you can never see its effects.All of our most sensitive positioning sensors are based on interferometry, which is limited to phase resolution of a given frequency of light. that light has a certain wavelength, and we can only resolve the phase difference, e.g. a fraction of that wavelength to a certain value, so its that fraction of a wavelength we cannot measure under, at-least for now. If you really want to dig into it, they actually had to tweak the uncertainty principle in there favor to get as accurate measurements as they do now.

author: Nominal Animal
author_rank: Super Contributor
timestamp: March 17, 2019, 11:00:23 am
content: Quote from: GeorgeOfTheJungle on March 17, 2019, 06:44:40 amAround Earths axis of rotation, yes. (r= 6371 km, circumferencep= 2 πr≃ 40030 km.pin 24 hours isv= 40030 km / 24 h = 1668 km/h.)ISS is not in a geostationary orbit, it's inlow Earth orbit.However, our sun rotates around the center of the Milky Way galaxy at about 217 km/s, or 781,000 km/h; with an orbital period of about 225 million years. When the dinosaurs roamed on Earth, we were on the other side of the galaxy. (Many of the stars near us have very similar orbits, of course.)So anyway, technically you're moving at around 782,000 km/h relative to the center of the Milky Way; at around 1700 km/h with respect to the center of Earth, and 0 km/h with respect to the ground under your feet.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: March 17, 2019, 11:44:15 am
content: Quote from: GeorgeOfTheJungle on March 17, 2019, 08:48:39 amA little, yes.I can't find a ballpark answer for how much is shed during red giant/supergiant phases, or the various superlatives of novas, but I'm guessing it's sizable (~solar masses).The nuclear mass fraction is fairly modest, a few percent give or take, as far as I know.By the way, light still has mass equivalence and so warps spacetime. If a star suddenly poofed into energy, you'd feel the same gravitational pull until the expanding wave of energy passes you, at which point... well, you'd be burnt to a crisp, because supernovas alone are utterly unimaginably powerful, let alone a total mass conversion. But aside from that, the gravity would stop at that point.Tim

author: T3sl4co1l
author_rank: Super Contributor
timestamp: March 17, 2019, 12:01:12 pm
content: Quote from: Beamin on March 17, 2019, 09:11:30 amI was afraid you were going to ask this. Hence why I added "classically".With an incredibly sensitive instrument, it would be just detectable, yes. (Gravity Probe B, orbiting Earth, managed a 19% error bar on this measurement.)QuoteWhat energy, length?The average wavelength of virtual (force-carrying) particles is irrelevant to most problems, and doubly irrelevant to classical and relativistic problems.One problem I'm quite fond of: treat the Earth-Sun system as a quantum bound system (i.e., a hydrogen atom, with the particle masses substituted appropriately, and charge replaced with mass). What is:1. The quantum number of this system?2. The energy difference between the quantum numbers N and N-1?3. What is the period (t = 1/f = lambda/c) of this energy, assuming it's emitted as a photon-like particle?Answers:1. Ridiculously large. Needless to say, the quantization of Earth's orbit will not cause any navigational or astrophysical complications.)2. This requires a roundabout calculation to avoid rounding; suffice it to say, it's fuck-all energy.3. Somewhere around 31.5e6 seconds. In other words, we've gone to the trouble of using quantum mechanics to solve for an orbit Newton already knew about...Tim

author: CatalinaWOW
author_rank: Super Contributor
timestamp: March 17, 2019, 01:53:36 pm
content: Quote from: Mr. Scram on March 16, 2019, 11:37:55 pmWhile a number of organizations and people are pushing microgravity, it is just as wrong as zero gravity. Micro-acceleration would be more accurate. It only really matters while you are learning. Those who understand what is going on won't be confused by the older term or the newer wrong one. And those who are just spectator parrots (most newsreaders for example) will mangle it whatever term is used. zero g has the advantage of being easier to say and conveys the physical experience.

author: GeorgeOfTheJungle
author_rank: Super Contributor
timestamp: March 17, 2019, 03:07:49 pm
content: Quote from: Nominal Animal on March 17, 2019, 11:00:23 amFlying at Mach 633 and still every hair in place!

author: apis
author_rank: Super Contributor
timestamp: March 17, 2019, 08:42:04 pm
content: Quote from: orin on March 17, 2019, 05:10:05 amYour physics teacher is correct, but so was I (explanation after calculations).If you're in a spaceship in orbit around the earth you experience the gravitational force pulling you inwards, which is\$ F = G \frac{m M}{r^2} \$You also experience apseudo force, thecentrifugal force, pulling you outwards:\$ F = \frac{m v^2}{r} \$Wherevis the speed.We can combine the formulas giving us\$ r v^2 = G M \$\$ G = 6.67408 \cdot 10^{-11} \space [ m^{3} kg^{-1} s^{-2} ] \$ (the gravitational constant)\$ M = 5.972 \cdot 10^{24} \space [ kg ] \$ (the mass of the Earth)If we knowvwe can solve forrand vice versa.TheISSorbits at an altitude of about 400 km (~250 mi), and the earths radius is about 20000/pi km, so the distance to the center of the earth is about:\$ r_{ISS} = 6.766 \cdot 10^6 \space [ m ] \$Solving for v gives us the orbital speed:\$ v_{ISS} = \sqrt{\frac{G M}{r_{ISS}}} \approx 7.7 \space [ km/s ] \approx 28000 \space [km/h] \approx 17000 \space  \$ .We could also solve forr. Say we want to know the altitude of ageostationary orbit. The Earth rotates around its axis once every day, so the rotational period is:\$ T_{Earth} = T_{GEO} = 60 \cdot 60 \cdot 24 \space[ s ] \$We want our satellite to orbit with the same period which we denote TGEO. The speed is distance over time, so for a circular geostationary orbit we get:\$ v_{GEO} = \frac{2 \pi r}{T_{GEO}} \$Combining it with our formula and solving forrgives us:\$ r_{GEO} = \sqrt{\frac{G M T_{GEO}^2}{4 \pi^2}} \approx 42 000 \space \$To get the altitude above the Earths surface we need to subtract the Earths radius, doing so yields an altitude of about 36 000 km (22 000 mi).The problem with the centrifugal force is that it is apseudo force, not a real force. The astronaut would experience the fictitious centrifugal force because the astronaut isn't in an inertial frame of reference. We have constant speed but circular instead of straight line motion*. So the astronaut is accelerating in towards the earth. Sometimes people say the ISS and other satellites are in free-fall.If we look at the satellite and earth from the perspective of an inertial frame of reference, for example, from another spaceship at thesun-earth L1point**, then we don't see any centrifugal force, only the gravitational force. Since the satellite is in a circular orbit (elliptic really) around the Earth the gravitational force would be the centripetal (center seeking) force and therefore \$ r v^2 = G M \$ (that explanation would perhaps make your physics teacher happier, but I find it a little less intuitive).* According to Newtonian mechanics, see below.** Of course, that isn't an inertial frame of reference either, it's in orbit around the sun, which is in orbit around the galaxy... But somehow it all works out so we don't notice. That line of thought leads us towards general relativity which concludes that gravity is really the bending of space time. These orbital trajectories are actually following straight lines through curved space time...

author: rstofer
author_rank: Super Contributor
timestamp: March 18, 2019, 02:52:02 am
content: Quote from: Beamin on March 16, 2019, 03:07:00 pmMay I remind you of July 20, 1969? No country on Earth has come close to recreating the Apollo 11 Moon landing of nearly 50 years ago.I don't see us playing 'catch-up' to any other country.

author: Mr. Scram
author_rank: Super Contributor
timestamp: March 18, 2019, 03:04:32 am
content: Quote from: rstofer on March 18, 2019, 02:52:02 amWhen's the next US manned launch?

author: Nominal Animal
author_rank: Super Contributor
timestamp: March 18, 2019, 03:35:09 am
content: Quote from: rstofer on March 18, 2019, 02:52:02 amNo, although at leastMars Climate Orbiterwas lost (in 1999) because a nincompoop used olden style units instead of the SI units specified in the contract between NASA and Lockheed.If we look at USPISAmeasurements for science education, it would look like US is behind many other western countries. However, if one looks at only white and asian US "scores" (in that Wikipedia article; 526/527 in 2015 for science), they're very near the top, at par with Canada (528), Finland (531), and Estonia (534); with only Singapore (556) and perhaps Japan (538) with notably higher "score" in science literacy.So, it's not like science education is lagging everywhere in the US, only that there are lots of people with poor science and math literacy in the US.

author: CatalinaWOW
author_rank: Super Contributor
timestamp: March 18, 2019, 04:08:44 am
content: Quote from: Nominal Animal on March 18, 2019, 03:35:09 amThat same dynamic applies in life span, birth survival and any number of other metrics where the US seems to fair poorly compared to the world. Many of the large, diverse countries show this pattern. China, Russia and others.

author: CZroe
author_rank: Contributor
timestamp: March 18, 2019, 07:22:40 pm
content: Didn’t read the thread, but gravity is essentially universal. It’s why we can detect gravity waves from merging neutron stars/black holes in other galaxies. Everything is relative up to the point where the expansion of the universe between overcomes the forces between.

author: apis
author_rank: Super Contributor
timestamp: March 18, 2019, 07:34:00 pm
content: Quote from: Nominal Animal on March 17, 2019, 11:00:23 amIt's easier to remember the other way around. The meter was originally defined as 1/10'000'000 of the distance from the north pole to the equator, so it's no coincidence that the circumference is about 40'000 km. Therfore r~=20'000/π.

author: rstofer
author_rank: Super Contributor
timestamp: March 18, 2019, 09:31:49 pm
content: Quote from: Mr. Scram on March 18, 2019, 03:04:32 amI think they're starting to look at it now. I read somewhere about a permanent Moon base and, of course, SpaceX just tested a Crew Dragon but that is only part of the solution - more like an orbiter for the ISS. I think the Chinese have everybody worked up after their 'landing' on the dark side of the moon.https://www.nbcnews.com/mach/science/moon-bases-being-planned-now-may-show-us-how-live-ncna855826I'm not sure when we will be returning but it can't be soon enough! We absolutely MUST control the Moon before the Chinese show up.

author: Rick Law
author_rank: Super Contributor
timestamp: March 19, 2019, 03:20:24 am
content: Quote from: Beamin on March 16, 2019, 03:07:00 pmIf I may introduce you how a technique (sometimes called the) "reasonability test" can apply here for a quick answer.1. We all know the moon is a captive of earth due to gravity2. We know the moon is a lot father than 100 miles to earth (about a quarter-million miles actually)3. If we know both 1 and 2 are true, it is therefore reasonable to assume gravity must work a lot father than 100 miles.

author: Circlotron
author_rank: Super Contributor
timestamp: March 19, 2019, 04:04:41 am
content: Quote from: Rick Law on March 19, 2019, 03:20:24 am

author: GeorgeOfTheJungle
author_rank: Super Contributor
timestamp: March 19, 2019, 08:26:50 am
content: Quote from: rstofer on March 18, 2019, 09:31:49 pmWhy? And who is "we"?

author: Circlotron
author_rank: Super Contributor
timestamp: March 19, 2019, 09:12:38 am
content: ^^ Larger version of South China Sea?

author: rstofer
author_rank: Super Contributor
timestamp: March 19, 2019, 02:16:03 pm
content: Quote from: GeorgeOfTheJungle on March 19, 2019, 08:26:50 amIf the Moon is going to be militarized, and it will, I would rather it be the US than China. Yes, there is a treaty about that kind of thing but treaties come and treaties go. Some last longer than others...What I don't understand is why all of the money that should have fed NASA has been diverted to less important work.If it wasn't a military project, why land on the dark side of the Moon where nobody can see what you are doing?Pay attention to the Panama Canal!

author: apis
author_rank: Super Contributor
timestamp: March 19, 2019, 02:24:50 pm
content: Most space agencies talk about an international lunar base with private corporations also participating. While the motivation for developing space capabilities are no doubt in large part military, a moon base probably would not be.

author: Mr. Scram
author_rank: Super Contributor
timestamp: March 19, 2019, 05:46:16 pm
content: Quote from: rstofer on March 18, 2019, 09:31:49 pmJudging from the roadmap the US has about 5 years of catching up to do before it may possibly launch people into orbit, which is what others are doing right now.

author: CatalinaWOW
author_rank: Super Contributor
timestamp: March 19, 2019, 07:55:04 pm
content: Quote from: Mr. Scram on March 19, 2019, 05:46:16 pmThat is both optimistic and pessimistic. "As others are doing right now". The Russians have shown an ongoing capability to put folk in orbit. The Chinese have shown they can do it every once in a while. No one else has an on going orbital launcher.The US roadmap has three primary paths. Two commercial and one government. The government plan is five plus infinity minus a couple from launching. The two US commercial teams should be putting people in orbit in a few months. There are a couple of other commercial paths that may beat the government path. I

author: Beamin
author_rank: Super Contributor
timestamp: March 19, 2019, 09:19:54 pm
content: Quote from: T3sl4co1l on March 17, 2019, 11:44:15 am

author: Beamin
author_rank: Super Contributor
timestamp: March 19, 2019, 09:26:06 pm
content: Quote from: T3sl4co1l on March 17, 2019, 11:44:15 am99.9% of the supernova and it's energy is in the form of neutrinos. That to me is crazy that super novas are 1000 times more powerful then what we see. I wonder what happens to matter that has been soaked in neutrinos like the effects we look for in our detectors on CCl4 molecules. Aliens probably have a use for neutrino treated matter. That would be an exotic material.Also some other facts a lot of the hydrogen in space stays as H instead of H2 because even in thick gas clouds we can see the density is still lower then a vacuum tube or even our best vacuums. So imagine how big a volume that would have to be to convert the atmosphere inside a vacuum tube into say a neutron stars density, or even air.

author: hamster_nz
author_rank: Super Contributor
timestamp: March 19, 2019, 09:31:15 pm
content: If you want to develop a bit of an understanding for this, there is a really neat App called "Spaceflight Simulator" by Stefo Mai Morojna.It is like Kerbal Space Program, but in a more 2D 'bubblegum' form.Build and launch rockets, land on moons, aero-brake to a Mars landing...Sorry for all the hours you will waste....

author: KL27x
author_rank: Super Contributor
timestamp: March 19, 2019, 10:00:05 pm
content: QuoteAnother practical limiting factor for planets is the atmosphere. If the geosynchronous orbit is so low that a satellite would encounter significant atmosphere, it will experience decay and cannot be stable without some occasional correction.OP: Magnets. If you want to visualize the effect of gravity over increasing distance, play with a couple magnets. Magnetic attraction is proportional to the inverse of radius (distance) squared, as is gravity.

author: mrflibble
author_rank: Super Contributor
timestamp: March 19, 2019, 11:15:11 pm
content: Ohnoez, I entered one of thoseinsightful questionthreads.While I'm here, have atopic related internet cookie.Fleeeeeeee!!!!!

author: Nominal Animal
author_rank: Super Contributor
timestamp: March 20, 2019, 06:15:59 am
content: If you think about Lagrangian points (where the forces due to gravity cancel out), and consider the entire Solar system, you discover theInterplanetary Transport Network.These are not necessarily suited for human transportation at all, because they are slow; they just require very little energy. What they could be used for, is transferring materials to and from between Earth and other gravity wells, and other locations around the system.Because such transfers would be efficient, but extremely slow (years and longer), a practical space economy would have hundreds if not thousands of "packages" en route at any given time. Our quartal-based economy cannot currently deal with that kind of time scales, though. Although micro-g materials science might prove an important field, I suspect He3surface "mining" (surface deposition from solar wind) at dwarf planets like Ceres, and cannoned to low-energy transfer orbits to the Earth-Moon system, might be a solution to humanity's energy needs (on top of local renewables like solar, hydro, and geothermal power). At only 0.029g surface gravity and 0.51 km/s or 1836 km/h escape velocity, the mass launcher needed is much weaker than e.g. on the Moon.

author: Beamin
author_rank: Super Contributor
timestamp: March 20, 2019, 01:18:10 pm
content: Quote from: hamster_nz on March 19, 2019, 09:31:15 pmCan you play that on the computer? I hate using things on the phone with a tiny screen and no mouse oh yeah and giving up my GPS data pics texts and phone book.

author: GlennSprigg
author_rank: Super Contributor
timestamp: March 26, 2019, 12:48:39 pm
content: Page-1... AArrgghh...Page-2... AArrgghh...Page-3... AArrgghh...'Gravity' exists between ALL masses in the Universe.It's 'force' is inversely proportional to the square of the distance to another object.It has NO boundaries !!!!!That's it !!!

author: coppercone2
author_rank: Super Contributor
timestamp: April 30, 2019, 05:48:03 am
content: i still want to know the ramifications of gravity having a deviation from the accepted equation under some condition

author: CatalinaWOW
author_rank: Super Contributor
timestamp: April 30, 2019, 09:14:48 am
content: You and everyone else in the world. But in reality there are NO consequences for us like in here. If there were we would have detected them earlier. The possible long range differences could impact the size and age of the universe and the eventual fate of same, but on the human scale there isn't anything to see.

author: hamster_nz
author_rank: Super Contributor
timestamp: April 30, 2019, 11:11:17 am
content: Quote from: GlennSprigg on March 26, 2019, 12:48:39 pmNo!All mass warps space-time in a consistent way (proportional to its mass), and masses will move based on the local gradient of space-time (along with their current momentum) unless a force is applied.There is no "gravitational force". You are measuring the force required to resist against the differences in gradient of space-time.This is why you can put an impenetrable barrier between two masses, yet gravity still works.There are no Faraday shields for gravity... unlike Colomb's law, which looks much the same ( F=k * q1 * q2 / r^2 ) but works completely differently.

author: Dubbie
author_rank: Unknown
timestamp: April 30, 2019, 11:19:05 am
content: I suspect that's why there where quotes around "force"If Beamin is having trouble with 400 year old Newtonian gravity, then I'm not sure the idea of spacetime gradients will be useful!

author: Nerull
author_rank: Frequent Contributor
timestamp: April 30, 2019, 03:24:36 pm
content: Quote from: Rerouter on March 17, 2019, 07:51:29 amThat may not be entirely true.There is a hard limit to how far we can "see" using electromagnetic radiation - the cosmic microwave background. Before this moment in the universe, it was not transparent to photons. It is the furthest, oldest thing we can see, and is expanding away from us faster than anything else.But it wasn't opaque to gravity, or gravitational waves. The possibility exists, though remote, that we we could peak past the CMB using non-EM observation methods, and get a sense of what is in there without "seeing" it.There are also a lot of pop-sci misconceptions out there about how superluminal expansion relates to the particle horizon:https://arxiv.org/pdf/astro-ph/0310808.pdf

author: Nerull
author_rank: Frequent Contributor
timestamp: April 30, 2019, 03:34:07 pm
content: Quote from: coppercone2 on April 30, 2019, 05:48:03 amThere is no observational evidence that this should be the case. There have been several attempts at modified gravity theories, but none of them really work. The fact that can isolate where dark matter is and that it isn't uniformly distributed is a major problem for any theory that tries to explain it via modified gravity.Some variation of "What if there's no dark matter, gravity just works differently on large scales?!?!?" gets posted by people who fashion themselves deep thinkers but know almost nothing beyond pop-science almost daily on physics threads, enough that its become kind of a meme:

author: paulca
author_rank: Super Contributor
timestamp: April 30, 2019, 03:47:21 pm
content: Go and playhttp://orbit.medphys.ucl.ac.uk/

author: Beamin
author_rank: Super Contributor
timestamp: May 01, 2019, 11:38:11 pm
content: Quote from: GlennSprigg on March 26, 2019, 12:48:39 pmIn theory but in practice it may have a limit think of a gravitational wave having an influence of moving a detector or anything 1 atom's length that's where we are at now, but if you saw that the gravitational wave has a smaller and smaller influence until say its moving the space time "ripple" one plank length. Then if its weaker then that, say 0.4 plank lengths for a ripple size there would be no ripple since you can't have 2/5th of a plank anything; the universe has pixels at that size even plank times! So once the gravitational wave goes below that value it is essentially zero. Would be interesting to see how small a wave a "LIGO/LISA" the size of the universe could detect. A plank length? More then a plank length?

author: Circlotron
author_rank: Super Contributor
timestamp: May 02, 2019, 12:39:01 am
content: ^^ Beamin is the new Archimedes Plutonium.

author: hamster_nz
author_rank: Super Contributor
timestamp: May 02, 2019, 02:19:16 am
content: Quote from: Circlotron on May 02, 2019, 12:39:01 amI quite like how he ponders things actually/I often think about things like "Could you siphon fuel from one rocket to another on the moon (i.e. in a vacuum)?"I'm just not the sort to post all my ponderings on EEVblog.

author: Circlotron
author_rank: Super Contributor
timestamp: May 02, 2019, 02:34:31 am
content: It's good to muse amongs you peers. I have often pondered whether a magnetic field can be made to rotate axially. The standard answer is no, but I did formulate a decision tree that leads to the awkward choice of two unacceptable conclusions. I'll post that some day soon.

author: paulca
author_rank: Super Contributor
timestamp: May 02, 2019, 06:37:34 am
content: Quote from: Circlotron on May 02, 2019, 02:34:31 amYea and if light is electromagnetism with the magnetic field 90* to the electric field and light can be polarised and rotated on all axis... can magnetic fields be polarised and rotated? I have no idea what I'm talking about but it is fun to ponder.

author: Beamin
author_rank: Super Contributor
timestamp: May 03, 2019, 05:32:21 pm
content: Quote from: hamster_nz on May 02, 2019, 02:19:16 amShe* But I guess since 99% of the posters on an electronics forum are male its a valid assumption.

author: hamster_nz
author_rank: Super Contributor
timestamp: May 03, 2019, 07:27:06 pm
content: Quote from: Beamin on May 03, 2019, 05:32:21 pmOpps, sorry. A very valid point noted

author: windsmurf
author_rank: Frequent Contributor
timestamp: May 03, 2019, 08:00:58 pm
content: Quote from: Monkeh on March 17, 2019, 05:45:24 amhttps://www.merriam-webster.com/dictionary/centigrade

author: CatalinaWOW
author_rank: Super Contributor
timestamp: May 03, 2019, 09:28:50 pm
content: Quote from: windsmurf on May 03, 2019, 08:00:58 pmBe kind. Perhaps he is not a native English speaker and is having trouble with the subtle difference between centigrade and centigradian.

author: Nerull
author_rank: Frequent Contributor
timestamp: May 04, 2019, 02:17:23 am
content: I kind of feel like if you set out to be obnoxious you lose the benefit of the doubt when it comes to polite responses.

author: TheNewLab
author_rank: Frequent Contributor
timestamp: June 06, 2019, 08:00:15 am
content: I apoligize. I just have alittle sister in physics that attacks me every time I make a slip.maybe it will never get straightened out..https://en.wikipedia.org/wiki/Centigrade

author: ebastler
author_rank: Super Contributor
timestamp: June 06, 2019, 08:27:22 am
content: Quote from: TheNewLab on June 06, 2019, 08:00:15 amI think we had all gotten over it in the meantime.BTW, your sister might have pointed out to you that "centigrade" is not a unit for angularvelocity(of satellites or whatever), as you had stated, but for angles?

author: tooki
author_rank: Super Contributor
timestamp: June 06, 2019, 02:22:57 pm
content: Quote from: Rerouter on March 17, 2019, 05:46:16 amThe metric system is extremely widespread in USA in the sciences, and more and more in engineering. The US isn't nearly as anti-metric as others think! (Nor isanymetric country actuallyfullymetric. Every place holds onto old measures in some disciplines.)

author: apis
author_rank: Super Contributor
timestamp: June 06, 2019, 07:30:30 pm
content: The US congress passed the Metric Conversion Act in 1975 "to coordinate and plan the increasing use of the metric system in the United States".

author: soldar
author_rank: Super Contributor
timestamp: June 08, 2019, 12:03:22 pm
content: Quote from: TheNewLab on March 17, 2019, 05:30:07 amYou can scream all you like but "centigrade" is commonly used and accepted and understood and does not lead to any misunderstanding or confusion. Being pedantic serves no purpose other than alienate others.Just because the Academy for Nerds, Squareheads and Smartypants says it should be "Celsius" does not mean they have any authority to impose their authoritarian rules over the free people of the world.OTOH, people who spell it "Celcius" should be hung by their ears or other soft parts and left to rot in the wind.

author: GeorgeOfTheJungle
author_rank: Super Contributor
timestamp: June 08, 2019, 04:48:50 pm
content: Centigrade is ambiguous => BAD. Max temp: 345 degrees centigrade, could be both 72 °C or 345 °C. What is it? You just can't tell => BAD.

author: ebastler
author_rank: Super Contributor
timestamp: June 08, 2019, 05:13:15 pm
content: Quote from: GeorgeOfTheJungle on June 08, 2019, 04:48:50 pmHuh?! I have never seen "centrigrade" used referring to the Kelvin scale. Would you have a reference for that?

author: GeorgeOfTheJungle
author_rank: Super Contributor
timestamp: June 08, 2019, 05:29:05 pm
content: A centigrade scale has 100 degrees between the freezing and boiling points of water.

author: ebastler
author_rank: Super Contributor
timestamp: June 08, 2019, 06:32:40 pm
content: Quote from: GeorgeOfTheJungle on June 08, 2019, 05:29:05 pmI had asked for a reference, not for you tomake upa definition.Yes, what you state is correct, but it is also incomplete. Do you have any reference for a use (historical or contemporary) of Centigrade as a temperature scale which doesnotdefine the freezing point of water as 0° Centigrade?

author: soldar
author_rank: Super Contributor
timestamp: June 08, 2019, 07:05:37 pm
content: - Johnny, at what temperature does water boil?- At 90 degrees Miss T.- No Johnny, water boils at one hundred degrees- Oh, yes, sorry, I forgot that the one that boils at 90 degrees is the right angle.

author: Nominal Animal
author_rank: Super Contributor
timestamp: June 08, 2019, 09:29:57 pm
content: Please, stop. You're all derailing this thread into temperature, while it started off being about gravity.The centigrade scale was standardized in 1887, with 0° at the temperature where water freezes at standard atmospheric pressure, and 100° where water boils at standard atmospheric pressure. (Actually, the inventor, Anders Celsius, used 100° for freezing point and 0° for boiling point. von Linné (Linnaeus) flipped it a few years later, and it got standardized some four decades later.)In 1954, the Celsius centigrade scale was standardized. It is actually derived from the Kelvin scale, with a fixed difference of 273.15. In particular, the triple point of water is 273.16 K, or 0.01°C.This means that technically, there is a difference of around 0.1° between degrees centigrade, and degrees Celsius centigrade (AKA degrees Celsius).Seehere, or W. E. Knowles Middleton,A History of the Thermometer and its Uses in Meteorology. Baltimore, Maryland. The Johns Hopkins Press, 1966.

author: soldar
author_rank: Super Contributor
timestamp: June 09, 2019, 08:14:22 am
content: Quote from: Nominal Animal on June 08, 2019, 09:29:57 pmAnd then you go on to write extensively about temperature.Thread drift is a normal occurrence and is fine. And before temperature came along there was electromagnetism and other things.Anyone who knows where gravity ends can still post all they want.And we're just having fun nitpicking and nitpicking the nitpicking.As far as I am concerned, and for everyday lay speech, centigrade is acceptable as is GMT (Greenwich Mean Time) even though they might not be acceptable in some very precise scientific environments.

author: Nominal Animal
author_rank: Super Contributor
timestamp: June 09, 2019, 08:21:21 pm
content: Quote from: soldar on June 09, 2019, 08:14:22 amWith references, in an effort to stop the referenceless arguing, in the last nine or so posts. I do agree the first line was terribly badly worded, but me fail English often that way. Sorry. I'd edit it if I knew a better wording.Even the centigrade stuff started from angular velocity, so it's notthatfar off the thread.Quote from: soldar on June 09, 2019, 08:14:22 amYeah, I wasn't arguing aboutthatpart at all. I don't know what is acceptable, and what is in common use elsewhere, and was actually pretty interested in that myself.Back to the core topic:For a couple of times now over a couple of decades, I've tried writing a simulation where particles in 3D Euclidean space interact with a simple \$r^{-2}\$ pairwise "force", but where that force, i.e. all information, propagates very slowly. The problem is, there is no "universal time", and that makes it hard. Essentially, each particle is affected by every other particle, but not at their current position, but from the position they had in the past, depending on how far they are. There are techniques one can use to solve the problem, like remembering the complete trajectory of each particle, but they all impose a rather small upper limit of particles if one wants to actually simulate anything.The non-Euclidean curved spacetime is even more interesting, but there I get stopped by a mathematical and conceptual problem: gravitational lensing. When there are multiple straight-line paths, how does that affect the interaction? Would Fermat's principle apply? That is, would the interaction be dictated by the minimum distance between two points? My intuition says there would be discontinuities, when the lensing entity moves, so that the minimum distance path changes discontinuously; how would that affect the interaction? Does that have any measurable effects?Essentially, the non-Euclidean curved spacetime has neither universal time, nor any fixed coordinate system. For this reason, I believe the pairwise interaction model won't work.The closest I've gotten to modeling non-Euclidean curved spacetime, is by modeling the spacetime itself using simplices (tetrahedra for locally-Euclidean 3D coordinates) forming a mesh, with each particle embedded in and specified with respect to the simplex it is in (using 3D coordinates), but the simplices having no universal coordinates; just sharing faces with neighboring simplices. Gravity is simply a "force" acting within each simplex, the gradient of spacetime within that simplex; and pairwise distances between particles are not needed.For fixed curvature, this works well. I even helped with a fellow on their CS thesis work: a ray caster that draws views of objects in highly curved geometries, tracing straight-line paths through that kind of simplex mesh.For dynamic curvature depending on the particles, propagating the changes in curvature at a "fixed speed" is a problem I don't yet know how to solve properly. (At least, not without a stupendous amount of information-carrying pseudoparticles propagating through the mesh, interacting only with the mesh, and other pseudoparticles with the same origin.)

author: hamster_nz
author_rank: Super Contributor
timestamp: June 09, 2019, 09:35:06 pm
content: Quote from: Nominal Animal on June 09, 2019, 08:21:21 pmPlease vorrect me if I am wrong, but isn't that the whole idea? How could pairwise distances between particles support waves, lenses, frame dragging or all the other exotic corner cases that are out there?Doesn't it all end up with the surface integrals being the contained mass, gradients being the local force, a few conservation laws and Noether's theorem? (to me this seems to be a sweeping generalization for nearly all field theories, just change mass to charge or whatever, and well above my brain-grade).

author: Nominal Animal
author_rank: Super Contributor
timestamp: June 09, 2019, 10:42:19 pm
content: Quote from: hamster_nz on June 09, 2019, 09:35:06 pmYou are absolutely right, of course.Thing is, current particle-based simulators I am aware of, all use Euclidean geometry, and a rectangular cuboid simulation volume. (Ab initio molecular dynamic simulators, those modeling the electron densities as fields, even require periodic boundaries.)Having each simplex cell have locally Euclidean geometry (i.e., the space in the cells is considered "flat"; distortions only occur at the faces where cells meet), also allows modeling fields properly, except that in a simplex (in this case, tetrahedra) the boundaries are ... uh, hard. I have trouble with the basics of electrodynamics; tetrahedrally bounded fields are out of my math-fu. (To be mathematically correct, I mean that although I know how those planar boundaries between tetrahedral cells transform coordinate systems, I do not have enough field math-fu to work out whether those transforms work (or if reflections and such should be considered!), and how those would be sanely implemented in a numerical simulation. The math itself is just the first step; implementing it efficiently and/or sanely, numerically, is usually much harder.)Quote from: hamster_nz on June 09, 2019, 09:35:06 pmDo recall that I am a physics code monkey, not a theoretical physicist; I only grasp the math just enough to implement it, but here goes:Surface integrals: Yes, except that in this discrete time and discrete simplices case, it simplifies to a sum. Each information-carrying pseudoparticle really just carries the total mass contained inside each particular cell at each particular time step, reaching each other cell at the proper time step. These propagate "outwards", modeling straight-line paths between cells, and can "split" and "vanish" whenever; only the information they carry has any meaning. (Note that the path itself is not straight; the constraint is that the shortest straight-line distance must pass through the cells the pseudoparticles propagated through. This is graph theory, and not too hard to solve/prove.)Gradients: For all conservative forces, yes: \$\vec{F} = \vec{\nabla} V\$. However, in simulations, you can often avoid calculating the potential \$V\$, if you can formulate the forces \$F\$ in some easier way. That is often the case. For example, for many elements, pairwise interactions suffice. Chemists use force-field models, which basically calculate forces between pairs, triplets, and quads (including angles between pairs of quads; "torsion"). Many metal atoms behaviour can be described using embedded atom model, which has a pairwise component, and a common electron field which all atoms contribute to. And so on. In the curved space case, I would model the conservative force \$F\$ to be constant within each cell, and changing discountinuously at cell boundaries (simplex faces).Conservation: Usually, conservation of e.g. energy is used as an indicator whether the simulation is sane or not. If energy is not conserved, but the system is closed with no energy exchange, then you know your simulation went bonkers. Typically this is because time steps are too long, and particle trajectories etc. are too coarse; equivalent to numerical integration with too few samples.Applying conservation requirements, say keeping some particles stationary in a simulation, is typically implemented by adding a suitable conservative force, for example a spring-like force that tries to keep the atoms in a specific plane. Just fixing their positions leads to unphysical infinite forces, which break the simulation. Another common one in molecular dynamics is to add a repulsive force, modeling Pauli exclusion, to avoid particles getting unphysically close (again, which would indicate very high energies); whether it is \$r^{-n}\$ or exponential, turns out not to matter. (It is like a skating ramp, where everyone starts on the flat region. If there is no friction losses, then everybody getting to the ramp exits it at the exact same speed/energy they arrived into it, regardless of the exact shape of the ramp.)In a dynamic simulation, conservation will probably require continuous modifications to the simplex mesh cell structure, joining near-empty cells together, and splitting crowded cells. (I suppose limiting the particle count to at most two per cell is impractical -- but nevertheless very pleasing as an idea.)Thing is, even working out all the patterns of splitting and joining simplex cells is probably worth a publication. Currently, finite element methods and similar tend to use hexahedra instead of tetrahedra; I am not aware of a comprehensive study of how to split or join 2 ..Ntetrahedra. I haven't done a proper literature search, though.It is very interesting stuff, and I do occasionally entertain myself wondering whether this implies anything about the underlying structure of our universe or not.