DrPhysics

I looked up the part of the book, and it is a horizontal distance of 20 ft. And nice work with the Rosharan conversion. That 261 inches works out to be about 6.6 m (which is what I'll use). First, we'll need to establish some guesses as to how strong Dalinar is. From what I could find, an NFL punter produces an average force of 2000 N (Football Physics by Tim Gay) or 450 lbs, and the foot travels about 0.5 m while in contact with the ball. Note: Much of that force comes from leg momentum, so keeping up that average force while kicking something much heavier (like a person) would be quite a bit higher. But, having a longer leg with more mass (thanks, shardplate) will help. Another data point would be single-leg extensions (the lift) which advanced lifters would be able to do 200 lbs (900 N) with a single leg. With that one, though, you don't get the momentum advantage. Based on those, I think Dalinar should be able to exert an average force of 1000-1500 N during the kick. Now, we need to figure out what force you need to send someone flying 6.6 m (20 Rosharan feet). @Xiahida ran into a problem where they couldn't eliminate time. We can get rid of it with a little bit of algebra (which I'm not going to recreate here). Thankfully, the person kicked starts and ends on the ground (Dalinar had knocked them over before kicking them), so we get to use the range equation: R=(v^2/g) sin(2*launch angle). Solving that for v (the launch speed) and taking into account that g on Roshar is 0.7, and estimating the launch angle to be between 30 (common from kicks) and 45 degrees (maximum range), we can find the launch speed: somewhere between 6.7 and 7.2 m/s. If we assume that the person goes from at rest to that speed while traveling 0.5 m in roughly a straight line (considering the arc of the foot wouldn't significantly change the answer), we can use kinematics to find their acceleration without needing the time: v_f^2 = v_i^2 + 2ad. That gives us an acceleration between 45 m/s/s and 52 m/s/s (or around 5 g's). Using the 125 kg from the earlier post, we get a force of 5,600 to 6,500 N Using the wiggle room in the force above (1000 -1500 N), we get the kick being 4-7 times stronger than expected, at minimum. (I've tried to err on the low side in these calculations). Other feats, like holding up the chasmfiend's claw probably would be and even bigger multiplier, but we don't have enough data to figure that out. If you can think of other scenes where a shard bearer shows their strength, we might be able to come up with some more limits.

Actually, a sphere is much more aerodynamic than a human: https://en.wikipedia.org/wiki/Drag_coefficient (Humans are close to a long cylinder. The rounding of the head helps a bit, but from what I could find on tests, our best drag coefficient ends up being around 0.7). A slightly pointed sphere would have even less drag. Navani would be much lighter than the sphere (the sphere is probably around 1000 lbs), so the lashing would have to be angled up by less than 5 degrees, or if one of the points was tilted slightly up, it could easily generate enough lift to hold her up. Everything else you describe would be correct, assuming they stayed at a constant 3 lashings, but we don't get many details on starting/stopping, so I bet they don't do that. The boring version: as much as Brandon says lashing isn't flying, he treats it like flying an aircraft whenever they have extended flights*. For example, Kaladin should never black out from G-forces while turning but would black out after about 10 seconds with a double lashing at terminal velocity. It's a part that I've just learned to ignore (or at least not think too hard about) with my physics brain. *This may be due to managing the reader's expectations as @Treamayne notes below. (This footnote was added after their comment)

I could see them getting there (either with soulcasting or cohesion) purely because of how useful perfect gemstones are. I can see it starting with someone using cohesion to remove imperfections and/or rejoin cracked gemstones, then building on that knowledge. Space age Roshar could have some amazing materials science.

Your theory still works if we have a solid crust with holes in it, then have a large mixing chamber near the center. If the mixing at the center makes the seethe, you could easily end up with flow patterns where the air and water vapor escape through some holes and others let the now fluid-like spores flow in. Or, it may even explain why the seethe stops and starts - when pressure is high enough to push back against the weight of the spores, it can force air up through the holes. As the pressure drops (as the spores in the center run out), you get a collapse where a bunch of spores rush in to fill the available space, start reacting, build up enough pressure, and then blow out again.

I talk about that in the other thread. The only way that would work is if the boundary was actively creating and destroying air molecules, which doesn't match the behavior of anything else crossing the boundary. Hopefully a space age story will supercede that particular WOB.

The active converting isn't probably very useful (the large forward suction would be hard to control), but I can imagine a soulcast-powered rocket. You fill a tank with chuncks of a material that's connected to a nozzle. Soulcaster converts a chunk at a time and the extra pressure is pushed out the nozzle. (This would be particularly useful for a rocket ship). But it might be more efficient (for an airship) to create a fabrial jet engine: an attractor fabrial to pull air in, a heating fabrial to rapidly heat it, then let it expand out the back. Give it a shape that takes advantage of the venturi effect.

Pressure waves can go through (sound does) without any air crossing the boundary. And maybe explosions have enough energy to break through. We just don't have enough information at this point. Helium 3 is not easier to handle. Regularly infusing with stormlight is much much much easier than containing helium-3 in an environment where fusion can occur. Using fusion where stormlight is available because we might crack a gemstone would be comparable to saying we should give everyone jetpacks (incredibly complex, expensive, and prone to error) because a car might get a flat tire.

I actually answered that one in another, longer post. Helium 3 would be useful for power generation, but since you could generate electricity with a simple heat fabrial connected to a Sterling engine, there really wouldn't be a need. Where it could be useful would be materials science and/or the semiconductor industry. There are specific alloys and crystal structures that simulations tell us would be more useful that what we have, but the technology to build and test them is very cost prohibitive. So, if a souldcaster could grow something by imagining the exact crystal structure (potentially including gemstones) that could be very useful. (Think commercially available spider silk for bridge construction, or a steel that lets us run plane engines a few degrees hotter, increasing their efficiency). The only other one would be nuclear materials for weapons, but it would be very difficult to soulcast those without killing the soul caster. (You don't want to just stand next to a big chunk of plutonium). Could make for some very scary suicide bombers. Edit to add: after posting, I realized that with how easy anti-light is to make, we wouldn't need kissable materials for a big bomb. Just two gems and a bit of raysium. Easy bomb: a tube weighted at one end (so that end stays down) with a stormlight filled gem at the bottom, and a little piece of Raysium on top of it. Second gem at the top of the tube held up by something designed to break away. Drop the tube, on impact the top gem will fall and hit the Raysium, connecting the two gems and mixing the lights. Once the gems are destroyed in the initial explosion, the light and anti-light are released mixing completely. Goodbye target. You wouldn't need ICBMs, just a windrunner with a backpack.

No. Those dents would leave gravitational anomalies that we'd be able to see through the gravitational impacts. Dark energy is trying to describe a different effect: something is taking the sheet and pulling,stretching it out, and that pulling is speeding up. We can describe that stretching with general relativity if we assume there is some other energy that we can't see (hence the "dark") filling the entire universe helping push.

Having investiture, matter, and energy all be different forms of the same thing tells us that you could create a black hole out of investiture (because it would bend spacetime around it just like you could make a black hole out of light if you got enough of it together), but that doesn't mean that a black hole will be a perpendicularity. Black holes would bend the physical realm, but that doesn't mean the physical realm will get closer to one of the other realms. Perpendicularities don't act like black holes. We don't see time dilation or increased gravitational forces around them at a noticeable level, so that means connecting the realms with investiture doesn't bend things like (or doesn't require the same physics as) a black hole. Black holes aren't traversable - you can't go into one and come out somewhere else. There are other things that bend spacetime (like the Ellis Wormhole) in a way that you can use it to cross from one point to another, but those aren't black holes.

The moons are weird, but everything I've talked about here could naturally exist.

TLDR: The Rosharan sun is somewhere between 1.03-1.18 times the mass of our sun. Post: I've been toying with figuring out the orbits of Roshar's moons, and while digging, I found this old post trying to figure out the size of Roshar's sun: and since the sun will probably be important to figuring out the moon's orbits, I wanted to tackle those first. How I figured it out: We know that Roshar's period is 1.1 earth years (see the coppermind). We also know from this WOB that the sun is white and larger than ours: The Physics: We know that the period of an orbit is: We can find the habitable zone of a star (where surface water can be liquid) using this equation: where L is the luminosity of the star, and alpha is a constant (0.53 for the maximum distance in Au if L is in solar luminosities, 1.10 for the minimum distance). To link the two equations, we can use this equation that relates luminosity to mass for stars that are near the size of our sun: (where M0 is the mass of our sun). Combining these and solving for mass gives: which gives us a mass range of 0.99 - 1.22 solar masses. However, we know that there are two other planets in the habitable zone, so Roshar will probably be close to the middle. If we limit its orbit to with 10% of the center of the habitable zone, we get a range of solar masses from 1.03-1.16. Which, (going back to the WOB earlier) is slightly larger than our sun, and is in the main sequence range (G1V-F8V) that a human would say was white (they have masses that range from 1.03-1.18). So, both the color and the gravity math agree. Roshar's sun is most likely 1.03-1.18 Solar Masses.

Thanks. I searched for "mass" and "faint", but somehow kept missing it. Sadly, the whole quote doesn't give us any more context. I had hoped there would be enough to make a few conjectures.

I went digging to find the quote for a bit more context, but I couldn't find the quote. Do you onow where in OB she talks about it? Though to answer your question, if stormlight does have mass, a gemstone leaking stormlight would get lighter.

This is something I wrote up years ago (before the Omnibus was available) but with Sanderson working on the prose version of White Sand, I thought it was a good time to pull it from Reddit, update it, and give it a home here. My goal was to see if I could invent a system that matched what we know about Taldain with minimal magic intervention. I couldn't invent one that could completely run on its own, but here's the one that got the closest. Background info In Arcanum Unbounded we learn this about Taldain: It is tidally locked between two stars in a Binary system The star that dayside faces is a blue-white super giant From the planet, it looks like it is the same size as our sun (found with a little geometry) The star that darkside faces is a white dwarf that: has a particle ring around it making it "barely visible" is bright enough to leave darkside in twilight but not full daylight the UV part of its spectrum is enough brighter than the visible part that you can see plants fluorescing (When answering this question, Brandon states that it acts like a blacklight) Additional info we have on Taldain: it was put there by someone (who put it there is a RAFO) magic can be involved in the planetary dynamics The Blue-White Super Giant Climate modeling is hard (weeks to months of super computer time), so instead I used these simple guidlines to calculate distance: Over a 24 hour period, the center of Taldain should absorb the same amount of solar energy as a spot on Earth's equator. Earth, on average absorbs 60% of the incoming sunlight, but deserts only absorb 30%. Sand, especially white sand, is very reflective. If possible, the star should look roughly the same size as our sun,as it does in the graphic novels. (Aside: If I had to break any of these rules, this would be the first. Luckily, I didn't have to.) Blue-white supergiants have a lot of variability, so when I was putting together the system I pulled in a list of stars with known masses, sizes, etc. and picked the one that fit best (9 Persei for those that want to look it up). That puts Taldain's orbit at about 95 AU from the star (1 astronomical unit (AU) is the average distance between the earth and the sun). At that distance, the intesity would be comparable to the sun at high noon in the early fall for those living between 40-50 degree latitudes here on earth. Since the sun never sets, the air would be much hotter, but you wouldn't need as much sunscreen. Cool side effect of this set up: it would probably be beneficial to have lighter skin living on darkside so that your body would produce enough vitamin D and skin cancer would be a lower risk. (Those are the two main evolutionary driving factors for skin color on earth, which is why those whose ancestors lived near the equator have darker skin and those living away from the equator tend to have lighter skin.) Having the main star be a blue-white supergiant adds some interesting options for an end-of-life for the system. Here are some potential future scenarios: The most probable, but also the most boring: The star continues burning through its fusible materials, slowly inflates into a red giant, then goes supernova. This is far enough in the future that it probably won't affect any plotlines. The star turns into a Wolf-Rayet star: If there is enough heat and pressure in the core, the star starts fusing carbon. The extra energy from this makes the star start belching huge amounts of its surface hydrogen. At the distance Taldain sits from the star, Day siders would see a huge hot plume belch out of the sun, then have somewhere between 1 month to 1 year to get to Darkside. When the plume hits, Dayside is annihilated. The star will continue to belch out hot hydrogen, turning the area into a nebula. The neighboring white dwarf will start gathering up the matter, then sometime between 1,000-10,000 years after the initial belch, the white dwarf will have gathered enough matter to reignite, triggering a type I supernova. The only thing left of the entire system would be atoms and dust. There wouldn't even be an asteroid. The initial belch could come at any time (or could still be a million years away). The star becomes a luminous blue variable star (slightly less likely than a Wolf-Rayet star). These stars feature many supernova-like outbursts that can come one at a time or several in a small burst, then wait a few thousand to a hundred thousand years inbetween. Dayside is raized, but some of the life living deep underground might survive, depending on the outburst. They'll see the outburst about a month before it hits. Once again, the white dwarf is likely to go supernova eventually, but it will probable take more time. The star just goes supernova. It's rare, and we don't know why it happens, but sometimes blue supergiants just explode. Daysiders might be obliterated in the initial gamma ray burst, which would hit them without warning the moment the light from the supernova reached the planet. Or, it could be small enough that people who were outside get radiation poisoning. Standing inside a stone building may be enough protection. They would have somewhere between two weeks and a month to get off-planet before it is destroyed by the ejected gas cloud. The blue supergiant leaves behind a neutron star. The white dwarf probably goes supernova sometime in the next 100,000 years, but no one is around to see it. Summary: There are a few world-ending scenarios that could easily happen within 1,000-10,000 following White Sand, all of which leave a race against the clock to get off the planet in order to survive. The White Dwarf White dwarfs are the left-over remnants of a burnt-out star that wasn't big enough to create a neutron star or a black hole. The intense gravitational forces that arise from having so much matter in such a small space makes their properties much more predictable. Therefore, instead of trying to find a real star that fit, I was able to invent one that fit. The result: a white dwarf with a temperature of 100,000 K (180,000 F), a mass that is 17% of the sun's mass, and a radius that is 2.2% of the sun's radius. Solar units are traditional and make the math easier, but I think it's fun to point out that the white dwarf fits the mass of 56,000 earths into a sphere that is only 2.5 earths in diameter. To create a semi-stable orbit, the start would be about 18 AU away from the planet. At that distance, there would be about 50 lux of visible light (think living room at night so you've dimmed the lights some). You'd be able to read, but just barely. From the surface of the planet, it would look roughly the same size as the planet Mars does from earth, but would be much, much brighter. In order to see the UV effects described, there would need to be something in the atmosphere that keeps ozone from froming on Darkside. That would make UV light 10 times brighter than the visible light and intense enough to make darker skin an evolutionary advantage. The people on darkside would face an exposure to UV that would be comparable to living in the mountains on the equator here on earth. It would also explain why plants have adapted to fluoresce. UV light has enough energy per photon that it can easily break many molecular bonds (which is why it can cause cancer). Plants would do much better with an analog of chlorophyl that absorbed some of the UV light and re-emitted it as a lower energy wavelength instead of breaking apart. It would both allow plants to make their own food and protect their DNA from the ionized chunks of molecules (free radicals) that would otherwise be produced. It is very improbable that a white dwarf and a blue supergiant would naturally form in a binary system (see notes above about the type I supernova), and so it was probably placed there when the planet was placed as well. Taldain - The Planet In our made-up system, it would take Taldian 1,200 years to orbit its star. Also, the gravitational forces from it's neighbors are so weak that the supergiant would burn out billions of years before the planet could be tidally locked, but once locked it would stay there. That tells us that the placement and being tidally locked had to be done by whichever power placed it there. The planet itself would have to sit in what's called a LaGrange point between the two stars. Generally speaking, the closer a planet is to a start, the slower it is. A Lagrange point sits where the second star pulls just hard enough on the planet that the planet can keep pace with the second star when it would normally fall behind. However, these points are what's called an unstable equilibrium. If there are any bumps or jostles (like the ones that come from having a moon orbit around it), the planet will fall out of the equilibrium into a new orbit. The omnibus refers to this as "Wombear's saddle", which is a nice nod to physics going on. (However, the explanation of finding it through observing stable and unstable orbits around the white dwarf isn't feasible. The orbits are unstable enough that nothing that is big enough to see (even with our modern telescopes) would form there and stay there long enough to figure out its orbit. Using some orbital simulation code I stole from an astronomer in our department, I found that Taldain would only be able to remain in its orbit for about 50-70 years without something else keeping it in place (most likely some form of investiture). Which leads to the question: "What would happen if the investiture stopped holding it there?" Three orbital bodies create what is called a chaotic system where tiny changes in initial conditions can lead to wildly different outcomes. I ran thousands of simulations to find out. The most common (and boring) was that Taldain settled into a new, slower orbit, no longer tidally locked between the two stars. Also, Taldain is so much lighter than the stars that the stars never significantly altered their orbit. Other final orbits that happened: Fairly common: Taldain is sped up and then continues to speed up a bit more each time it passes between the stars, slowly increasing its orbit until it slams into the white dwarf in somewhere between 5,000 and 100,000 years into the future. Fairly common: Taldain starts orbiting around both stars in a figure 8. Everyone freezes to death within 100 years the first time it orbits the white dwarf. It usually happens within 5 orbits (6,0000 years) Rare but super awesome: Taldain is slingshotted out from between the two planets at incredible speeds. Everyone freezes to death within 200 years. Before freezing to death, the acceleration reaches somewhere between 0.25 and 2 g's. If you were standing on the day/night line on one side of the planet, you would feel up to 3 times heavier. On the other side, gravity might not be strong enough to keep you on the surface and you would be left behind, along with rock and other rubble as the planet is torn apart. The lower accelerations aren't strong enough to rip the planet apart, but would be strong enough that you would have to lean into the direction of the acceleration to keep from falling over. Some people would spend their entire lives leaning in as the planet slowly got colder. The Moon Taldain's moon constantly orbits the day-night line around the planet, and the residents count each orbit as a day. Due to conservation of momentum, the moon's orbit should drift around the planet as it orbits the larger star. From a space perspective, the moon keeps orbiting in the same plane as the world turns beneath it. We couldn't find any simulations (tiny tweaks in orbital angle) that would keep the moon orbiting the day-night line for more than 10-15 years. Whatever is holding Taldain in place would also have to keep nudging the moon in (probably why the cloud around the white dwarf blinks every seven days, according to the omnibus). As far as figuring out the orbit goes, we're a lot more limited in the details. Since the text doesn't mention the moon having a tail, we know that it is probably rocky (rather than icy like a comet). If it was comet-like, the tail would always be pointed away from the supergiant, towards Darkside. For stability, we'd want the smallest possible mass that would still be round, which would make the Taldain moon roughly the size of Saturn's moon Mimas. Assuming Taldain is about earth-sized, and that 1 "day" is close enough to one earth day that it matches human biological cycles, the moon's orbit would be 4-8 earth radii away from the surface (which also makes it far enough away that it won't break up due to Taldain's gravity). Therefore, Taldain's moon would appear 1/4 the size of our moon at the smallest up to just a little bit smaller than our moon at the largest.

Except you can't make an Alcubierre drive with speed/slow bubbles. Since the bubbles also scale gravity to act as expected, the bending breaks down. When that happens, general relativity breaks down (there are other signs too, like bubbles don't destroy everything on the boundary which the gravitational discontinuity you need would) and you can't apply the math. FTL could be as simple as finding a way to get a ship to enter a speed bubble without changing direction (like on a fixed rail), then messing with identity so that the bubble attaches to the ship and travels with it. Stack up a few, and you break the external speed of light without breaking the internal speed of light pretty quickly. Surgebinders could probably warp spacetime that way, though. It's tough to tell because we haven't seen enough about what happens in the immediate vicinity of someone using gravitational lashings (the tidal forces that occur in the flip from the lashed gravity region to the regular gravity region).

Aluminum doesn't oxidize the same way as iron. Aluminum bonds oxygen fairly quickly, so it does rust, but because the oxygen will only bond to the outside of the crystal structure, it forms a protective layer that then stops further oxidation. You'd have to continually scrape off or otherwise remove the rust layer to get more of it to rust. You could get it to corrode in other methods, but you'd have to sustain a few different chemical reactions (e.g. stick in in seawater with a bunch of brass). However, since objects tend to show up as a whole in the Cognitive realm, I don't know if you could soulcast the rust/corroded layer separately from the rest of the metal.

So, I'm super late to this party, but the answer is yes. A group of Italian researchers (sorry if the link is paywalled- I can't tell if it's free or if I just have access through my University) figured out that you could with flippers. In case it is paywalled, I attached their video of someone doing it under simulated low gravity (aka help up by a fancy rubber band). Also, here is the important bit: So, as long as they dropped their mass to less than 20%, dropping that mass doesn't slow them down, and they have flippers (or something similar), they could run across water for 7-8 seconds (not in the quote), and the time gets longer for lower gravity. The forces scale like the area of the foot, so if they were in regular feet only it would be possible at 3% of their normal mass, but at that point buoyancy and air drag start mattering a lot more and the math gets weird. pone.0037300.s002.mov

Thanks.

I was recently involved in a discussion about Windrunner physics, and this WOB came up (spoilers for Stormlight archive): https://wob.coppermind.net/events/315/#e10357 Here's the bit relevant to this topic: Does anyone know how someone with the relevant math experience (aka me) might get involved? Or have any information on what might be going on?

Where this breaks down is all the times they describe reorienting so that the ceiling is "down". If it started on one side and worked its way over, that would feel like getting pushed toward the wall/ceiling, not falling towards it. And if you made the lashing travel fast enough for those scenes to work, it would be too fast to get the scenes right when a windrunner is "flying". There isn't a physical answer that can get both of those situations to agree. It will have to be a cognitive or spiritual explanation that works in-universe. Right now, the only explanation I can think of is the Doylist: "Brandon thinks flight should be like a fighter jet, but gets gravity right in all the other places" or "most of my audience expects flight to be like jets, so I need to treat it that way, so they aren't taken out of the story." Since there are no jets on Roshar, we can't really use the excuse that lashing work weird during flight because Kaladin believes they should work like a jet. It definitely makes it difficult to predict anything about what spaceflight will look like on Roshar. Some of the odd physics mistakes (usually violating Newton's first law) that pop up with steel pushes are easier to explain because most people don't understand the first law, and so those behaviors are expected. (Like Vin slowing down and stopping when she pushes herself straight up. Her momentum should keep her going, so she'd overshoot, then fall, and keep bouncing up and down. However, we're used to straining upwards and stopping when we do things like standing up on our toes.)

Well, your next steps would be to test it out numerically and see if that gives you any insight into figure out the general solution. Mathematica has some good built-in numerical solvers and most universities have access to a free license for students (it's how they market - if we get you hooked as a student, we'll keep you hooked when you employed.) Or, you could write it up using Euler's method in python. These wouldn't give you general solutions, but they would let you run several test cases and see how they behave.

There have been some great answers already. Here's my small contribution: Yes, we can plug Investiture into the energy requirements, but that doesn't mean that all of the investiture needed to accomplish feruchemy is stored in the metal mind. If it were, the weight that Wax loses would increase the weight of the metalmind by the same amount, then add in extra weight to account for whatever investiture is needed to maintain an increased weight for a while. Instead, I like to think of it as a relay, a device which uses a little bit of current to open a switch that allows a lot of current to flow through a circuit. A feruchemist stores enough investiture to essentially open the gate to the spiritual realm and allow out the investiture needed to accomplish the feat. So when you say: that idea doesn't work. They aren't storing all the investiture needed, they are storing enough to access what they need.

This is where you went wrong in trying to solve for forces. Your model doesn't assume these things. It assumes that x(t) = h · tanh(at)². Could that be a result of those assumptions? Sure. But it isn't built on those assumptions. As I said before, that doesn't mean your model is useless or you should throw it out. It just means that it won't work if you try to generalize it to situations where motion might not be x(t) = h · tanh(at)².

Every one of these systems is built starting from first principles using forces, and the description of motion comes second, so you can tweak it by adding/removing forces and seeing how that impacts motion. Your model is built on a description of motion, and you are adding in forces second. So, you can change motion and see how that impacts forces, but you can't change forces to see how that affects motion. What you are doing is equivalent to what happened with the Rayleigh-Jeans law and the Ultraviolet catastrophe. Short version: They came up with an equation that fit pretty well to the spectrum of a blackbody. It was an empirical formula designed to fit what we saw (like your motion equation). But, when we tried to use it to describe the thermodynamics/statistical mechanics of what was going on, it broke at infinity (specifically, every blackbody would emit an infinite amount of energy in Ultra-Violet and shorter wavelengths). It worked well to predict spectrum, but it couldn't be used on more fundamental ideas. Later on, Plank constructed what we use now from thermodynamic principles, and his solution became part of what inspired Einstein to describe the photon. But before then, the Rayleigh-Jeans law was still very useful in describing the radiation we see coming out of black bodies. Thermodynamics creates the radiation, so you can use thermodynamics to describe the radiation, but you can't use something that purely fits the radiation to describe thermodynamics. Similarly in your case, forces cause changes in motion, so you can use forces to describe that changing motion, but you can't use something that purely fits motion to describe forces. That doesn't mean what you have is useless, it just means it has limits. Exactly this. x(t) can potentially describe a push while under gravitational pull, with a max of h. Anything you derive using your x(t) will have that same limitation. Even if you find a general and particular solution for your differential equation, it will still be bound by h because it was bounded by h when you created it. It only blows up at infinity if you don't let h go to infinity as well.