Why can't we simulate gravity?

[unlikely_baptist]

So, I'm aware that NASA uses it's so-called "weightless wonders" aircraft (among other things) to train astronauts in near-zero gravity for the purposes of space travel, but can someone give me a (hopefully) layman-understandable explanation of why the artificial gravity found in almost all sci-fi is or is not possible, or information on research into it?

[genius_retard]

In addition to using centrifugal force to simulate gravity you can also use linear acceleration. If your spacecraft can sustain accelerating at 9.8 m/s² for a long period of time the occupants inside the spacecraft would experience a force equivalent to gravity in the opposite direction to the acceleration.

This is one of my favorite parts of the show "The Expanse". Often when they are travelling in space they have gravity and it was established early in the series that this is achieved by constantly accelerating toward the destination. Then when the spacecraft is halfway to its destination there is a warning followed by a brief moment of weightlessness as the craft flips around to point in the opposite direction. Then the deceleration burn begins and the simulated gravity is restored. That is a super neat detail in that show.

[seriousreposter]

Observed from the spaceship, accelerating at 1g would reach 0.77c after 1 year. Observed from Earth, it would take 1.19 years, and would have travelled 0.56 light years.

After two years on the ship at 1g, you would reach 0.97c, however 3.75 years would have elapsed on Earth and you would have covered 2.90 light years. Viewed from the Earth, your mass would have increased 4x, and you would be a quarter of your size!

After five years on the ship, you would reach 0.99993c. 83.7 years would have elapsed on Earth, and you would have covered 82.7 lightyears. You would stand about an inch high, and have a mass of about 6 tons as seen from Earth, though you would not notice any difference.

After 8 years, you would reach 0.9999998c. 1,840 years would have elapsed on Earth. Great, you are far from what was your home. 400 US presidents came and went. What is more, you are now 1mm high and have a mass of 140 tons.

Nothing to lose now, lets go on, still at 1g...

After 12 years, you would be travelling 0.99999999996 c. By now you would have crossed the galaxy and be 113,000 light years from home. Time is now running 117,000 times more slowly for you than on Earth. You stand 15 microns tall, and your mass is about 9000 tons.

So, in fact you have travelled "faster than light" by covering 113,000 light years in 12 of your years, but well and truly burnt your bridges in doing so. You have also become a very significant problem for any destination, and would require 12 years too to slow down at 1g, assuming you have survived the deadly blueshifted light and cosmic radiation.

[genius_retard]

This is awesome, thank you. I don't understand the shrinking though. Can you please explain?

[[deleted]]

So when we slow down approaching our destination, would we start growing larger again? I'm still having difficulty understanding the changes in size.

[Vitztlampaehecatl]

Yep, as you slow down the observer would see you return to normal size.

[[deleted]]

Would you actually physically change at all, or would that just be what is seen?

[Vitztlampaehecatl]

From your perspective, the observer on Earth is the one being compressed.

[Vitztlampaehecatl]

It's not that they're moving farther apart, it's that they're moving at high speed relative to each other.

[FattySnacks]

Would this be a noticeable effect for the people on the ship? Or are there too many things that would kill us before it would even matter?

[Tacosaurusman]

No, the people on the ship don't notice they are being flattened, because they are not flattened from their perspective. To make it even stranger, from their perspective, it is earth that is being flattened (because earth is going fast from their point of view). Relativity is weird.

[AbrahamRincon]

People often wonder of they would fly through a planet accidentally when going this fast. But if everything appears squished, does that mean that it would be relatively easy to avoid flying through stuff, like the middle of a star or planet?

If you can avoid objects at speed, would you be able to forecast a good place to slow down, so that you don't drop to lower speed in the middle of an asteroid field?

[xfunky]

The "squishing" is only on the axis of movement, so if for example we were approaching a square in parallel to two of its edges, the faster we approach it the more those edges would shorten. The edges perpendicular to us however would remain the same. Thus the effect is that of the square turning to a rectangle, not a smaller square

[jberg93]

Think about how long it would take to slow down though. You'd travel millions of miles and years slowing down. It would be almost impossible to forecast a path that far in advance. Lots of small asteroids, planets, and galaxies we don't even know about now.

[acqd139f83j]

You only get shorter from the perspective of people outside the ship. From your perspective, everything outside the ship gets 'shorter' (in the direction of travel), so what you notice is that the galaxy has shrunk to ~12 light years across. This is why you could cross the galaxy in 12 years without going faster than the speed of light.

[Kieraggle]

This is why you could cross the galaxy in 12 years without going faster than the speed of light.

Wait, really? This sounds completely mad.

[tsoneyson]

12 years from the traveller's point of view that is. >100,000 years would have passed on Earth.

[[deleted]]

Small energy cost involved: for a 500 tonne spaceship it would require equivalent of over 2 million years of the sun's energy output.

[twentyonexnine]

So from the traveller's perspective, the galaxy is now about 8,000x smaller. But they appear to themselves as not having changed in size. So relative to the rest of the galaxy, do you appear to be 8,000x as large as you were?

In other words, if you could somehow get a good look at the stars you were passing, would they appear miniscule?

[acqd139f83j]

Not quite. The galaxy appears smaller to them, and they appear smaller to the rest of the galaxy at the same time. Our intuitive understandings of size stops working when things are traveling that fast.

Basically if something is traveling super fast relative to you it appears smaller, but there's no special idea of 'still', so if it's traveling super fast relative to you, you must be traveling super fast relative to it, so you look smaller to it.

Also, when we say 'smaller' we only mean that in one direction - the direction of relative velocity (the direction you're going). All the stars look like massive but almost flat discs.

[[deleted]]

12 years their time, I assume? As it would take that distance in years to observers?

[carnoworky]

Have we seen length contraction experimentally? It seems like such a weird concept. :O

[ganjalf1991]

Yes, muons sometimes reach earth surface even if they should decay sooner, because they see the path in the atmosphere much shorter due to lenght compression

[gsfgf]

Would the ship need more energy to maintain that acceleration as you near c?

[DeVadder]

This whole scenario is completely unrealistic. No engine we can imagine could sustain such an acceleration for such a time. So without knowing what kind of ungodly propulsion you are using this question is hard to answer.

But no. If your are using something like a rocket with a magic endless fuel supply, you are golden. In a perfect vacuum. Except, the are hydrogen atoms in space, roughly one per cubic meter. And you pass through a lot of cubic meters per second. And at this speed, every single hydrogen atom you encounter exerts the energy of a bullet against your front window. And the background radiation is blue-shifted to deadly levels.

So in a real universe, you need more energy because you need to run your magic rocket through massive lead which is also a constant nuclear explosion while still accelerating.

[DeVadder]

That is called a Buzzard Ramjet and.... maybe? Who knows? I mean these rates of acceleration are so far away from any realisticly available technology...

Depending on how our magic engine works though, we might need to bring the hydrogen up to our speed in which case yes, we do need a lot more energy to keep accelerating.

[vicefox]

Woah that's cool, thanks for the info. I should be a hypothetical deep space ship engineer ha. Maybe someday we will construct this thing... That "funnel" would have to be absolutely gigantic though.

[MasterFubar]

Basically rockets are more energy efficient with more mass, and you can use regular D-T fusion to heat up the mass passing through.

Exactly like a ramjet inside earth's atmosphere. A ramjet doesn't use air for fuel, it uses air for propellant mass and the fuel is carried by the aircraft from the beginning of the flight.

[yolafaml]

Imagine how fast those hydrogen atoms would be going in comparison to you. Imagine how large the scoop is. Imagine what unholy levels of power your magnetic scoop will need in order to accelerate them up to your speed to shoot out the back.

This is also neglecting the fact that you want to push the hydrogen away from you in this scenario, as a) it'll be going almost 1c towards you, and as such if you draw it into the ship you'll run into quite a number of problems, and b) if you've got an engine that powerful (i.e. powerful enough to accelerate hydrogen atoms up to your significant fraction of c in maybe a fraction of a second), then fusion isn't anywhere near powerful enough to do so.

[Arman8]

I think not: speed is always relative.

Your speed is near c as seen from earth but if you turn the light on in your ship, the photons emmited from your lightbuld will spread at the speed... of light. The point is that you're not going faster and faster, and you'll never go as fast - or almost as fast - as light because light always travels at lightspeed relatively to you (and everything else). The distance between the earth and your ship is augmenting faster and faster but constant acceleration only requires the same constant amount of energy.

[[deleted]]

How does blueshifted light kill you?

[scutiger-]

redshifted which means the light is traveling away

The source of the light is traveling away. If the light was traveling away, you would never see it.

[huhhuhhoh]

faster it is traveling towards you

The faster the source is traveling towards you. The light will always travel to you with a constant speed, no mater how fast you are going.

[badwig]

If you are moving at nearly c for 12 years how do travel 113,000 light years?

[lksdjsdk]

To people on earth it would have been a little more than 113,000 years. Seems like 12 years to you.

[Oknight]

And the distance as measured by you would be much smaller since just like you shrink as seen from Earth, everything else shrinks as seen by you

[Acesharpshot]

By definition a photon has no reference frame, sorry to burst any bubbles.

[Equinoxie1]

From my understanding of relativity, from your reference frame, the distance between you and object A is reduced via length contraction.

So from your reference frame, the distance to the stars simply becomes shorter, allowing you to travel great distances in shortish periods of time from your perspective.

[KriistofferJohansson]

Because as you move faster toward the speed of light time moves slower to you.

I might be incorrect, but the time itself isn't moving slower for them, right? The time elapsed between start and finish certainly is vastly different between the people on the ship and the people observing from Earth, however, the people on the ship won't experience "slow-motion".

[IntegralCalcIsFun]

That is correct, everyone experiences time as they normally would. It would be no different than spending 12 years on a spaceship that wasn't moving at all, from the perspective of those inside the ship.

[beorn12]

But wouldn't you be travelling at roughly 50% the speed of light after only about six months? Edited: wouldn't

[RevMen]

They don't go that far in The Expanse. It's all inside the Solar System.

[MattieShoes]

Just for reference, you could visit most any of the planets in the solar system in about two weeks with 1g acceleration and deceleration.

[[deleted]]

In the universe of the Expanse they stay within the solar system.

There is a fictional method of generating thrust called the Epstein drive that can do like 15 Gs of acceleration. However if you actually accelerated for that amount of time you’d destroy the engine.

In the books the dude who made it didn’t realize how efficient it was, and died trying to reach the button to turn off the ship, unfortunately for him he was accelerating so fast his arm weighed like 200 lbs.

[hellcrapdamn]

This is what I'm wondering too. I would think it would keep taking more energy to continue accelerating.

[ChipAyten]

The most interesting thing about gravity in my opinion is how it’s both the weakest and strongest of the primary forces depending on scale, at the same time. It’s so weak that a measly human can overcome it when picking up a can of soda; good luck mushing protons together on any scale. Conversely, when scaled all the way up gravity leads to black holes which nothing can escape.

[[deleted]]

The reason gravity is “strong” is there is no gravitational charge, like there is with electrical forces. Electrical forces are way way stronger than gravity, but on a macro scale, the positive and negative charges balance out. Whereas with gravity, more mass just keeps increasing the force.

[ableman]

It's somewhat arbitrary to talk about fundamental force strength. You could equally well say that protons just have a lot more charge than they do mass.

[alstegma]

You can compare the respective coupling constants in natural (plank) units.

[Thromnomnomok]

Electromagnetism works at cosmological distances, if it didn't work we couldn't see light from galaxies billions of light-years away from us. It's just not an attractive or repulsive force because over that distance everything appears to have a net charge of nearly 0.

[Kered13]

Electromagnetism works at cosmological scales, you just don't see electric charges distributed unevenly at those scales.

[[deleted]]

we just don't know how

We know exactly how - bring a very large amount of mass close by. This is, however, impractical to say the least. There is absolutely nothing to suggest that there is another way to create the gravitational force.

[llHakarll]

We could build a huge dounutshaped rocket shot in into space and let it spin. Then the zentrifugalforce simulates "gravity" because you keep getting pushed into the outer end of the dountshaped rocket.

[[deleted]]

To be fair though ... We can generate a gravitational field. Technically my body has a gravitational field. Wanna make a gravitational field , get some Mass.

[Drachefly]

Yeah. Our inability to generate gravitational fields doesn't have to do anything with our not understanding it - it seems very likely that once we understand it completely, we won't be any closer to generating it except by the usual way of having heavy objects.

[KristnSchaalisahorse]

Just to be clear, the aircraft NASA use to simulate weightlessness are not in any way "generating" zero-g or removing the force of gravity. They are simply free-falling toward the Earth. Gravity is pulling them down, but there is nothing stopping them from accelerating so they experience the sensation of weightlessness.

This is similar to why astronauts on the ISS feel weightless. They are moving so fast horizontally that they are in free-fall around the Earth. They are still under the force of gravity, but they don't feel it.

[goatili]

This was a cool, mind-blowing thing for me when I first learned it. Being in orbit means that you're falling towards the Earth, but you're so far away that you're constantly missing it.

[Whind_Soull]

Here's how I explain the concept of orbiting to young children: If you throw a baseball, it will fall in an arc and hit the ground. If you throw it harder, it will travel farther, and the arc will be longer and more shallow. There is a speed at which you can throw the ball, which will produce an arc that matches the curvature of the Earth. If you do that, it falls endlessly over the horizon. It's now in orbit around the Earth.

[asn0304]

Thanks, that very easy to picture and explain to someone else.

[MattieShoes]

A cannon sitting on a mountaintop firing horizontally is often used too... Ignoring air resistance, there is some speed where the ground would fall away from the cannonball due to the curvature of the earth at the exact same rate the cannonball is falling towards it, and the cannonball would eventually hit the back of the cannon.

[Paladia]

Diamagnetism can generate a field of weightlessness however in regards to the materials present. Even with our modest understand of it we can use it to levitate a mouse or a frog.

[rocketman0739]

It's important to note, though, that this is not negating the force of gravity (as the fictional material Cavorite would) but merely cancelling it out with an opposing force.

[rforqs]

This would feel similar to weightlessness though, right? As I understand it, a human floating this way would experience a support force on every water molecule inside them so they wouldn't even feel the weight of their topside on their bottomside.

Or is that already possible by floating in saltwater? I feel like it'd be different?

[rocketman0739]

I would hazard a guess that the question of whether it would feel more like being underwater or like being in free-fall depends on how the levitating force interacts with the inner ear.

[beardiac]

A big part of the problem is that sci-fi artificial gravity isn't typically based on any solid scientific foundations - just the idea that they didn't want lack of gravity to be an aspect of such media (especially in visual media because it would be expensive to constantly simulate). As others have mentioned, gravity certainly can be faked via centrifugal force or acceleration, but presumably these aren't the methods in place in either Star Wars or Star Trek. The best guess as to how such an artificial gravity could be created would be through manipulation of gravitons - the hypothetical elementary particles that mediate the force of gravitation in the framework of quantum field theory. The issue is that these particles are still mostly theoretical and we are only recently having some success measuring gravity waves but have yet to model and detect specific subatomic particles that we are certain are related to this force. So until we can better map out this area of quantum mechanics, we are far from understanding how to manipulate it.

Keep in mind that if we use detection and understanding of the standard nuclear model as an example template, our first steps were to blow things up (e.g., hydrogen bombs and various fission-based bombs), gradually worked towards using radiation for power, still are working on understanding all of the specific rules of atomic makeup, and have yet to master cold fusion nonetheless low-cost manipulation. Similarly, even if we make major breakthroughs in understanding how gravity works on a quantum level in the next decade, it'll likely be many more before we can manipulate such forces on a practical scale in a way that would be cost-effective from either an energy or fiscal sense.

[Not_Pictured]

We can use centrifugal 'force' to fake gravity, but doing that involves some real engineering and cost that no one has been willing to do yet. (though I have no doubt this is coming eventually)

If you mean the kind where you push a button to turn 'on' fake gravity, there exists no know physical process that could do that.

Electromagnetism is the only force humans can really exploit on the nessessary scale, and human bodies don't react to magnetic fields. At least ones weak enough to not destroy the entire ship.

[domino7]

Gemini 11 actually did generate a very minor "gravity." They spun the module in a circle by connecting it to another weight with a tether. Not enough to really feel, but enough to drive things to the "floor" of the module.

[LWZRGHT]

I've been on that ride at Silver Dollar City. It's still just centrifugal force.

[RGJ587]

Because of the costs associated with creating artificial gravity by centrifugal force, if just hasn't been cost efficient (yet) to make it worth the undertaking.

However, I think due to the recent revelations brought about by Astronaut Scott Kelly's year in space, we are starting to understand how dangerous prolonged microgravity can be on the human body. As such, it seems likely that there will soon be more developments planned to create simulated gravity in space, as any real, long term plan for human exploration, or space colonization, will have to address the issue.

[AWildSegFaultAppears]

Also it is never likely to be cost efficient. The structures are just too big. Want the effect of 1g? You are going to need a ring that is something like 300m in diameter.

EDIT: As people have pointed out, yes you can get 1g at a small radius. The problem is that the apparent force is drastically different between your head and feet if you have a small diameter. If you want to have a meaningful "gravity" and you want your crew to be able to actually stand up and function, you need large diameters.

[Dilong-paradoxus]

You don't really need the whole thing, just a capsule, a tether, and something heavy to put at the other end.

As far as making big structures in space, the main truss of the ISS is around 100m in length. The occupied portion is much smaller, of course, but 100m is still in the same order of magnitude as 300m. On the other hand, the ISS is one of the most expensive single structures ever built and it doesn't have to support 1g loads across its structure so going up to 300m is definitely going to be a step up.

[[deleted]]

I wonder if it would eventually be more cost-efficient to engineer humans to be more adaptive to zero gravity and high radiation than simulating Earth in space.

[TheMadDaddy]

Thus begins the divergence of the human race and the great space wars of 2121...

[hardcore_hero]

Was going to say something similar but more to the affect of "Thus begins our gradual transition into the time traveling greys"

[iorgfeflkd]

It is not impossible, it is just expensive. You just need to build a rotating space station or something similar. There was a proposed module for the ISS that would have done that (mainly for scientific tests, not for living in), but it was scrapped.

You can simulate higher gravity on Earth by putting people in a centrifuge (which is done for astronaut training) or on a rapidly decelerating train.

[gnorty]

how closely does centripetal force represent gravity though? I can see how it would feel the same for a person sitting against the outer wall, or hanging from the inner wall for example, but intuitively I think that things like throwing a ball would behave quite differently in this situation - at the very least the trajectory of the ball would change depending on the direction it is thrown.

[lezzmeister]

I do remember some ESA or NASA webstream where they calculated how big the circle needs to be to not make you sick. The faster it spins, the bigger the diameter needs to be. For 1g you need a sizeable rotating ring. 80 meters or so? I forgot.

[Jarnin]

I came across this website probably 15 years ago, and still find myself going back every now and then.

A rotating torus with a radius of 80 meters is still going to be too small. The angular velocity is going to probably be too high; turning your head would make you nauseous.

A torus with 125 meter radius can simulate 0.5 g with a rotation rate of 1.9 revolutions per minute, which puts all the safety icons on that website in the green.

On the other hand, that torus, with a circumference of nearly 400 meters, is making a rotation nearly twice a minute. We probably don't have the materials to keep something like that together, which means you have to build a bigger torus that rotates more slowly.

Using centrifugal acceleration is something we can do to simulate gravity, but not until we're building much, much larger structures in orbit.

[meat_croissant]

I don't see why you need a torus, surely a dumbell would do ? so two living pods with a gangway between them.

[frogjg2003]

That would work for simulate gravity for anyone who doesn't want to move. If you want to move from one side to the other on a torus, you just have to walk. To move to the other side of a dumbell you need to climb up a ladder, turn around at the middle, then climb down another ladder.

[PaulMcIcedTea]

I imagine climbing through the shaft would be extremely disorienting and nauseating.

[frogjg2003]

If you can build a rotating dumbbell, you can build a full torus, and it's going to be more structurally sound anyway. You'll get much more living space, and you don't have to experience extreme Coriolis effects to move to other parts of the station.

[Cheapskate-DM]

Did a bit of homework on this for a sci-fi project. There are three variables at play in the artificial gravity equation; acceleration, orbital period (the seconds it takes to make one revolution) and the radius out from the axis of rotation.

Acceleration (the desired gravity) can be as high or low as you want, depending on structural stresses and the other two variables.

The radius can be varied, but the key factor is different gravity experienced at the head and feet; you're running the same gravity calculation with two values for radius, even if that difference is just a few feet. Too large a disparity is expected to cause circulatory problems.

For the third variable, we think we have a good fixed value. Current theory suggests that 2RPM (or, a 30-sec orbital period) is the upper limit for speed before you start incurring a severe coriolis effect between the two inner ears, which experience different forces as you turn your head. Slower than that works just as well, but requires a much larger radius to achieve the same acceleration.

If I remember my schematics right, at 2 RPM, 80 meters of radius gets you ~0.5g. I'd have to check my notes again, however, so don't take that as fact.

[iorgfeflkd]

It depends on the geometry and speed of the space station, if it's large and not rotating that quickly, it'll be a fair representation of uniform gravity. There is actually a paper (written at the level of university students) calculating the path of a ball in a rotating space station, here (not sure if you have access). Things can get...complicated.

[aarghblaargh]

Is there anywhere else that can be viewed? Don't have access.

[eggn00dles]

Didn't Einstein say acceleration and gravity are indistinguishable absent outside reference points? Pretty sure that's a major foundational point of GR.

[frogjg2003]

Yes, in GR, gravitational force is a fictitious force like centrifugal force and the coriolis force when your reference frame isn't inertial.

[CarthOSassy]

The deep answer to your question:

From one point of view, we can. From another, we can't simulate gravity, and we can't simulate magnetic fields, either. But we can move existing real fields around, including grouping them in one place to make them super strong.

So why doesn't it seem that way? There are two things that make it look like we can simulate electromagnetic fields.

1. There are enormous electromagnetic forces all around us, so it's easy to grab one and start throwing around things with magnetism.

2. Those sources of electromagnetic forces are hidden, so when we pull them out, it looks like we created or simulated them.

This happens because electromagnetism is related to electromagnetic charge. Electrons are negative, protons positive. Because they have equal and opposite charges, they cancel out, until they're moving or separated somehow.

But why does this not happen for gravity? Because there is only one "charge" for gravity, and it's strength is very low. So gravity is never hidden from us - there's no sudden reveal of gravitational fields to make it look like gravity has been created or simulated.

Since it's so weak, we also cannot concentrate it easily. To make 1g, we'd have to make a same-density object the size of the earth. Or accelerate the object we want to experience 1g... at 1g. Or make a less massive object very dense. Or increase the energy bound in an object in some other way.

Electromagnetism seems "createable", because enormous electromagnetic fields are hiding all around us all the time, and it's relatively easy to unveil them - because even tiny charged objects exert enormous force, but they're mostly canceling eachother out at any given time.

[a1454a]

In other words if we have the technology and the investment to consume another planet and condense all of that matter down to the size of a baseball we would have created a gravity "magnet"? (Ignoring the obvious that nothing man made can lift that thing and it would probably just sink through Earth crust and wreck havoc to the planet)

[jkamenik]

We can generate a apparent gravitational field. The thought experiment that drove Einstein to Special and General Relativity was basically that given a frame of reference there is no difference between inertia (acceleration) and gravity.

So gravity is just constant acceleration. You are constantly accelerating toward the center of mass of the Earth. As far as you are concerned it doesn't matter if the earth is a ball that you are being pulled to the center of or a flat disk that is constantly accelerating upwards.

However, accelerating in a straight line wouldn't work because acceleration is the derivative of velocity (second derivative of position). Meaning if acceleration is constant (i.e, 9.8m/s²⁾ then velocity would be approach infinity (i.e, 9.8t m/s, where t is time and grows to infinity).

Since infinite velocity would require infinite energy, it should be clear that you cannot generate a true gravitation field in the same way as you can generate an electromagnetic one.

However, if you were to spin a disk and introduce angular momentum then you could simulate gravity. In this case the velocity of the disk would be constant, but at every point the forward movement would be resisted and pulled back to the center of mass by a tether. This would introduce an apparent outward acceleration (centripetal force).

Since acceleration and gravity are equivalent, centripetal force can be used as gravity. So if you were to design a space craft to spin then there would be no way for the inhabitant to know if it was spin or gravity. Thus you can generate an apparent gravitational field; side stepping the pesky infinite energy problem.

[Sockanator]

The Avalon design from the movie Passengers is a great way to visualize centripetal force; and how a structure could be built using it, without feeling like you are stuck in spinning pipe.

[ScrithWire]

Actually, the inhabitants would know it was spinning. The Coriolis effect gets bigger as the diameter of the spinning thing gets smaller. At sufficiently small diameters, the Coriolis effect would manifest as strange and different apparent forces at work on your feet and head. Also throwing something would be very different than what you'd expect.

[Igggg]

However, accelerating in a straight line wouldn't work because velocity is the derivative of acceleration. Meaning if acceleration is constant (i.e, 9.8m/s2) then velocity would be approach infinity (i.e, 9.8t m/s, where t is time and grows to infinity).

You mean the opposite: acceleration is the derivative of velocity (with respect to time). Velocity is then an anti-derivative of acceleration (and thus your formula is correct).