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A Walk in the "Ark" with Newton and Einstein

“Here we are,” you say, as you unstrap and step out of your super-deluxe time machine, helping Einstein and then Newton out of the machine. “This is what we call the Ark,” you spread your arm out, addressing the surroundings with a flourish, as you lead them down a lush, forested path. Birds chirp, and the sound of cascading water bubbles out through the local ferns. You come to a stop in a clearing, near a small pond. Newton and Einstein look around and then, as if they both see it at once, their mouths open a bit and they crane their necks. Something is definitely wrong here. The ground is curving up, and the farther up they look, they see more ground, and it eventually ends up above them, upside down.

Artificial Gravity, Rotating Cylinder in Space

“What is this place?” Newton asks, in awe.

“Gentlemen, welcome to the 23rd century. The year is 2246 and we are orbiting the Earth in a large ship, shaped like a cylinder. You are on the inside of the cylinder and it spins, providing us with artificial gravity.”

“This thing is enormous,” Einstein exclaims, waving his hand toward the distant fields on the other side and above them. “How big is it, exactly?”

“About a kilometer in radius and four in length,” you say, pausing a second, then continuing, “which means in order to give us the feeling of Earth’s gravity, it rotates about…”

“Once a minute,” Newton interrupts, having already calculated it .

“That’s right, almost once every minute, which means it is slow enough, and large enough to not confuse the balance and coordination centers in our human brains, as long as we stay on the ground level at least.”

“You mean there are other levels?” Einstein asks.

“Yes Professor, if you look over there,” you point behind them, “you’ll see structures that look like spokes, and other, lower gravity levels, branch off from them, where we conduct experiments, and even play low gravity sports.”

“Wow,” Einstein begins, “Then the center, where we see that other cylinder, where the spokes connect, are you weightless at that point?”

“Yes, you’ve got it, complete weightlessness.”

“Well,” Newton sighs, “well, well…I never thought we would get here this soon. I mean, I did think eventually that we would leave the planet, but this? Wow.”

You nod your head, and explain, “I know you both have many more questions for me, and we’ll get to some of them, but the reason I brought you here is similar to our last visit. I want your opinions, your take on what exactly is going on here, physically. I’ll set the stage a bit, then let you respond. The “Ark” is a masterpiece of modern engineering. With over a hundred countries working together, it took about 80 years to build, some materials coming from Earth, some from the Moon, and others from asteroids. Many of the materials were manufactured here in space. The Ark’s main purpose is to ensure that some of the critically endangered species on Earth have a habitat in which they can survive. This is why the Ark is divided into 11 separate bioregions, with species unique to each in their respective habitats. It orbits the Earth once every hour and 45 minutes at an altitude of about 1,000km, high enough to be above the atmosphere and most of the other satellite debris, and low enough for humans to still access it relatively quickly from the Earth. As we discussed earlier, its rotation rate of about once a minute allows the two kilometer across and four kilometer long cylinder to give the lifeforms access to perfect artificial gravity (what we call one gee) on its inner ground surface. At the central hub, the rotation axis, there is no gravity, weightlessness. In between, there are varying levels of gravity, more gravity being farther from the central axis of rotation.”

“So, that’s the basics, and now for the reason I brought you both here. Let’s begin with this: Explain to me the physics of a circular orbit. How can a satellite, such as this Ark, orbit our planet with correct initial conditions, but later, needs almost no input from us to maintain that orbit? Sir Newton, if you will begin?”

Orbiting Satellite, gravity, spacetime curvature

“Certainly,” he starts, clearing his throat, “Well, if you have studied any of my work, you would know about my book called “Philosophiae Naturalis Principia Matematica,” in which I have explained this. Basically, all objects move in straight lines at constant speed until a force acts upon them. In the case of planets, moons, and even “artificial satellites” as you call them, the force of gravity acts upon objects that would otherwise be going in straight lines, pulling them into orbits. If they did not start out with tangential velocity, they would not end up in an orbit.”

“Can you explain what you mean by tangential velocity?” you ask.

“Let’s put it this way. Throw a rock straight up and it will come straight back down because gravity pulls it back down, but throw a rock sideways (horizontally, toward the horizon) and it will land somewhere else. Throw it sideways faster and it will land farther afield. Throw it fast enough and, if the air did not get in its way, it would eventually orbit in a circle. Faster still, it will orbit in an ellipse, and faster than that, and it will escape the gravity of the planet it is on!”

“Wow, so you are saying that a circular orbit is achieved by making an object travel a certain speed in a tangential direction (90 degrees from straight up and down).”

“Yes, and here up in space, where I assume there is no air, there’s nothing to slow it down, and only gravity to pull it into its nice, circular orbit.” At this point, Newton turns to Einstein, “Ok Professor, your turn to prove me wrong!”

“Well,” begins Einstein, “First let me express my deepest gratitude for your insights and your scientific genius. Without your foundations, our modern science would never have been built.”

At this, Newton nods his head, ever so slightly.

Einstein continues, “But in this case, as you have guessed, I must disagree with your assessment. The circular path that you witness of an object in orbit is simply the path of least resistance, the geodesic I spoke of in our earlier conversation. It is the straightest path through a spacetime which has been curved by the mass (or energy) around which it orbits. This Ark is orbiting the Earth in part because of the tangential velocity you describe, and the other part is curved spacetime. This means that as it orbits, if nothing in space hits it (no particles or photons), there are absolutely no forces exerted on it. A force would cause it to deviate from this circular orbit, and accelerate. Now, as you know, there is always light from the Sun hitting it out there and many other celestial particles and energies besides that, so there is no such thing as a perfect orbit in space around any object, but with minor corrections for these particle collisions, a satellite can orbit indefinitely.”

“Wow, an answer for everything,” Newton exclaimed, “But, for an idea as strange as this, there must be some proof?”

“Indeed there is,” answered Einstein, “In 1919 and 1922 astronomers, during solar eclipses, witnessed the bending of starlight around the Sun that can only be explained by curved spacetime. Another good piece of evidence has to do with Mercury. Do you know about Mercury’s strange orbit around the Sun?”

“In my time, the readings on these things were not very accurate, so no, we may have had hints that its orbit is weird, but these may have also been false measurements.”

“Well, by my time, with more accurate tools, larger telescopes and extremely accurate clocks, we had good knowledge of discrepancies in Mercury’s orbit around the Sun. Its precession was moving an unexplained 43 arcseconds per century. Your Law of Gravity could not explain it. Curved spacetime solved the problem, even predicting this movement.”

You add, “Yes, and there is a lot more evidence today that this is the case. Spacetime does indeed curve around mass or energy. Now, I wish we could discuss this further, but we must move on. Sir Newton, if you would be so kind as to explain your understanding of how a rotating cylinder, such as this, can produce artificial gravity, that would be wonderful.”

“Ok, well, it’s simple to do with my Laws of Motion. Take a person riding in a

Horse and Carriage, Forces, Newton, Einstein

carriage for example. If the horse turns left, due to your inertia, your tendency to keep moving straight ahead, you are thrown to the right of the carriage and only a force you put on the inside of the carriage to the right can keep you upright, instead of falling over. When you put a force on the inside of the carriage to the right, the carriage in turn pushes you to the left, and all is well. The forces are balanced. You remain upright. Now gravity is a downward force on your body. You respond to this in much the same way. In order for you to stand up, you put a downward force on the Earth, which pushes you up. Are you with me so far?” Newton pauses quickly as you and Einstein both nod.

“Good, then let’s continue to a spinning cylinder then. On Earth’s surface, a spinning cylinder would have a couple of forces on it, a downward force due to gravity, and an inward force, holding the cylinder together as it spins. If a person were placed inside this cylinder, he would need not only to push against the cylinder’s sides to stay “upright” but also against the floor, due to gravity’s pull. So, take a satellite like the Ark, which while falling around the Earth feels weightless, and do the same experiment and you will find that there is now only one force felt on the body, the force pushing you inward. You respond to this by pushing with your feet outward on the inside as we are now doing. Spinning it at the correct rate for its radius will give you exactly the same feeling as standing on the surface of the Earth.

Artificial Gravity, Rotating Cylinder, g forces, acceleration

But I can also see why it is important that the cylinder is really large like this. If it were smaller, then the difference in how fast your feet are going around versus how fast your head is going around would be greater, causing you to feel weird, maybe nauseous or dizzy. Am I right in assuming, wait….” At this, Newton bends down and picks up a small rock, tossing it high up into the air, straight up and watching it fall into the pond. He picks a second one and throws it straight up again, watching it all the way down. “Yep, that’s what I thought.”

You and Einstein smile as you all three watch the rocks land many feet away, in the middle of the small pond, both in the same direction from where you are standing, almost in the same spot. “Yes,” you say, “you can clearly see the effects of the rotating Ark. It causes thrown objects to all curve in the same direction. Professor Einstein, you want to have a go at the cylinder question.”

“Yes, certainly. May I?” Einstein says, as he bends down and picks up a small rock as well, and with your nod, he tosses it straight up, chuckling when it hits almost the same spot in the pond as Newton’s rocks did. “That’s wonderful. Ok, getting back to the discussion, let’s take what you said one example at a time, and I’ll tell you what I think. The carriage. Your sideways motions and forces are well-stated. I agree, you are pushing yourself right in order that the carriage can push you left so that you remain upright. But, as you may have guessed, your downward vertical force does not exist in my theory. Only the upward force of the ground on the carriage, and the carriage pushing up on your body is what you feel here. Indeed, have you ever wondered why you feel like you are always being pushed on by the ground? It is because you are! Your inertia is what resists this upward force, and again, your inertia causes you to feel as if you have weight (a downward force on the carriage).”

“Ok, now we come to my favorite part. When I formulated my General Theory of Relativity, I realized that acceleration was the key to understanding gravity. Indeed, if you accelerate a ship in space at the same rate you are accelerated on Earth’s surface, then you feel the same effects as if you are on Earth and there’s no experiment you can do inside your ship that will

Equivalence Principle, acceleration of gravity, Einstein
Same results, accelerated in space vs. on Earth

fail to be the same as the ones you do in the accelerated reference frame of the Earth. So, when it comes to the Ark, I agree with Sir Newton. The artificial gravity feels the same as on Earth for the same reason you have to hold yourself up, in the carriage. However, while falling around the Earth in its orbit, Sir Newton would say the satellite is being accelerated, even if it weren’t rotating. I, on the other hand, say that it is simply following a geodesic, a local curvature of spacetime around the massive Earth. As it does this, the Ark is truly weightless, as are all objects since gravity is not a force. Therefore, inside a weightless vessel, when the centripetal force of the spinning Ark is supplied to our feet, with our inertia we respond naturally, and stand up with our heads pointed to the center axis, adorning ourselves with the artificial gravity as if wearing our favorite clothes. You are quite right, this is an absolute marvel of engineering.”

"It is, at that," you say, "Now, if either of you has questions, we have a few minutes before we have to head back."

"I have one for the Professor," Newton says, "Once I realized that gravity was causing all of the motions we witness with the planets and moons, I was always vexed with the problem of forces acting over distances through space, without any mechanism to transmit those forces.

It seems you have found a way to solve this, yes?"

"Yes, I believe my theory does just that. You see, during my time, scientists had figured out that the speed of light through empty space does not change no matter where it comes from or how fast you are moving toward or away from it. Based on this, I understood that only when space and time are variable, only if they change when objects move fast and accelerate, can the speed of light be a constant. Time itself changes when you are near a massive object; it slows down. Space itself changes as well near massive objects; it curves, it contracts. The two are related; thus we have the term spacetime. There is more to the theory, but those are the basics. That is how I arrived at a more robust theory of gravitation, and solved the problem of forces acting mysteriously over vast distances of empty space."

"Intriguing," Newton admits, "but what causes the mass or energy to bend spacetime?"

"Indeed," Einstein concedes, "that is the next big question which I leave to others to solve. But, speaking about bending spacetime, have you ever heard of black holes? Tell me kind sir," Einstein says, turning to you, "is there any possibility you have found such objects in space in the 23rd century?"

Black Hole, Messier 87, Einstein
First Image of a Black Hole

"Absolutely," you say, "even by the end of the 20th century we had good evidence of them, but only in the 21st century did we bring back images from the event horizons of many black holes, most at the centers of distant galaxies, but several in our own galaxy as well. In fact, we even got an image of the massive black hole at the center of the Milky Way, called Saggitarius A*. But my good Sir Newton, you must be wondering what we are going on about."

Newton raised his eyebrows a bit.

"Yes," you continue, "well, correct me if I am wrong Professor, but Einstein's Theory of General Relativity predicted many aspects of our universe that could not be known with evidence during the early 20th century. Black holes are one of the most bizarre consequences of curved spacetime. You see, it was predicted that when stars die, or when they collide, if massive enough, the resulting matter would collapse to an infinitely small point, causing unbelievable density. This, in turn, would curve spacetime so much that the escape speed from the center of such an object would exceed the speed of light. Thus, a black hole. We now have confirmation that supermassive black holes exist at the centers of galaxies, and also when massive stars die, they create smaller, local ones."

"Wow, I never imagined such a thing," replied Newton.

"Yes, and even though my mathematics led to their discovery, I also doubted that they existed at one point," said Einstein, "It just seemed too much like fantasy. Tell me this, then," he continued, turning your way again, "I don't suppose we'll ever find them, but are there any hints of the existence of gravity waves?"

Gravity Waves, Einstein
Artist's depiction of Gravity Waves from 2 Black Holes

"O ye of little faith, we also have found gravity waves," you respond. At this, the Professor covers his open mouth in disbelief, as you continue, "Early in the 21st century, almost exactly a hundred years after you predicted them, in 2015, we found the first gravity wave. After that, we found many more, and even discovered the cosmic background gravity waves of the universe, which many scientists believe date back to the beginning of the universe."

At Newton's confused look, Einstein added, "Gravity waves come from the way spacetime is rippled under extreme circumstances, like perhaps when black holes collide. They travel away from the energetic event at the speed of light, like the waves in a pond rippled when the rocks were thrown in."

"Yes they do," you say, looking down at your vibrating watch, "and with that, it is time to make our way back."

As you lead them down the path back to the machine, Newton states, "I daresay among the Professor, you, and this place, I have been given enough to keep me thinking for quite some time."

"Yes," Einstein responds, "thank you for this. It has been inspiring."

"It has been my pleasure," you say, and after saying the proper good byes, you return both to their own spacetimes.


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