The Science of Everything Podcast - Episode 1: Explaining Gravity

Episode Date: July 11, 2010

A discussion of gravity, beginning with a history of the concept from the ancient Greeks though to Newton. Also includes an explain Newton’s universal law of gravitation, how orbits work, how astronauts experience gravity in space, and how gravity causes the tides. If you enjoyed the podcast please consider supporting the show by making a paypal donation or becoming a patreon supporter. https://www.patreon.com/jamesfodor https://www.paypal.me/ScienceofEverything

and welcome to the Science of Everything podcast. I'm your host James Fodor. In this podcast, I discuss a wide variety of topics in both the natural and social sciences exploring the many fascinating insights that the scientific method yields about the world around us. Now, the topic for the first episode this week is explaining gravity. So in this episode, I want to look at first the historical background about different theories of gravity before moving on to explaining Newton's theory of gravity. And then we'll look at how orbits work, the topic about gravity in space and on the moon, etc. And finally, we'll have a bit of a look at the tides. So, let's dive into it. Theories about gravity basically go back to the times of the ancient Greeks. According to ancient Greek through particularly proposed by Aristotle, they didn't really have a concept of gravity like we do today as a force.

They believed that all objects in the universe or on Earth were made up of four different elements and that different elements had different natural tendencies to go in different directions. So, for example, fire had a natural tendency to go upwards, seek the heavens, so to speak. And so if an object had lots of fire in it, it would tend to go upwards. Whereas if an object had lots of earth in it, it would tend to sink downwards. And the ancient Greeks also believed that the circle was sort of a perfect form, a perfect shape. And so circular motion at a constant speed was sort of seen to be perfection, sort of the universal and natural form of motion.

And so it was believed that all the planets had a circular orbit around the Earth. And that idea of a geocentric universe was put forth by Aristotle, and later on it was sort of codified and consolidated in the Ptolemaic model. Ptolemy lived in, I think, the second century AD, and he adopted basically an Aristotelian worldview of gravity in the orbits, except that more accurate observations of the planets had showed that there was a phenomenon called retrograde motion. Basically, that means that normally the planets move around in a certain direction, which we now know is caused by the rotation of the Earth and also the movement of the planets around the sun.

But it had been observed even in the time of Ptolemy that sometimes the planets sort of moved backwards across the sky. And this couldn't be explained by the Aristotelian worldview of perfectly certain. So Ptolemy adopted the idea of that basically each planet and also the Sun orbited around the Earth on a perfect circle, but then on that circle it also, the planet orbited around a smaller circle called epicycles. So basically that you can think of a point called a deferent which orbited around the Earth on a big circle, and then around that deference, around that point orbits the planet in a smaller circle. So it's kind of like a moon orbiting, a planet orbiting the except in this case it was just a planet orbiting nothing orbiting the Earth. If you can think it like that. And by adjusting the the speeds and timing and size of all of these deference and epicycles, Ptolemy was able to construct, to get his theory to match exactly with the observations of the planets. And so that theory of the Ptolemaic model of circular orbits with Earth in the center

and epicycles and deference remained essentially the main theory that was held in the west right up until the 16th century. Now, in the early 16th century, an individual by the name of Nicholas Copernicus proposed what he thought was a simpler model planetary motion, where he had all of the planets orbiting around the sun, and retrograde motion was in this instance explained by the relative order of the planets.

So basically, in his model, planets that are further out from the sun, which would be Mars, Jupiter, and Saturn, would be overtaken by the Earth as it orbits, the Sun, so you can think of Mars just slowly orbiting the Sun further out and Earth coming in from behind and overtaking Mars and then moving past it on a smaller circle. So if you sort of work that out, it turns out that Mars, from Earth's perspective, appears to move backwards in its orbit, in its motion across the sky, for a short period of time.

So the Copernican model could explain retrograde motion. However, the problem with the Copernic the Copernican model was that it still assumed perfectly circular orbits and so there were still discrepancies in the observational data that couldn't quite be explained properly and so Copernicus still had to rely on epicycles and deference and those things so it wasn't a complete break with the old Ptolemaic model. In the late 16th century there was a I think he was Danish astronomer called Tycho Bray he basically spent his life drawing together a large body of extremely accurate astronomical observations about the planets and their orbits around the earth and so on. And then based on all this data, his protégé, by the name

of Kepler, constructed what are now known as the three laws of planetary motion. He constructed these laws based upon the, as I said, the extremely accurate observations made by Tyke Bray, but he constructed the laws so that they were mathematical in nature, which was a very unique achievement, being able to construct very sort of simple mathematical laws based on this vast body of experimental evidence that he had there. I should also point out that Tyker Bray did not have access to a telescope. So he made all his, he lived before the telescope was invented. So he made all his observations with, well, I don't exactly know how he did it, very precisely aligned observatories and other things like that. It's quite impressive. Anyway, Kepler's three laws

of planetary motion. So his first law was that planets do not orbit the Sun in circular orbits but in ellipses with the Sun at one foci. Now an ellipse is sort of, it sort of looks like a circle except it's elongated in one direction. So an ellipse has two foci, sort of central points around which the ellipses focus. So Kepler's first law was that the planet orbits in an ellipse with the Sun at one foci. Now, This idea of an ellipse finally allowed Kepler to explain the various discrepancies in the orbits of the planets that had plagued astronomy for thousands of years since the Greek times. So this idea of ellipses plus the order of the planets going out from the sun, so the heliocentric model plus ellipses finally enabled all of the problems in the orbits of the planets to be solved, and therefore there was no longer any need for epicycles or deference.

and so those were gotten rid of. And that's actually a very powerful reason for why the Copernican model and Kepler's laws and so on were accepted because they were so much simpler. They did away with the need for these complex epicycles. Okay, so Kepler's second law was that the planets always orbit the sun such that they sweep out equal areas of their orbit in equal times. So if you think about what that means, so if a planet's in an ellipse, it means that it, in different parts of orbit it's at different distances away from the sun.

You know, when it's at the further end of the ellipse, it's further away than if it's at the closer end of the ellipse. And once again, you can look up a diagram online if you're having trouble visualizing this. So Kepler's second law basically says that if the planet's at the point at its orbit where it's closer to the sun, the sort of radial distance between it and the sun is less. And so in order to sweep out a certain area,

it has to travel faster. When it's further away from the sun, the distance between it and the sun, the planet and the Sun is greater, so it doesn't have to travel as fast around the circumference of the ellipse in order to sweep that same area. So basically, Kepler's second law says that when a planet is closer to the Sun, it moves faster, when it's further away, it moves slower. And Kepler's third law is stating a similar thing just in more mathematical terms. I won't go through that now because it's basically just a mathematical relationship between the semi-major axis and the period of the orbit. So once again the basic idea is that the further away a planet is, the longer, the slower it goes around the sun or whatever it's orbiting, and the closer in the faster it is.

So we see this in the planet, so Mercury has an orbit of I think 88 days takes to go around the sun, whereas Neptune takes many, many decades to go around the sun once. Okay, now those are Kepler's laws, so now we move on to Newton. He did some very important work on optics but probably is most famous for his laws of motion and his universal law of gravitation. Now Newton's real, his biggest insight, his most important contribution was the fact that he realized he was really the first to come, or the first significant person at least to come up with the idea that the same forces or the same processes that caused an apple to fall off a tree or any object to move on the earth, to move to fall down on the earth, are the same ones that

kept the planets moving about the sun. Because before these people really had no idea why the planets moved about the sun or about the Earth or whatever they thought they orbited around, they just sort of did. Newton connected the idea of apples falling from a tree with planets rotating around the sun. And in doing so, he formulated, obviously, his universal law of gravitation. And in doing so, he developed his laws of motion and his universal law of gravitation, and then he plugged in all the numbers and he was able to derive all of Kepler. All of Kepler just from the things that Newton found. So that was a very strong proof that Newton's laws were accurate. Of course, another big proof was the fact that he was able to predict, they were able to use

Newton's and Kepler's laws to accurately predict eclipses, which was a pretty big thing. Okay, so what is the universal law of gravitation? Basically, it's that the force between any two objects, the force of gravity between any two objects is determined by the mass of both of those objects and the distance between those objects. And there's also a constant in there, which is the gravitational constant. That just defines how strong the gravitational force is. Now, it should be pointed out that the gravitation, contrary to everyday experience might tell us, the gravitational force is actually very weak. Let's take the example of a magnet. When you put a magnet on the fridge, the electromagnetic force of that magnet between the magnet and the fridge is greater than the entire gravitational force that the earth, the entire earth, exerts upon that magnet.

And you think about how big the earth is compared to the size of the magnet and the fridge, you can see how much stronger the electromagnetic force is compared to the gravitational force. And the nuclear forces that act on an atomic scale even stronger again relative to the size. I'll talk about those in probably later podcasts. The reason that it seems like gravity is so important is because, unlike the other three fundamental forces, electromagnetism and the nuclear forces, gravity doesn't have, there's no such thing as far as we know as negative gravity or negative mass. So gravity is always attractive. So you can think of, for example, if you have positive and negative charges, they can cancel each other out and the whole object can be neutral. So on a macroscopic scale, there's no electromagnetic forces between most objects. gravity never cancels out, so it always builds up, it's always cumulative, so that's why on a scale of, say, planets in a solar system, gravity rules the day. So, as I said, the gravitational force between two objects is dependent upon the mass of those two objects and the distance between them. And now that the gravitational force diminishes by the square of the distance between the

objects. And basically, the reason, the intuition behind that is, is sort of that you've got, you can think of the gravitational force as diminishing proportion to the surface area of a sphere. And the surface area of a sphere, obviously being two dimensions, length times width, it's a squared term. So if you double the length, the surface area of the sphere goes up, or if anything, goes up by the power of two. If you think about two objects, say, 10 meters away, you can sort of draw a line between them and draw a sphere with a center point at one of those objects and then let's say we move the object, object two, twice as far away from this initial object. And so the radius of this sphere doubles. When we double that radius, the surface area will increase by four times. That's how you get the inverse square law of gravity.

Okay, now another interesting thing about gravity and something that Newton's law clearly showed is that all objects inside a gravitational field of a given strength accelerate at the same speed, or at the same rate. Now this seems counterintuitive to a lot of people. For example, if you ask someone classic question, for example, if I drop an egg and a rock of the same size off of the top of a building, which will hit the ground first. And natural inclination is to think that the rock will hit the ground first

because it's heavier, and that's what Aristotle thought. But in fact, they both hit the ground at the same time, ignoring the effect of air resistance, of course. This is the reason we actually get confused. is because air resistance usually comes into play. That's why feathers and other things like that takes so long to fall. It's not because the force of gravity accelerates them to a lesser extent than it accelerates anything else. It's just because if you look at a feather or a leaf or anything like that, the surface area is massive relative to its mass and the greater the surface area,

the more air resistance acts against it. So the greater, the greater surface area, the more air resistance acts against it. So the greater the surface area of an object relative to its mass, the more air resistance it will have, and therefore the slower it will fall. But that's not due to any difference in the force of gravity. So on Earth, every object will accelerate downwards at a rate of about 9.8 meters per second, regardless of the mass of the object. Now, the reason for this is because basically the mass cancels out, the mass of the object, that's falling, cancels out.

So remember we said that the force between two objects is proportional to the mass of those two objects, so you would think that if you had a more massive object, then it would fall faster. And that is true, there is a larger force that acts on this, that will act on the larger object, the more massive object. However, exactly counteracting that is the fact that the more massive object has more inertia because it's more massive, and so it requires a larger force to bring it to the same acceleration. So those two factors, the extra, the extra, extra force acting on it and the extra inertia that it has, they're both dependent upon the mass of the object. So they both exactly cancel each other out. And so that's why the rate of acceleration is

totally independent of the mass of the object. This fact that the two, that the mass exactly cancels itself out is quite interesting and is actually one of the factors that led Einstein to develop his general theory of relativity. But that is definitely a topic for another podcast. Okay, so now I want to move on to look at orbits. Now, what does it mean when an object orbits another? I'm sure everyone listening to this podcast has heard about the moon orbiting the Earth, the Earth orbiting the Sun, satellite's orbiting the Earth, but what does that actually mean?

Basically, the basic idea of an orbit is that when an object is in orbit around another, let's talk about a satellite orbiting the Earth. So when the satellites orbiting Earth, it basically means that the satellite is perpetually falling to the earth. It's forever falling down to the earth. You might think, well, why doesn't it hit the earth? The reason that it never hits the earth is because it has sufficient velocity perpendicular to the direction in which the force of gravity is pulling on it, so that it always manages to escape falling down. Now this is to Earth. Suppose that we were to shoot a rocket up into the air. Now, generally if we did that, what would happen is that, well, let's say we don't

shoot it straight up in the air, we shoot it at somewhat of an angle, just to make this example a bit easier. Now, normally what would happen, it would just go up, and then it would sort of arc over and fall back down to the ground again. But let's suppose we shoot it faster and faster and faster. And as we shoot it up faster, it gets to a higher altitude before it exhausts sort of all its velocity, and its gravity pulls it back down again. Now, you can imagine that if we shot this rocket fast enough, it would actually be able to, you know, escape the Earth's, move out of the Earth's atmosphere. And if we shot it faster still, it would take a big arc curve through space

until it came back and hit the Earth. And we can extend this line of reasoning further until we get to a speed where the rocket is shooting so fast that it actually never falls back and hits and hits the ground again. It perpetually goes around the Earth. I should say that the velocity, that enables us to happen, it's called the escape velocity. In order to get satellites or anything into orbit,

we have to accelerate them to the escape velocity of the Earth. And the escape velocity is rather high, and so that's why you need massive rockets to get into orbit. That's why it's so expensive. This might seem a little counterintuitive. How can you just sort of never fall down? Well, think about it like this. According to Newton's laws, an object always tends to go in the same direction,

at travel in the same direction, at the same velocity, unless an unbalanced force acts upon it. upon it. So suppose you have the Earth just sitting there and we have a rocket that's travelling or a satellite, we'll call it a satellite that's travelling perpendicular to the Earth. So you've got the Earth sitting there and the satellite coming along and sort of moving past the Earth, not towards it but perpendicular past the Earth. Now in order for the satellite to move in a circle around the Earth, there needs to be a force continually pulling the satellite towards the Earth. Because

because an orbit is a circular motion. And remember, objects do not naturally move in circular motions. They naturally move in straight lines. Now, that force, pulling inwards, pulling the satellite inwards, will be provided by the force of gravity acting upon the satellite. That's, you know, why things fall down. It's because the force of gravity is acting upon them. So you can think about the satellite moving perpendicular and a perpendicular motion past the Earth, but it slowly curves sideways a bit towards the Earth because it's being pulled by the gravity of the Earth. However, it still has all of that initial forward velocity perpendicular to Earth. So it doesn't just careen directly to the Earth. It still has that initial forward velocity, and we know from the law of inertia that it's not going to lose that just because we have an

extra force acting on it. So it's still moving forward. It's just also curving slightly towards the Earth. And this is important because the reason that objects are able to never fall down and hit the Earth is because the surface of the Earth itself also curves. Remember, the Earth is more or less a sphere. So if the rate at which you're being pulled towards the Earth, the rate at which the satellite is curving towards the Earth is sort of the same rate at which the Earth itself is curving, then the satellite never moves relative to the surface of the Earth. The way you can think about it is that the satellite is falling to the Earth. It slowly moves towards the Earth, but the Earth is falling away from the satellite or curving away from the satellite

via the curvature of the surface of the Earth at the same rate. And so the satellite never hits the Earth. You may have noticed that I've been talking a lot about sort of velocity perpendicular to the Earth. That's important because in order to have, from my description of what an orbit is, what's crucial is the perpendicular speed relative of velocity relative to the Earth. So in order to orbit the Earth, the Moon or the satellite or whatever it is, has to be going at a sufficiently fast speed. Otherwise, what will happen is that it will be pulled to the Earth, but it won't have moved far enough in the perpendicular direction. When I say perpendicular, by the way, I'm referring to, if you think of the line along which the force of gravity acts between the object, between the satellite and the Earth,

perpendicular refers to the direction perpendicular to the line of that force. If you have perpendicular velocity relative to this force of gravity, but the velocity is not enough, you will fall to the Earth faster than the Earth curves away from you, and so eventually what will happen is you'll spiral in woods and you'll crash into the Earth, or whatever you're orbiting. So to get satellites in orbit, we need to give them, we're not only have to get them out of the Earth's gravity, well, we have to move them up out of the atmosphere. We also have to give them a lot of perpendicular velocity, and we also have to periodically give them boosts from their engines as well

because even when they're really high up there's still a little bit of atmosphere left there which means there's still a little bit of drag acting on them so gradually their perpendicular velocity perpendicular to the earth gradually diminishes as a result of that frictional force and so if left alone they'll spiral into the earth that's called decaying orbit you may have heard of that that's why satellites generally won't stay forever in their orbits because they're too close to be in a stable orbit unless they get periodic boosting in their rockets to keep them up.

Okay, so now I want to move on to the topic of gravity in space. Now, I've kind of already covered this. It's often said that when astronauts are, say, in Earth's orbit or in the space station or whatever, that there is no gravity. And that's not exactly true. It's accurate to say that they don't feel gravity. or they don't feel the force of the Earth's gravity. Why is that? Well, it's interesting to note that the reason we feel gravity while we're on Earth is not because of the force of gravity itself. It's because of things that are resisting the force of gravity.

So, for example, I feel the gravity of the Earth acting upon me, not because of the actual force of the Earth's gravity on me, but because of the force of the chair or the ground pushing back against that gravity. That's what I actually feel. Another example, if you jump off a building, the force of gravity is acting upon you all the time as you fall down. But you don't feel anything until splat you hit the ground. So it's only when you make contact with something else that resists your motion that you feel the force of gravity. So astronauts in the space station are falling towards the Earth in an orbit.

Now, as we've seen, they're in perpetual free fall. This is what the state's called. It's free fall. They're perpetually falling to Earth but never hitting the Earth because the Earth's curving away from them as they fall. But the space station or spaceship that they're in is also falling to Earth at exactly the same rate. Remember that the force of gravity doesn't depend upon the mass of the object in question. So the space station, the astronauts, and everything else in the space station are all falling to Earth at the same acceleration. Nothing is acting against the astronauts to make them be able to feel the force of gravity.

And so that's why they don't feel gravity. Now, on the moon, unlike in Earth orbit, there is gravity on the moon. This is a common myth that there's no gravity on the moon. The moon is a massive object, and so obviously it generates gravity. The moon is not as large as the Earth, so it doesn't generate as much gravity. The force of gravity is less. In fact, if you go onto the Moon, the acceleration due to the force of gravity will be about one-sixth as strong as it is on the surface of the Earth. On Mars, it would be about a third as strong.

Now, this fact is important because often you'll see maybe in a science fiction movie or something, people from Earth going onto other planets and walking around just as if they were somewhere on. Earth. Now that's inaccurate for many reasons, but for one thing, unless the mass of the planet they were on was pretty much exactly the same as the Earth, the force of gravity would be dramatically different, either much more or much less, depending on how large the planet was. And so, you know, either they'd be leaping above the trees or crawling around the ground on their bellies, essentially. And this is most extreme if you ever see, if you ever see, like on some episodes of Star Trek, for example, the astronauts land on, or in some movies they land on

They land on asteroids to do some mining or whatever. And they walk around, generally they'll show them walking around with a little bit of a spring in their step. But if you're on an asteroid, asteroids are very, very small compared to the Earth. The force of gravity, yeah, there'd be some gravity there, but it'd be so insignificantly small compared to the Earth that you'd probably be able to put yourself in orbit just by taking an ordinary step. So there would be very, very little gravity on an asteroid, unless it was made of some extremely dense material. Okay, so finally, we're going to look at the tides. Now, the tides just refer obviously to the changing height of the water, particularly the ocean,

at different times of the day and of the month and so on. Now, this is caused by, you may have heard that the tides are caused by the moon, and that's basically correct. A tidal force just refers to, or tidal forces as a general concept, refers to the difference in forces between two different parts of an object. So it's tidal forces that are responsible for the tides on Earth. Now, how does this work? Well, you think of the Moon, sort of sitting there on the right-hand side of the Earth.

Now, remember, the force of gravity diminishes with the square of the distance, or the inverse square of the distance between the two objects. That means that the side of the Earth closer to the Moon will be acted upon by a larger force than the side of the Earth farther away from the Moon. The effect of this is to sort of stretch the Earth out a little bit. Now, that effect acts upon the land and the sea, but because the land is, well, it's made of mostly solid, you don't see the effect as much. Water being, well, sorry, the oceans being made of water, the sort of stretching effect is more noticeable. So basically, the ocean bulges relative to the land.

That is what causes the tides. Now, the reason we have two tides every day is because the Earth is rotating. So you think about it. Now, think about the Earth and the Moon, and picture the Moon orbiting Earth. Now, sort of tip that up on its end so that you're, if you weren't already, picturing it this way. So you've got the, so you're looking at a circle, the moons moving around the circle, and the Earth is at the center of the circle. Now, think about the Earth as more or less a circle or a sphere,

but think of the oceans, the water on Earth, as sort of an ellipse, or a bit of a stretched circle, which is sitting on top of the circle of land, which is the earth. Now you'll notice that if you sort of can picture this in your mind, if not look it up on Google, you'll see that the water sort of sticks out at two ends of the earth, so it protrudes from the land at two ends at two ends, but at the two other sides, the earth sticks out relative to the sea. And that corresponds to the high and the low tides,

where the water is higher, you get a high tide, where the water is low tide. And because the earth is rotating sort of within that elongated, body of water, you get the two tides per day. The sun also plays a role in creating tides because of tidal forces of the sun acting on Earth, but the size of that is only about one-third of the total effect. So if we didn't have the moon, the tidal, the tides on Earth will be much smaller. It should also be noted that the size of the tides and the particular timing of them and so on, it's very complicated, it's more complicated than just where the moon is.

is also affected by the shape of the ocean floor and the outline of the continents and all those sorts of things. One last thing I want to talk about is the Roche Limit, which is a bit more of an advanced concept, but I think it's quite interesting. You can think about the tidal forces, as I said before, as being the difference in the forces

that acting upon different parts of an object. So as you move closer to a massive object, say, for example, a planet, the force of gravity acting upon that object increases. And so also the difference in the force of gravity between, say, the near and the far part of that object also increases. If the difference in those forces, or those tidal forces, increase to a high enough level, they'll actually rip the object apart. Now, the Roche limit refers to the distance from a massive object, inside of which, tidal forces exceed the gravitational attraction between 82 objects, and so no object that it's held together solely by gravity can survive within inside the Roche limit.

And this is why gas giants, notably Saturn, have rings. Ordinarily, all of that dust and rocks and stuff that comprises Saturn's rings, that would collect together in form a moon or several moons. But because this stuff is inside the Roche limit, tighter forces acting upon, that would act upon a moon at that distance from Saturn would be too great and it would be ripped apart. Now, you might think, well, how come we can put satellites in orbit then? And we can have the space station there, which is really, really close to the Earth.

The reason for that is because the space station and shuttles and other things like that, probes, they're not held together by gravitational forces. They're held together by the electromagnetic forces acting between the chemical elements and atoms that make up these objects. So the tidal forces are not great enough to rip them apart. However, if you went to a sufficiently dense object, like a neutron star, for example, maybe I'll talk about those in another podcast, but they're really, really dense objects, or read close to a black hole, the tidal forces would become so great

that they would exceed even the electromagnetic forces, keeping your spaceship together, and your spaceship and, in fact, your body would literally be ripped apart. So, on that happy note, that ends this episode on explaining gravity. Hopefully you learned a bit from listening to this podcast. Now, you may have noticed that I didn't really say anything about general relativity or the curvature of space time. And I believe that this is best left for

a separate podcast because it's a hard topic to understand and to explain. So in this episode, we just looked at gravity from a Newtonian perspective. If you enjoyed this podcast, please help to spread the word by posting a positive review on iTunes, or by sharing the podcast with a friend. If you have any questions, comments or suggestions about the podcast, please feel free to contact me. You can reach me at my email, Fods12 at gmail.com. That's F-O-D-S-1-2 at gmail.com. You can also find the show notes for this podcast and leave comments at fods12.

Podbean.com. Thanks for listening, and I'll talk to you next time.