Greetings and welcome to the Introduction to Astronomy. In this lesson, we're going to look through and discuss orbital motion, so how orbits work in astronomy, and in terms of things that can talk about things like planets, we can talk about comets, but we can also talk about orbits of stars around other stars and galaxies around galaxies. The basic understanding and what we need to understand is still the same, regardless of what type of objects we are looking at. The basics of orbital motion and gravity are still the same. So let's get started here with a few definitions, and let's look at these. What we have here are perihelion, which is the closest approach of an object to the Sun. Aphelion is the furthest approach of an object from the Sun. And we also have heard, you may have heard, perigee and apogee. They're very similar. The prefix here, peri, is referring to close, and ap is referring to far. If we talk about helion, helio, helion refers to the Sun. So this is the closest approach of an object to the Sun, or of a planet to the Sun. This is the furthest approach of an object for the Sun. If we look at the same word for the Earth, it would be apogee. Ap is still meaning far away, and g for Earth. So when the moon is at apogee, it is far from the Earth. When it is perigee, it is close to the Earth. So in this case, in our picture here, we would see perihelion, there's our Sun in the center, perihelion is on this side, when the object is closest to the Sun, and aphelion would be on this side, when it is furthest from the Sun. So let's look a little bit more about what else we know. Those are a few basic definitions. Let's look at what else we know about orbits. What the orbits are defined by Newton's law of gravitation. So they really depend on gravitation and his laws of motion. This works to give us very accurate positions for the planets. So why can we predict very accurately when, for example, something like an eclipse will occur? And that is because Newton's laws are so well tested that we can time that down to a tiny fraction of a second. We know the exact positioning in this case of the moon and the Sun. And we can determine when the moon will exactly pass in front of the Sun. Not that it will just happen sometime in a year or in a month or in a week or in a day, but narrow it down to a tiny fraction of a second at any specific location on the Earth. So it is a very accurate model that we can use. Now what do we use? What do we learn when we study orbits? And if you've looked at previous lessons, you've seen some of this, but we find that based on gravity that the planets closer to the Sun move the fastest. And that makes sense as we start to understand gravity. That's when the forces are the largest. So that is when the objects would be moving the fastest. So the Earth moves fastest when it's closest to the Sun in January and moves slowest when it is furthest from the Sun in July. So that means that the Earth moves faster in winter, making winter a slightly shorter season than summer for the Northern Hemisphere. So what it is, if you look up the lengths of each of the seasons, the winter is actually a couple of days shorter than summer. And that is because of the speeds changing. We also know that the orbital eccentricities, recall that those tell you how squash the orbits are, they are small for the planets. The planets have almost circular orbits, which is why we use circular orbits for thousands of years. There was not an obvious difference. If the orbits had been extremely elliptical, we would have been able to tell that much early on. We find that the planets orbit in the same plane. What does that mean? That means that when you've drawn a picture of a solar system on a piece of paper and put the Sun there and all the planets orbiting around it, that was not a very bad approximation of reality. The orbits are very flat and you can almost draw them on a flat piece of paper. There are some slight variations and we can talk about those, but it's not a very large change. They also all orbit in the same direction, so we don't have some planets going around clockwise and some going counterclockwise. This again, these three apply to the planets. When we talk about comets and asteroids, they're quite different. Asteroids and comets can have very eccentric orbits, much more elliptical. Comets, for example, can come in very close to the Sun and move very far away. Their closest approach could be in closer than the Earth and their furthest approach could be out in the depths of the solar system, out to Neptune or beyond. So orbits of other objects, as does this, does not apply to everything. These apply specifically to planets. On these three, comets and asteroids do not necessarily orbit in the same plane or even in the same direction as the rest of the, as the planets do. So let's look at, start off looking at satellites and satellite orbits here. For satellites, one of the very earliest satellite was Sputnik, launched at October of 1957. So we've had satellites now in orbit for nearly, for over 60 years, for many decades, we have had satellites orbiting around the Earth. Now, when we look at that, what do we need to get something into orbit? If you throw a ball up in the air, it doesn't go into orbit, it heads up, it slows down and it turns around and comes back down, much as number three here. If you don't throw something with enough velocity, it slows down and comes back down to the Earth.  If we throw something with a small velocity and that's pretty much anything we do here, the object will return to Earth. If we throw it with a large velocity, then that's path two here. Path two, we throw it with a large velocity, it can actually escape from the Earth and not return. So some planetary, interplanetary spacecraft that have been sent out, such as Voyager and others have left the Earth not to return. Now, note here it does escape from the Earth, but it never escapes the Earth's gravity. Just as a review, the force of gravity was gm1, m2 over r squared. There is no way this is ever zero. No matter how big the distance is, there's always some tiny force of gravity. So even the Voyager spacecraft, which have left the solar system, are still being pulled on by the Earth. What it just means when you reach an escape velocity like path two here, it simply means that you are no longer able to slow it down enough. The force of gravity of that object is insufficient to be able to slow it down and bring it back as it did in orbit three. Now, to get something into orbit, we need an intermediate velocity. In that case, the object can attain a circular or an elliptical orbit, and that is path number one. If we launch it just enough, then it goes into an orbit around the Earth, and that will continue over and over and over again. It is now in a stable orbit, and that continues. So that's what we do with a satellite. We are getting it into orbit around the Earth. Now, let's look at some examples of interplanetary spacecraft, or one main one here, and that is the Voyager 2 spacecraft. So Voyager 2 is one example. Voyager 2 here actually visited four different planets. It visited Jupiter, Saturn, Uranus, and Neptune between the late 1970s and the late 1980s. So over a decade, it actually visited four planets. Now, how do we get something to escape? We have to, to escape the Earth, we have to achieve what we call the escape velocity. We have to be moving fast enough that the Earth's gravity is no longer sufficient to pull us back down. If you throw an object up in the air, again, it goes up and it turns around and comes back down because you could not throw it with a sufficient velocity. However, if we launch a rocket with a sufficient velocity, then it can escape from the Earth and head out into interplanetary space. We also find that we use the planets in their gravity to modify the orbits of the spacecraft. So when Voyager 2 visited Jupiter, Saturn, Uranus, and Neptune, it had to be redirected. They weren't all lined up in a straight path and of course those paths are constantly changing as the objects orbit the Sun. So it actually hadn't been modified when it went by Jupiter. It was passed at just the right path of Jupiter to head it off towards Saturn. Then it passed by Saturn at the exact right distance so that Saturn's gravity could propel it on to Uranus and so on. Now, the Voyager was an example of a flyby mission. So you'd get a couple of days where you'd be really close to the planet and able to get some images. That's different than what we do, a lot of what we've sent now have been orbiting missions. And those are things like the Cassini spacecraft that orbited Saturn for over a decade, the Juno craft around Jupiter, that are just a couple of examples of craft that have been in orbit. Now the difference is that you can have craft here orbiting for years and you can study changes in the planet. Flyby missions, you can flyby the planet and you have the option in this case of being able to visit four planets but you only got a brief view of each one and in fact to date our only understanding of Uranus and Neptune, our best understanding and our best images come from the Voyager spacecraft. That's the only time those craft have been visited. Now, this can be, what we've looked at with orbits is that it's only, we've looked at like just two objects and object trying to leave the Earth, the Earth and the Moon or the Earth and the Sun. It actually gets a lot more complicated that and that's when we start looking at gravity with more than two objects. This becomes significantly more complex because it is harder and harder to calculate all of those and we look here at a globular cluster, a grouping of stars and all of those stars are pulling gravitationally on each other. It's very difficult to do those calculations if you have 100,000 stars or when we get to galaxies you can have millions or billions of stars and you have to calculate all of their interactions between each other. In fact you have to look at the gravitational force between every pair of objects. So not just individual stars but pick a star here and it's gravitational force but you have to look at how this star pulls on each of them and how this star pulls on each of them and how each of these stars pulls on every other star. Certainly the nearby stars are going to have a greater impact but you can't ignore the impact of these more distant stars as well. So in order to figure out what's going on in some more complicated objects you actually have to do detailed calculations of the gravitational force between each pair of objects but this is really, this is real astronomy. Real astronomy is not just two objects, it is many more objects orbiting each other. Now let's look at an application of this so how does this work? And one example of this would be the discovery of the planet Neptune. Neptune was not one of the original planets that was known and in 1781 we actually found the first new planet and that was Uranus which was discovered in 1781 less than 100 years or so after the publications of Newton's work on gravity. One of the problems was when Uranus was discovered it was not orbiting exactly in accordance with Newton's laws and the big question was why? Why was it not orbiting? Were Newton's laws wrong? Remember at this point they were still relatively new and had not been fully tested at this, tested. They'd worked great but they were not fully tested and why was this not working and one of the things you could say was perhaps Newton was wrong. So was Newton wrong? Well one of the other options is that there could have been another planet. So what we could have had, there could have been another planet orbiting not Neptune or not orbiting the sun and influencing Uranus. So not Neptune, they're actually Uranus being influenced and you could make a calculation based on Newton's laws of gravity. You could make a calculation and say well where would another planet have to be to influence the orbit of Uranus and what was found was that it had to be, there should be a planet at a specific location and telescopes were pointed there and Neptune was found very close to that predicted position. So that was a very great triumph for Newton's laws of gravity in terms of being able to predict the position of a new planet. So instead of throwing out Newton's laws, it really reinforced Newton's laws. So let's look at our summary, what did we learn here? Well we talked about a couple of terms and those included apheleon, the furthest approach of an object from the sun, how far away it gets and perihelion, how close it gets to the sun. Those apply specifically to objects orbiting the sun, you can change them for others. For example, perigee for objects orbiting the earth or apogee, again for objects orbiting the earth. So these apply to the sun, for the earth we would use these two. The escape velocity we talked about, that is enough velocity to be able to escape from the object and never return. The gravity of the object is still pulling on it but it no longer is able to return. It's no longer able to slow it down enough. When we talk about orbits, the reality is extremely complex. We don't just have two objects, which is what Newton's gravity tells us, we have many more objects. In fact, we can talk about stars and planets with multiple objects orbiting each other. We can talk about galaxies and clusters of stars and even clusters of galaxies that have many objects that are interacting with each other. So to really do the calculations is much more detailed. And we mentioned the discovery of Neptune and talked about how that was a triumph for Newton's gravity by predicting the existence of a new planet. So that concludes our lesson on orbits. We'll be back again next time for another lesson. So until then, have a great day everyone and I will see you in class.