 Greetings and welcome to the Introduction to Astronomy. In this lecture we are going to talk about orbital motion and how what we've learned over the past couple of lessons as to how we determined orbits in the solar system can actually be applied and learn some definitions here as to how we look at the specific orbits. So let's go ahead and get started here and what we see is, let's give some definitions here first of all and I've mentioned some of these before but let's go ahead and look at them again. Parahelion is the closest approach of an object to the Sun. So anything orbiting the Sun will have a Parahelion. Earth will be closest to the Sun at its Parahelion which is in January. Now Apheleon is the furthest object is from the Sun. Apheleon for Earth would be in July that's when we're furthest away from the Sun. Now we also see the semi-major axis labeled here that is half that major axis across the longest diameter of the eclipse. Now we use Apheleon and Parahelion note the helio section there which means Sun so that is the closest and furthest approach from the Sun. We can also talk about perigee and apogee if we're talking about things orbiting the Earth such as our moon or satellites. So let's continue and look at some of this. How do we determine orbits? Well orbits of an object are determined by Newton's universal law of gravitation and his laws of motion. This gives extremely accurate positions for the planets and we find a number of different things. First of all this was far more accurate than any of the previous models and now that we have an exact understanding of what that underlying cause is in terms of gravity. We find that planets closer to the Sun move faster and we saw this in Kepler's third law. We see that the orbital eccentricities for planets are small. None of the planets have highly eccentric orbits. We note that all planets orbit in the same plane and in the same direction. So we see those here if we look at the planets here the inner planets labeled for you can see Mercury, Venus, Earth and Mars and this image goes out to Jupiter a little further out. Now the black circles for the planets are all relatively circular. Mercury being the most deviant from a circle. The blue asteroids you can see their orbits are a little bit different that they do have more eccentric orbits and the red orbits of comets can be even more extreme. So even more eccentric orbits for the comets and the asteroids. So when we look at satellite orbits how do we put something into satellite? Well we look at Sputnik launched in October of 1957 and if we launch something with a small enough velocity of course this is not how we launch satellites but if we launch something or throw something with a small velocity which would be position A here it returns to Earth. Gravity pulls it down. If we use a little bit larger velocity it continues further along and if we could could send it with a high enough velocity it would actually go into orbit and come all the way back around and strike you again. Now that only works if there's no atmosphere so of course atmospheric resistance would cause these so even something with a very high velocity would lose so much energy in its trip around the Earth that it would never make it that far. But paths A and B will give you a circular or sorry object will return to Earth that we can get a circular or an elliptical orbit if we get it far enough and if you give it an even larger velocity it will actually escape from Earth. But note that it does not escape from Earth's gravity. Gravity never ends. It goes on forever so no matter how far away something is from Earth you can calculate how much force of gravity is pulling on it. It could certainly be negligible enough that it's never going to pull the object back but there is always a force of gravity between any two objects with mass. So we can put things into orbit this way and we in order to get away from the Earth we do need to achieve what is called escape velocity. So things like the Voyager spacecraft here achieve escape velocity from Earth. Now even though it's out in the depths of the solar system way beyond even the strong influence of the Sun now they still are being pulled on by Earth. They're moving fast enough that Earth can never slow them down enough and they will never return. But we can use to send something interplanetary we just have to achieve escape velocity to get it away from Earth. We can then use gravity to modify its orbit. So in order to make things more efficient you could make a really high powered engine to accelerate something very fast or you can use the energy of the orbits of the planets. So if a craft heads out towards towards the moon it can go around the moon and get a boost in gravity. So it can accelerate the craft a lot and the moon loses a tiny bit of its orbital energy. However because of the gigantic distance between the mass of the moon versus the mass of the spacecraft the moon will never notice it. And Voyager 2 used this as it used a gravity assist from Jupiter to get to Saturn and then another one from Saturn to get to Uranus and finally from Uranus to get to Neptune. So because of a gravity assist like this Voyager 2 was able to visit all four outer planets fortunately because of their positioning in the solar system at that time. Now when a mission gets to a planet it has two choices. We can either plan a fly by mission or an orbiter. Fly by missions are far easier. You pass by the planet take your pictures and continue on. In order to get into orbit you need to lose some energy to get into orbit around the planet. So it requires more fuel at that point to be able to adjust the orbit or again multiple orbital maneuver maneuvers to get the to adjust the speed to the correct speed to bring it in to an orbit. So we tend to use orbiters now certainly because they can stay for a long time and study that study the object for years and even a decade or more. Whereas a fly by mission a lot easier in terms of energy and planning only gets one chance to observe that object. Now what if we look at more than two objects? Well it gets very complex as we look at more objects. Here we see a globular cluster and if you really want to figure out the orbits here you need to look at every pair of stars and calculate the gravitational force and step forward in time and do all the calculations again. If there are hundreds of thousands of stars there are billions of different pairs you can look at and you have to calculate all those gravitational forces. Now when we look at things within the solar system it's a little bit easier the main influence for gravity is of course the Sun. So unless an object passes close to one of the other planets its gravity is its orbit is pretty much determined by the Sun. But passing close to Jupiter or Earth or any of the other planets can adjust that orbit and this can be very difficult especially for very small objects like comets whose orbits can be significantly impacted by a passage near one of the planets. So let's see how this could have been used and how it was used. Uranus the first planet to be discovered was discovered in 1781. This is less than a century after Newton published his work on gravity. As we tracked its orbit we found that it was not orbiting exactly in accordance with Newton's laws. Big question is why? Why was it wrong? Did Newton's laws not apply at that far out in the solar system? Or was there another planet out beyond Uranus that would influence its orbit? Well astronomers Adams and Laverier calculated the position of this potential planet and Neptune was found in this area. So a great triumph for Newton's law of gravity in that a prediction was made in terms of its orbit. Now this was tried again with Mercury when Mercury wasn't quite following its orbit and it was postulated that another planet might be orbiting closer to the Sun than Mercury that had never been discovered. That would be a hard planet to see and people did the calculation and look for the planet but never found anything and in this case we found out that Newton's gravity was wrong and it took general relativity to be able to explain what was happening there. So let's go ahead and finish up as we do with our summary. We talked about Aphelion and Parahelion which were the furthest and closest distances to the Sun of an object orbiting the Sun. We looked at escape velocity which is you escape from the object never to return you're going fast enough that the object can never slow you down. In reality everything is much more complex you have lots of objects interacting together and finally we looked at the discovery of Neptune predicted to exist because of deviations in the orbit of Uranus and it was a great triumph for Newton's gravity. So that concludes this lecture on orbital motion. We'll be back again next time for another topic in astronomy. So until then have a great day everyone and I will see you in class.