As I suggested earlier, one of the best ways to really understand things like Jupiter, figure out what's inside of them, figure out where they came from is to go find more of them. We have four things that are big and orbit around the Sun. Two of them I would call Jupiter-like. Two of them are these ice giants, which are very different things. We really could use a lot more. I remember when I was in graduate school getting my PhD in astronomy, around 1990, this was considered a big deal. People really wanted to figure out how to find other planets, around other stars, and people talked about it many different ways of doing it, and nothing had been successful. Tried to directly see planets around stars, but the planets themselves are so faint. The stars are so bright, it's just nearly impossible. People had tried to see the effects of planets on stars, and here there was at least some hope. You can imagine, that if there's a star is here and a planet is out here going around the star, the planet is going around the star but in a sense, the planet is going around the center of mass of the star and the planet. And the star is going around the center of mass also. Star goes this way, planet goes this way. They're both going around this one common point which means that the planet is causing a wobble of that star going back and forth. People had tried very hard to measure positions of stars and detect these wobbles, nothing had really worked out. The one method that people were very excited about was to instead of looking at the position of these wobbles, was to look at the star and if you were over here somewhere with your telescope looking. That's supposed to be an eyeball, not a telescope. But you're looking in this way. And one of the things that you can measure from a star very precisely is how fast it's coming towards you or how fast it's going away from you. Going away from you is red shift and coming towards you is blue shift. The spectrum of the star, the lines of the star are shifted by its velocity. So you can imagine, if it's doing this. It's blue shifted, red shifted. Blue shifted, red shifted. By measuring the velocity of the star and the time it takes the star to execute a little wobble. You're actually measuring how long it takes this planet to go around. The problem is, the amount of wobble caused by something even the size of Jupiter is tiny. Well, it's tiny in our solar system because Jupiter's pretty far away. The further way this planet is, the lesser the wobble there is. The further way this planet is, is also the longer it takes for this wobble to happen. Jupiter takes 12 years to go around Sun. So if you want to see this happening for something like Jupiter, you have to sit and watch for 12 years. And astronomers have done that and they were patiently collecting data to see if perhaps things like Jupiter could be found when extremely unexpectedly they found instead bigger wobbles at periods of something like three days. Bigger wobbles but because three days means that the object has to be much closer, something the size of Jupiter could induce these big wobbles, if something the size of Jupiter was in orbit around the star with a three day period. Now to put this in perspective, Mercury, the closest planet in our solar system has a 58 day period. Mercury is a toasty, toasty place. You would not want to live on the Sun lit side of Mercury. Something with an orbit of three days, that's almost touching. One of the things you can't know in just by looking at the motion of that star, you see it going back and forth, but you don't know how much it's going in this direction. In this direction, I'm assuming that the eyeball over here again, you don't know, maybe it's not, maybe the planet is on an orbit that's exactly edge unto you in which case that's stars only moving back and forth and all the velocity you see is caused by the planet. What if instead the planet was on an orbit that was inclined by 45 degrees to you for example. Well, really the star is going this way, and this way, and you only get something like 1 over the square root of 2 of velocity in this direction because that's the only part that you can see. In that case, you think the planet is actually less massive than it really is because it's actually causing a much larger velocity and you only see a part of it. If planet were face on to you like this, the motion of the star would be this way and this way and you wouldn't see any motion at all. And you would think there was no planet there and whatsoever. It's an interesting thing though when I drew this one very, perfectly edge on to us, you might have thought about the possibility that at some point if this planet is going around the star. And it's exactly edge on at some point that planet would pass directly in front of the star. If it does couple of things would happen. First, the light from the star would dim by just a little bit. How much? Well Jupiter is about a tenth of the radius of the Sun, which means that the projected area of Jupiter is something like about 1% of the projected area of the Sun. So if I drew the sun and I drew Jupiter on top of it, I would be blocking 1% of the light of the Sun by that Jupiter sized thing going across it. 1% on stars that are pretty bright stars is a pretty easy thing for astronomers to do. And so as soon as these hot Jupiter's began to get discovered astronomers started looking for these potential transits going across. They had help in a couple of different ways. One is, if you know the motion of the star is coming toward you here is going away from you here is going toward you here is going away from you here, you know exactly when the transit should occur if it's going to. We draw a new picture for you. I'm going to now draw a top-down view of this planet and I'm going to draw the transit occurring right here. We're still looking over here. I want you to think about when the transit occurs as this planet is moving this way at its maximum speed right here, that's when the star is moving towards you at its maximum speed. Down here, the planet's moving towards you at its maximum speed. The star is moving away from you at its maximum speed. So at the point halfway between when the planet is moving towards you and moving away from you at this point, is when the transit has to occur. The transit won't occur when it's over here. It won't occur when it's over here. It has to be right there so you know exactly when to look for the transit and you know exactly what it should look like. The only thing you don't know is whether or not this planet is really lined up this way. And the plane that I'm drawing could look like this, but it could be tilted like this and you'd totally miss the transit. There's another reason that transits are good, and that is early on there still was a lot of uncertainty from astronomers about what really was going on. Was this it's really a planet that was going on in this crazy three day orbit or what we seeing some kind of weird phenomena of the star pulsating in some way or something else. Most astronomers were pretty convinced that it was really a planet but still seeing something like the dimming of the light as the planet went in front would be a pretty amazing thing. There's one final way in which astronomers were greatly helped by the fact that these Jupiters were so close to their stars. If I draw a star again and I draw Jupiter out here. The distance, in terms of now diameters, those Jupiters and 3 each day orbits were something like 4 diameters away. What that means is the probability of having a transit is much much higher than if Jupiter were way, way, much further away. Think about it this way, okay, we don't know what this inclination is of the planetary orbit with respect to the star. Could be this, no transit. Could be this, no transit. Could be this, no transit. Could be this, no transit. It could be this, there is a transit. The transit will occur if it's anywhere between this and the planet's right here, and this and the planet's right here because this will transit just the very top of the star. This will transit just the very bottom of the star. This will transit the very middle of the star, and this is now simple geometry. This distance here is the diameter of the star, d. And the question is, what is this distance compared to all the places where the orbit could have been. So it is, this distance d divided by this entire circumference d over 2 pi times this radius which should had been 8d and we should multiply by 2 because the transit would equal likely occur of the orbit like this, as it well with orbits like this. So we'll take away 2 here, and we get that the probability of a transit, for one of these sort of 3-ish day orbits, is something like 1 over 8 pi, with is pis about 3, 8s about 8 so that's about 1 over 25, which is about something like 4% chance. 4% chance is not huge but it means you have detected 25 of these hot Jupiters. You're likely going to come across one that happens to be going right in front. And sure enough, within a few years at exactly the predicted time, one star HD 209458, even I remember this one. And this is now a very famous license plate number for a star. The star HD209458, exactly at the right time had a little 1% dip in its brightness and that was the final dead certain proof that these exoplanets, these hot Jupiters really were hot Jupiters going around the star. Trends is nice because it does a couple of things too. First, it tells you that that orbit is exactly edge on, and if it's exactly edge on it tells you what the real mass of it is. You no longer have to say well it might be like this or it might be like this, you say no, it is exactly edge on. I know the mass, and as an added bit of excitement, it tells you the size of the planet. The amount of deep in the sunlight that occurs as this planet goes across the face of the star. It tells you precisely how big the planet is with respect to the star. So, we now have two things, we have a size and we have a mass both able to be measured pretty precisely and that gives us a favorite parameter that we could start using to explore this new hot Jupiter and that is the density. The density we can only measure in this transiting exoplanets. Exoplanets that don't transit that might have any inclination at all. First off we don't know their mass precisely. But more importantly, secondly, we have no idea what their size is. But once you put a transit, you get a very good measurement of the mass, you get a very good measurement of the size. We get a very good measurement of the density, and we will use that in the next lecture to start exploring what we know about these exoplanets.
