Introducing Astro Computation: Live with the R&D Team

Hello, welcome to another live stream by the developers at Wolfram Research. Today, Jeff Bryan and myself, Jose Martin Garcia, will be talking about the new functionality for Astro computation that we just added a few months ago in the last version of Perform Language. So let's get started with some very simple examples. So, one of the main functions we have added is astroposition, which can compute the position of any celestial object with respect to any frame from any position in the solar system. So, for example, here we evaluate the position of Mars as observed from our current location here in Champaign. And by default, the coordinates are being given as azimuth and altitude in a number of degrees. Can use any celestial frame, for example, this will return equatorial coordinates like right ascension and declination. Or we can also use the ICRS system, which is a frame centered at the center of the solar system. And now we ask that the coordinates are returned in Cartesian coordinates. And if you click here, we can see the XYZ coordinates in astronomical units computed in the ICRS frame, the International Celestial Reference System, as computed on this date. So these are very simple examples of how we use this very powerful function, astroposition. Another function we have added is called astrographics. And this function is responsible for the computation of maps of the celestial sphere. And so here we are asking for a map of the area around the constellation Scorpius. And we want the map in the equatorial frame, which sets the orientation of this map. In some other frame, this map would look rotated. So here we have Scorpius, the main line of the constellation, the region of the constellation, etc. For example, this is another map of a smaller region of skies. This is going to take a range of about 10 degrees of skies centered at Venus. And we are asking for representation in the horizon frame. So the horizontal frame at your current location. But on this date, which is yesterday at 7pm and we see how Jupiter and Venus were very close, right? If this is 10 degrees, this is about 1 degree or so. Here you see some lines. This is the projection of the equatorial plane of the Earth. And so this is the equatorial celestial plane. This, this is the ecliptic plane. Of course, planets and the sun will be moving along this line. We can also have maps of the whole sky. Like for example, in this case we use galactic coordinates and we also use a background image of the galaxy. So the galaxy looks aligned in this, in this map. Okay, so that was a very, very quick introduction to the two main players of this functionality. So this talk is going to proceed as follows. We have seen Some very simple examples, just to show the type of thing you will see. I'm going to explain how we use reference frames and time systems. These are very important to get precise results. We will have a deeper look at astroposition. We will see other functions to do astro computation. We will then see astrographics, how to produce more maps of the sky. We will see some applications of astrographics to visualize various events in astronomy. We will have a look at constellations and then we will end up showing a future view of a view of future 3D visualization functions we are working on. You can ask questions at any moment during the live stream. We will try to address them as well as we can. So let's go ahead. So in order to perform very precise computation, the sort of computations that are used in modern astronomy with precisions of milliarcseconds or even better, we need to be very specific about which frames we are using. These frames are always associated to either the Earth or some important plane and directions in the sky, etc. So here we have a representation of these will be in blue, the ecliptic plane. In green we will have the equatorial plane of the Earth. So some frames are called equatorial and so. So we have a family of equatorial planes frames, and there are several variants. ICRS is the most important one. It's one that doesn't move with respect to the distant stars. And then we have others fixed with respect to the center at the Earth or fixed with respect to the true equator, true equinox elements, mean equator, mean equinox, etc. We can go into details of what this means if you ask about them. We have ecliptic frames too, associated to the ecliptic plane, again using the true equinox or using the mean equinox, the galactic plane. Some frames are corrotating with the Earth. This is the Terrestrial Intermediate Reference System. This is the International Terrestrial Reference System. There is a small difference between them, but we can handle that. And then of course we have finally the horizon frames in which we can also handle things like refraction.

It's.

It takes into account the fact that you are at a given location on the Earth and how that affects the observations. We also have to be very careful with time systems, which is how we measure time. There are various ways to do that. We have time systems associated to atomic time, a time system associated to the rotation of the Earth, which is irregular, so it doesn't give seconds or counting of seconds as atomic time does, and other time systems associated to various Places and motions in the solar system. Because relativity changes time if you are moving at a given speed or are inside a gravitational potential. So we take care of all of that for you. So for example, take the current time. It's that in our time zone we can change time zones and we get that, but we can also change the time system. And now we have for example, the same time expressed in atomic time. And you see the numbers do not match. This was a shift of a number of fixed hours in of time zone. But now you see the time atomic time is counting seconds differently. Or if we use the so called terrestrial time, which is the most important one used for astronomy, we see again there is a difference of about 70 seconds or so. This is very important. Another important factor to always take care of with respect to time is leap seconds. So this is a curve that shows how this time, the time about the rotation of the Earth is being shifted with respect to to TT. And so currently in 2022 we are about 70 seconds shifted. And so these two curves are 0.9 and 0.9 seconds added or removed from the difference between these two objects. And we get the two orange lines. So what we are doing is changing UTC in blue, so by an integer number of seconds since about 72, so that the blue line always stays inside. Right. So as I said, the orange lines are observed, measured very precisely. And then we have to keep adding ellipseconds to keep this line inside. It may happen if this goes down in the future, that we have to remove in the next 10 years or so, a LIP second. That would be the first time that a LIP second is removed. Okay, so that was a very quick introduction to time systems. Nicola Riviera will be talking about time and dates next time in much more detail. So if you are interested in this area, attend the talk next week. Okay, so now that we know about time systems and reference frames, let's go back to astroposition. Astroposition is modeled on the successual function geoposition for geography in perform language. And it takes three arguments. Coordinates. You can put any array of coordinates. Here, the frame defining what those coordinates means and the coordinate system, which can be Cartesian, spherical, cylindrical, right? A section, declination, longitude, latitude, et cetera. Again, let's look at the moon, for example. Here we see the Moon. It has an azimuth. This is an angle measured clockwise from north and altitude. This is an angle measured from the horizon. And because it's negative, it means the Moon is currently from our position in Champagne below the horizon internally we store multiple things. This is something very nice of Wolfram language. You always have access to what is being stored, so you have full access to extracting any part of it. So we see the azimuth angle, the altitude angle. This is the distance to the Moon very precisely computed in astronomical units. And here you have metadata when the observation was performed, from where and in which coordinate system. We can change coordinates to any other system, Like Cartesian in ecliptic frame. Right. So this would be now the ecliptic coordinates in Cartesian form of the Moon as observed from the center of the Earth. We can do this dynamically. This is interesting. Do we see how the coordinates of the Moon are changing in real time, mostly due to the rotation of the Earth? If we do it with respect to a frame which is fixed in orientation with respect to distant stars, we see that the Moon is moving very little. Now, this is the true motion of the Moon around the Earth. And of course we can extract properties. If you have that object, you. We can ask explicitly for any of the properties. We have other functions in Wolfram language to say, okay, let's go and represent it in multiple other ways as the position knows also everything about directions in space. So what's the thin it in horizontal coordinates? Okay, it's exactly a direction right above me. So altitude 90 degrees. That's the north celestial pole, which is the projection of the instantaneous rotation axis of the Earth on the celestial sphere. And we have other objects like the true equinox, which is the x axis in the true equatorial true equinox frame, but it's not the X axis. It's very close, but not exactly that in some other frame like the J2000. Right. So that's the fact that this frame is moving with respect to this one is something called precession. We have other motions on the Earth, something called notation, which makes the equinox move too. And so we have this little angle here. Again, these are technical details. And if you are interested in some of these, we can stop and ask about them and. Sorry. And discuss them. So ask about them if you want. So here is another fun example. Imagine that we want to observe our location from the Moon. In the previous slide, we were observing the Moon from our location. Now we are going to do it in reverse. We are going to be observing our position here in Champagne from the Mare Tranquility. That is so we see that it has this altitude. We are seeing very high in the sky from the Mari Tranquility, that is on the surface of the Moon. We can do that. We can observe here from the center of the coordinates, from the origin of the coordinates on the Moon. And we see that we are very high in the sky. This happens because the Moon is always facing us. This point of the Moon is. Is always facing us. So any point on the Earth will look very high up in the sky. We can compute that for any object, any and any date. So this is, this is going to be a counter of days starting this month. So d =1 will be today, d =2 will be tomorrow, etc. Always observing from this position on the Moon. And if we plot that function, here's what we see. We see this global motion, which is the motion of the center of the Earth. So what we are seeing here is the librations of the Moon, the fact that the Moon is wobbling a little bit with respect to our line of view. And that's this line. And then what we see here is simply the rotation of Champagne around the center of the Earth. So we can subtract both functions and we get this effect of the rotation of the Earth. And depending on the relative orientation of the Earth, Champagne, the Moon, we get these various situations. You see that it's about one degree of oscillation. So you see that you can observe anything from anywhere in the solar system. Okay, what other functions do we have to do Astro computations? Something very important will be astro distance. This is a function that computes distance from any point to any other point. By default is distance from our location. So these will be right now the distance to the center of the Moon from Champaign. We can convert it into kilometers. And this is something that is changing all the time, right? The distance from ourselves to the Moon. Again, we can compute it for a variety of dates through this month. And that's what we see again. A combination of the motion of the Moon itself and the rotation of Champagne around the center of the Earth. Another very important function is angular separation. Astro angular separation. This is going to measure the angle in which two objects are observed from a third place, which by default, again is here, Champagne for us. We can compute this function again to say what's the separation between Jupiter and Saturn for a given year? We compute it. We can pass the year here as a real. It will be interpreted as what is called a Gregorian year, which is, for example, this year 2023. This will be a real number going from 2023.0 at the beginning of the year to 2024 at the end of the year. And so we see that around 2020, the end of 2020, the two planets were very close to each other. Right? We are now about here. We can use the powerful functionality and the rest of Wolfram language to compute when that happened. So that's this function. And we can convert that into the Gregorian year calendar, which is what we were using originally, or the standard civil calendar. And we see that was the date and the time when that moment of closest approach in angular in the celestial sphere happened. And this was the distance between the two planets on that date. So less than a tenth of a degree for comparison. Remember that the size of the Moon is about half a degree. So they were very close to each other. Okay, so those were some examples about Astrographics. And now we are going, sorry about astroposition. And now we are going to be talking about astrographics. So we will start with maps of the whole sky. So by default, Astrographics is going to show you this type of map, let me put it bigger, in which we see the local horizon. That's this gray line. And then we see other lines here. In blue we see the equatorial plane. In yellow we see the ecliptic, the trajectory of the sun. So the sun will always appear on the ecliptic. And then in red we see the plane of the galaxy. We see some stars. We see that now the sun is at this position, so it's about midday. So it's very close to south and just about south, more or less, etc. Of course, we cannot see the stars because it's daylight, but they are there. We can do a manipulate. This is very interesting. So take the same situation. But now let's compute what happens today. So we are going to be moving H from 0 to 24. So we will explore the whole day today. And we are going to be also changing the latitude of the observation point. That's this control. And the longitude of the observation point too. That's the observation point. Okay, so let's start first with time. So if we increase time, we see that, for example, this is, this is the morning, this is sunrise. The sun crosses the horizon. And then this is more or less what we got before. This is our current position about midday. And then that's going to be sunset. Notice how the sun travels the sky always very parallel to the equatorial plane. Okay, now let's stop like here, for example, and let's change latitude. So now we are observing from different place on, on the Earth. So if we go to higher place and sorry, to higher latitude, then we see how the sun gets close to the horizon, actually, because we are in winter, if we go like 85 degrees, we get below the horizon.

Right.

And now if we change the time of the day, you see how the sun never goes above the horizon. Right. By the way, notice how we are also handling refraction. The fact that these lines curve slightly when they are below the horizon. That's a refraction effect. Reflection is very strong near the horizon. And that's how we represent that effect. Okay, so if we go to the other side, like something like there, then that's what happens. Right. So we are now very close to the equator. You see how the motion proceeds? Okay, we can use other frames. This is the equatorial frame. Now we have a rectangular projection of the sky. That's the equator, the equatorial plane. Again, the ecliptic. We see all the planets moving and the sun along the ecliptic. That's the moon. We can change that map slightly to the ecliptic frame in which now this is the line that becomes straight. And now, of course, the equatorial plane becomes curved. So now we have all the planets aligning along the ecliptic. That's the galactic situation. And notice how, by default, for galactic coordinates, we change to the movaide projection, which is standard for galactic maps of the sky. We can choose your own projection. We have hundreds of them, as in the Geography project. And this is a map of the sky in the equatorial frame using the Winkel triple projection. That's the sun. We can add a background image, this what we call the galactic sky image. And now you see how the red plane, the galactic plane, aligns perfectly with the galaxy. For example, another manipulate is a manipulate here in which we are going to show in the ecliptic frame what happens during a full year. So this is now counter of days from 1 to 365. And so we have the sun today. And if we advance, you see, first you see how fast the Moon is moving. Right. It has to move 12 times across the sky in a whole year. We see how the sun is moving more slowly. And notice, for example, Venus here, how it's moving backwards and the Sun. Right. Because Venus has to be always very close to the sun. So. Right. So there is this period here where it moves in the opposite direction. And then it turns again in this direction to follow the Sun. Okay, so you see how with a very easy combination of astrographics and manipulates, you can simulate what's going on in the solar system. We can now look at maps of a smaller region of the sky. So this is the sky Around Raijo with a radius of 20 degrees. So from Rigel to here, we have about 20 degrees. Right. So this is a circle of a diameter of about 40 degrees in coordinate in angles. Let's zoom, for example, now. Right. So now the scale is this s right. We are going to be moving from 30 to 1. So we have Orion here in the middle. But now as I decrease the scale, you see how we are getting closer and closer. We have these things representing nebulas, various types, global clusters, etc. And so we can start in the opposite direction, can get closer and closer. We're zooming in towards that star. Right. So that's what we get. These are other stars with their identifiers and designations. We can also produce a nice map like this. Now we are including two things. We are including this star, which is this one, and this point, which is the 00 in galactic coordinates. So this means it's the center of the galaxy. Right. It's a point, it's wide, it's very large. It's that point. This is the galactic plane. And notice that I'm also adding grid lines in galactic coordinates separated by one angular degree. So these are the lines, Right. And of course, they go through the center of the galaxy. Okay. Yeah. And you see Scorpius is the constellation in that region. We can show, for example, the Andromeda galaxy. And we represent galaxies with ellipses. We don't have images yet. And what we do is just plot an ellipse for orientation. Okay, so those are examples of maps of small regions of the sky. Let's do other fun things, like for example, zooming in around Jupiter. So again, we are going to be looking at a range of about 30 days in equatorial coordinates around Jupiter. And we first, for example, do this. We see how Jupiter is moving, notice how Venus has approached these days, Jupiter. And also we see this, the. The moon at some point moving very fast. Yeah, let's see. Yeah, there it is. That's the moon moving very fast. Now let's take, I don't know, this date and zoom in. So we approach Jupiter and at some point we start seeing the moons of Jupiter. Right. And they move around Jupiter, of course. And also notice that as we move through the sky, I mean, the Jupiter system is moving through the sky. We see other things passing by. It's actually Jupiter that's moving, of course. Okay, this is another interesting example of retrograde motion of Mars. So what we do here is that we take a range, a date, range of dates from July 22 to July 23, in steps of seven days. So this is week by week. We compute the positions of Mars every week. And now we plot them in a map with a background that corresponds to today. Right? So this background is today, but these are the points of Mars, the position of Mars every week. And we see how it moves in this direction. Then it goes back a little and now we are about here, that's March three. And then it will continue going in this direction. So this is a way to represent retrograde motion. Okay, let's look at another fun thing which are solar eclipses. And let's choose the famous solar eclipse used by Eddington to demonstrate general relativity. So the we can consult solar eclipse. We just say, okay, I want the first eclipse that happened in 1919 and it's this one May 29th. We know Eddington was in this island, Principe Island. And what we do now is again as usual, we say, let's use astographics. I want to look at the sun in the Astro reference frame, which is the equatorial frame on that date with a number of hours that we are going to be moving. And from our location, right this one, we will be looking at one degree of sky. And yep, here this means we have added a bunch of options for nicer visualization. So that's the result. And what we see here is the moon going, you see? And so with this we see perfectly when the eclipse happens. We can look at the number of hours that is being added. That's the control. At this moment we see that it's a total eclipse of the sun because we don't see any part of the sun being shown here. And we can visualize the whole process of the eclipse. It's possible also to do the computations about general relativity, but I will not do that here. It's in the documentation if you are interested. By the way, another eclipse that's going to happen next year, sorry, this year in October is a, is a partial eclipse that will be visible for example, from this city in the US So we do the same thing. We show one degree of sky. And now we say this other notation that we want the date to go from this date to that date if in steps of one minute. So if we do that, we see already that the sun is not going to be able to cover, sorry, the Moon is not going to be able to cover the sun. So this is going to be an annular eclipse. Because we have very precise information about positions of objects and distances. We can know the angular sizes of all the Objects involved. And again, that's the. Yeah, if it goes, it will go in this direction. Okay, so you can check all eclipses with this approach. And I'm going to talk about constellations for a bit. So if we ask, for example, for the region of the sky about the Polaris star, and now is a very large region, 35 angular degrees, we get a map like this in which we have Polaris Ursa Minor constellation here. And what we have done is that we have constructed nice illustrations of all the 88 constellations in the sky. And so this is a map that asks for the constellations to be shown as illustrations. So we have now the same map as before with the 35 angular degrees. And we see now the Ursa, the Bear. And we see how Polaris is at the end of the tail of the bear. And we see other nice constellations like Draco, etc. For example. This is another area of the sky around Rigel. So now we are seeing Orion. And as I said, we have the constellations, the illustrations for the constellations. For 88 of them, we have very fine control on all the possible styling characteristics of the constellations. And this is a map in which we make use of most of them. And so this is Scorpius. We put a galactic image behind. We see the. This is, remember, in yellow, we have the ecliptic plane. So this is one of the constellations of the zodiac crossing the ecliptic. And here we have again the line of stars, the illustration. This is the region corresponding. The sky is divided in the 88 polygons corresponding to the constellations. And this is the region of the Scorpios constellation. Okay, this is another one, Ophiuchus and Serpents. Here we have two constellations at the same time. And Ophiuchus is a constellation that also crosses the ecliptic, but it's not in the zodiac. It could have been, but historically was not included. And the final one I'm going to be showing is this one, the constellation of Arias. And here we see again ecliptic. And that's a very nice example too. Okay, I think I will stop here and let Jeff take over.

All right. Hello, everyone. Jose did a pretty good job of introducing the kind of the technical basics behind all of our computations. We're going to deviate just a little bit now and we're going to cover something else. We're going to cover some future directions. We're going to go among many other directions we're planning to go. But some things I'VE been playing with is more of a 3D approach. All the astrographics we've seen up to this point have been essentially 2D related. They're basically just 2D star maps. But if you want to simulate how something is going to look in the sky, say through your telescope, it's usually easier to take more of a 3D approach. And so we've been playing with that. I'm going to share my screen here and the basic ideas we're going to explore are they're all basic. There's basically three basic points here. We've got some data that we get from entity values. So here for example, we have Mars. You can ask for the entity that corresponds to it, the textured surface and the radius. So if I evaluate that, you'll get three things back. Once again you get the entity which you fed in anyway. There's the textured surface, this is an actual 3D object. So I can rotate it with my mouse here and then there's the radius. So these just come from entity value. The next step, which Jose did talk about a little bit at the very beginning of his presentation is we've got the Astro position. So not only do we need a 3D model of Mars, we need to know where it's at in the sky. So here you can see I've asked for the ICRS coordinate system. So that's centered at the very center of the solar system. And we want that for right now and as observed from our location. And we want the resulting Cartesian coordinates. So we want the xyz. If I evaluate that, gotta download a little bit of data there and you can see here you get an astral position back. This is the computed position of Mars and we can even modify that further and we can ask for. Oops, I didn't mean to do double brackets there. Sorry about that. There we go. And if you ask for the data for that, you just get this triple. So this gives us a 3D 3 dimensional XYZ coordinates that we can then use inside of graphics 3D. And then the only other piece we need to know beyond that is how do we rotate the 3D model once it's been positioned at this position such that when we look at it from the Earth it's rotated appropriately so that you see the right surface. And we've got this. Currently it's an undocumented thing. We're going to be possibly making more use of it in the future. But it is currently in 13:2. But if you evaluate this, you can get back a 3D rotation matrix that actually tells you how to rotate a 3D model by a certain amount to represent the position at a given date. And so building on these basic ideas here, I've been able to write some code that'll probably come out as a Wolfram Function repository item sometime in the next month, I would guess. I'm still cleaning up the code a little bit, but here's some examples that I've come up with already, just to show some interesting events that are actually going to happen or already have happened in some cases. So here I've got this function that, you know, I want to look at Mercury and I want to look at it on a given date. So here you can see I've set it for the year 2067, July 15th. I've set the viewing position to be at the North Pole. And the viewing angle is very narrow here. So this is about 20 arc seconds. So when you do that, you notice that not only is Mercury here in the middle of the scene, but Neptune is right next to it. On this, on this date, there's actually going to be an occultation of Neptune by Mercury. And so here you can see that we can reproduce that event by just using 3D graphics and the actual positions of the objects. And I can even move the view around. So it's like kind of like I'm moving my telescope here a little bit. So this is what it would look like through a telescope if you had enough magnification, though 20 arc seconds is a pretty small field of view. You're not probably going to see clouds and stuff on Neptune from Earth. The atmosphere is going to make the views a little bit fuzzier. Another example, I've taken care for things like Jupiter to make sure that the Great Red Spot is in the correct position. So here I've specified I want to see Jupiter on this particular date. So this is November 19th at 258am and you can see I'm viewing from champagne. And in this case I've got 60 arc seconds is my viewing angle. And you can see Jupiter here and the Great Red Spot is right in the middle. If I change this a little bit by, let's say, let's add a few hours here, reevaluate, download a little bit of data there, and you can see the Great Red Spot has disappeared. I back off, come back a little bit closer to the center, you can see that the Great Red Spot is moving. So we've, in this case here for Jupiter, we actually make, I take care to make sure that the texture rotates accordingly so that the position of the Great Red Spot is in the right position. Something else we can do. Jose showed some of this with those 2D astro graphics, but here's a 3D representation as well. We've got the planet Jupiter right now, or at least it was when I evaluated. If I reevaluate this, moons will move. Moons have moved just a little bit there. So here you can see Jupiter. Currently you can't see the Great Red Spot on here, but you can see at least three of the moons here. Callisto is probably outside the bounding area here. I could increase the. The view angle just a little bit until we get. Let's go out to 500. Yeah, here's Callisto starting to come in. I'll come out a little bit further. So here's Callisto way out out here on the edge. It's the outermost of the big moons of Jupiter. So I had to zoom out a little bit to include Callisto at the current time. But here you can see all. All four of the Galilean satellites of Jupiter. And you can see that I've told it to include only the satellites that you see there. But we have the ability to include the other fainter satellites as well. You just won't see those through a telescope. They're too tiny. So I didn't bother to include calculations for them. Somewhat more recently, too, this is actually late last year and December 7, Mars disappeared behind the moon. So here you can see where I've been able to simulate looking at Mars at a particular time. When I got it, just as Mars was disappearing behind the edge of the moon, I actually was able to observe this from my driveway and actually got some pictures of it. So show that we're able to reproduce the occultation events pretty well. Here's a case where I've zoomed in on some of the fainter moons of Saturn. So you can see I've zoomed in on the moon Prometheus, which is on the outermost edge of the rings, one of the shepherd satellites of the rings. And you can see that I've included the major moons as well. So you don't really see those too much. But I can reevaluate this here. So take a second to render the. The rings of Saturn are actually quite complicated. This is actually a rather detailed texture that we use here. So the render time is kind of significant, but I can still drag it around. You can see Mimus, the tiny moon Anthony hiding in there. So you can See Epimetheus.

So.

Fun little function to play around with here. I'll do another one here. This is more of a telescopic. Telescopic type view. This is what you're more likely to see through a backyard telescope on a particular date. So you can see Titan over here. Now, I've actually scaled the moons up to make them a little bit more visible in this view here. I can also enlarge the graphic. So I've made them a little bit bigger just to make them more visible. Some of these moons are very hard to see through a telescope, so I've actually made them 10 times larger than they actually are. Titan would not look this big, but you can see the actual positions of the moons that I've asked for here. And then here's another occultation event. This is a famous one that happened back in 1771. So we can go back in time. See here we've got Saturn and the planet Venus. So this was an occultation where Venus actually transited across the face of Saturn. That would have been an interesting site. Although back in those days, probably nobody would have had anywhere near this good of a view, given the telescopes available at the time. But we can make much better images here. So anyway, this is just kind of a preview. Hopefully, we'll be able to fold some of this 3D type technology in. Right now, it's just going to be kind of a Wolfram function repository item. So you'll be able to, you know, if you keep checking back there, you might see this function that's currently. I'm calling it Planetary Telescope View. I'm not sure if I'm settled on that name yet or not, but I need to do a little bit more checking. But probably in the next couple days I'll submit it. And then once it gets reviewed and published, anybody should be able to use this function and do similar calculations like this. It's currently set up to handle planets and moons and technically Pluto. Although because we're doing this in 3D, in order to see Pluto, you have to set the view angle very tiny. In other words, you're zooming way in. And honestly, I can do that as a test real quick. I'll set the view angle to just 1 arc second. It looks very rough. And this is actually. Even though this is actually a rendering artifact, it's a. It's true that from Earth, Pluto would look very, very tiny. And in fact, you wouldn't be able to resolve any features from the service of Pluto. That's actually a required new Horizon Space Probe to go there to see any features. So what we're seeing here is actually just limitations of the front end rendering such a tiny sphere with a texture on it. But honestly, through the. To a telescope it wouldn't look very clear anyway. So technically we can handle Pluto with this function. But because it's such a tiny sphere with such a tiny view angle, it runs into rendering artifacts and kind of gives you something more realistic to what you would see if you tried to zoom in on Pluto from Earth. So just kind of a fun little aside there. So let's see here. Somebody asked earlier, is there a way to offset the view in the Jupiter moons example could be off. Could you offset the center of view? There's a couple ways you can do that. So for example, here, here is a. I think this is the one that was being referred to. I've got the view centered on Jupiter. So you could either change the function so that it's centered on one of the moons. If you want to track one of the moons. You could probably play around with the View center option. I don't use that very often, but that is. Try that.

I don't know.

I don't use View center very often. I'm gonna abandon that attempt there. Probably the easiest way to do that is to just center on the object that you want to be on top. This is currently designed to not take coordinates. It's designed to take entities. So it's gotta be centered on an object. I could possibly generalize the function to be centered on coordinates as well, but right now it's the. The current early implementation is just specifically on entities. So it's gotta be something that has known coordinates. But you can center on an object and then you can expand the view angle as necessary to include other nearby objects. You can interactively, of course, move it around. This is like moving your telescope here. So if I just click and drag, that works. So that somebody asked, does it include data for new events or objects? For example, can you show where the green comet would be right now? This current implementation is based on kind of giving you a nice. I'm not covering comments yet. Right now this handles planets and moons and just Pluto mainly because those are objects we have textures of so that you can actually see what they look like. This is not intended to be a full blown three dimensional sky chart yet, which I think is kind of the direction you're going. You want to be able to point at any object in the sky and do that. We don't have textures for comets we don't have any photorealistic comets. You could do that with Astro Graphics. Jose showed Astro Graphics earlier that Astro Graphics would definitely be able to show you where the comet is. And in fact, we actually had a community post that I created actually a couple weeks ago talking about the comet. Side note, the reason it's called the Green Comet is it's not an official name. It's a very media driven name. So every comet is essentially green if it has dust coming off of it and it's because of doubly bonded carbon that gets excited by ultraviolet radiation and then glows on a particular green color. So the fact that the media is calling this the Green Comet is just because the name of the Comet C 2022 E3 is not easy to remember. So people find it easier to talk about the Green Comet. But yes, it's. That comment's kind of moving away and it's a lot harder to see now. All right, so this is just kind of a preview. It's not, it's not a full fledged functionality. It's kind of a direction we're going, but the ability to have these 3D type things. Hopefully it'll be expanded to be more like a full fledged Astro Graphics, maybe an Astro Graphics 3D at some point. But right now it's kind of limited in scope, but it's something that we are playing with and hopefully we'll see some stuff with that in the forthcoming versions as we move forward.

There was also the part of how is the database updated? So we are currently using the planetary fmris from NASA JPL, the DE405, the latest released. Sorry, 4. 440, right? Yeah, 440 and yes. So whenever the fmreads are updated, we will update our files and automatically the system will know that there is new data. There is also important data to be updated every day about the orientation of the Earth, which is unpredictable. So it has to be measured every day. And so you will see sometimes when evaluated our ASTRO functionality that there is a temporary blue window downloading data that's downloading the current data for today about the orientation of the Earth so that we can return very, very precise results. This another question. Is it possible to create animations that reproduce planetary movements at an acceptable rate? Well, the computation of the positions is quite fast. You can get, I mean in a fraction of a millisecond positions of everything in the solar system. But then of course it depends, as Jeff was showing, on the resolution of the textures and it's more a graphics question. Than a computational astronomical question. At this point, I'm not sure I'm really answering your question.

I'm trying this real quick to see how it responds here. So here you can see my function here. I just hooked it up to manipulate, and I made it so that the date changes. So it goes from now to a month from now in steps of a minute. And now I can drag the slider here. And this is fully 3D. And you can see the moons of Jupiter going around Jupiter. So, yes, you can. You can update this pretty, pretty quickly. I can. Also, I'm not used to using a Mac here, but I think this is the right way. I can zoom in if I want to. See. I've even got textured versions of the moons there. So the moons themselves are actually. They're actually three times their normal size here you can see I've got satellite scaling factor set to three. So you can actually see hints of the textures on this. I've seen amateur pictures taken of Jupiter and its moons. And if you have a really big homemade home telescope, it is possible for some of the bigger moons of Jupiter to see some detail on it. I've actually seen it. It's kind of impressive when people are able to pull it off. But the atmosphere of the Earth typically gets in your way more than anything else. But if you're lucky and you have really good optics and really good seeing, you can actually resolve subtle features on the moons of Jupiter. So, yes, it is possible to create animations that reproduce planetary movements at an acceptable rate. Okay, any other questions?

If there are no more questions today, you can always contact us directly at Wolfram or in the Wolfram community post dedicated to our live streams or directly to us.

Right. Okay. Well, hopefully everybody learned a few things about how to do some early astronomy here in the Wolfram language. And with each version, we'll hopefully increase our functionality coverage more. One last question. It does look like somebody says would be nice to see side by sides of actual telescope views compared to some of these. Oh, yeah. So you could actually try to get an actual Hubble Space Telescope image. It doesn't even have to be that. Somebody could take a camera picture to show that the results that we get match the actual computation, match the actual observations. Somebody's also asking, is tidal locking of moons visible? In theory, yes. You'd have to zoom in quite a bit. It might be hard to see in this kind of a simulation by tidal locking. What they mean is that, for those that might not know, is that many of the moons in the solar system. Just like our moon. Our moon is tidally locked with the Earth so that we always see one face facing the Earth. That is true of many of the moons in the solar system. Just because of tidal interactions with their host planet. Most moons have one face that always faces the planet. I think it's. There's only a few exceptions where the. The moon actually rotates differentially with respect to its orbit. So in theory, yes, you could do that. I'm not set up to show that really easily here, but I guess if I zoomed in enough and you looked very carefully, you would see that the textures. You can see Ganymede there. You. I don't know. I think probably the, the tangential movement. Yeah, it's not gonna be easy to see on this simulation. Technically, yes. Just hard to see it here because of the quick change of time and the position changing of the moons. Another question coming in. It looks like.

We still got a.

Few minutes left in our time slot here, so we'll see if any questions die off here. Okay, just a comment, not a question. One of the things that I was able to do, although it doesn't require 3D to do this, I was able to actually reproduce Galileo's observations. Like if you go back to his old manuals or his, his, his notes that he took when he did his observations in 1610, before he realized that these were moons, he didn't know what they were. They were just these stars that kind of like appeared to move with, around Jupiter from one night to the next. And he actually did little sketches showing they looked like little asterisks that he put on either sides of. Of Jupiter from night to night. And we were able to. I think I did a community post on this a while back. I was able to actually do these as a column. And you could actually see our. I computed the results of the positions of Jupiter's moons on the nights that he did the observations. And I changed the rendering so that instead of using these 3D graphics, it used points and asterisks. And so it actually looked kind of like Galileo's observations. And it was all done computationally, but it did match when you compare it side by side with what he saw, keeping in mind that his telescope was extremely primitive and did not have very good resolution. So sometimes he couldn't see the two moons were right next to each other. So sometimes to him it looked like one, one. One little point of light, when in actuality there were two just really close. He just couldn't resolve them.

Jeff you remember that Stephen did that in his blog post for 13:2.

And when 13.2 came out, I think that was one of the examples he put in his blog. I believe he actually showed. See if I can find that.

Right. Look in the chat in Rocket Chat.

Oh, here we go. Thank you. So this is Stephen Wolfram's blog that came out when 132 released. And if you scroll down here, one of the first things he talks about is astronomy. And scroll down further here, some computations, some of the things we've Jose showed and focused on here earlier in the talk. So here you can see some of the tech. Here we go. I'm getting down into the. This is, this is the kind of sketches that Galileo was able to do. And you can see he, he drew Jupiter with this big circle and then he drew the moons with these little asterisk looking things. And if you rotate the view here, we've set the date for Padua, which is where Galileo did his observations on January 7th of 1610. And you can see you've got 12 moons on one side and another moon on the other. And if you rotate the view, you can see here's Callisto IO. He couldn't resolve. There's another moon that's hiding in here. And then you can see Ganymede over here. So this is Ganymede, this is IO, and that's Callisto. So we're able to reproduce pretty much what Galileo said. Just this is in a tilted frame. We're observing in a horizon coordinate system as opposed to ecliptic. But so, yeah, we were able to reproduce Galileo's observations. All right, well, I don't see any other questions coming in, so I think we'll wrap up at this point. I want to thank everybody for attending, and we do these every Wednesday, so next week we'll have another talk. I don't, off the top of my head, know what the topic is, but we, if you follow the community post, we always announce ahead of time what the topic is going to be. So feel free to check back in next Wednesday and keep an eye on our new releases of Mathematica and the Wolfram Function repository for any new astronomy functionality that could be introduced as we move forward. All right, thank you very much.

Bye.