Live CEOing Ep 647: Language Design Review of Astronomy Continued

Are we ready here?

I am.

Okay. All right, Well, I think we're ready. Okay, so for people joining this live stream, we are continuing our review of Astronomy functionality. And where have we got to.

Okay.

Yesterday about astroposition and about the second argument of astroposition.

Right, exactly. And, and thinking more about it, I wanted to elaborate on. On an important idea that I wasn't able to articulate yesterday properly. And so to do that, I think it's easy or useful to compare to the geodesign. And so in geo, we have two main types of objects. We have the geoposition and geoposition, xyz, et cetera, which are absolute identifiers of position on Earth. Like we have these two, for example, then we have the GEO displacements, which are like relative identifiers. And so we can say, give me the displacement from this first position to the second position. And so we get. This is the distance in meters, this is an angle. And so now, of course, the main point here is that the geodisplacement does not remember where it started. So we can use geodestination to say if we start at this first geo position with this geodisplacement, we get back the second one. Okay, so. So your destiny displacement is. Is instructions on how to compute a.

Geodesic on the Earth which are managed to be set up so they're independent of the base point, which is not obvious. You could do. I mean, if the Earth was a weird shaped, you know, one of those weird shaped moons that has, you know, whatever.

No, no, no, no, no, no. It's very important to know the first. So we cannot compute the geodesic we. Without knowing the.

I know, but you've got parameters that are independent of where that first. The, the parameters of the displacement.

Yes.

You know, if you imagine a metric.

Yeah.

Okay. What is the analog of this in general relativity? So we've got.

Exactly. That's the thing we are going to discuss here. But the main point is that to compute a geodesic in any situation, you always need a point and a vector. The, the, the point and, and the vector that indicates the direction in which you start. And of course the length of the geodesic. So this is essentially the vector. This gives you the direction in which you have to start. And because the Earth is flat. Sorry, it's flat. It's plane is two dimensional. We just need an angle and then the distance. But this idea always works. A point and a vector. Now, what is the situation in Astra? So if we did this in relativity, we would have to start with events, we would have astra events. They would be the equivalent of geoposition. We would have coordinates and then we would have to say in which coordinate system this is given the analog of.

Geoposition, xyz and things like that.

I would say the analog. Yes, the analog of any of these, which are all four absolute positions. It would be an aster event. We just give numbers and a coordinate system. Right. And then we would take two of these events, which are like points in space time, and we. We will compute the displacement between them. Right?

Yep.

This GEO coordinate system is datum, right? It's like which geo, ellipsoid, etc.

Yes, yes, exactly. Yeah, I think of it that way. Yes. It's the thing that physically gives meaning to these numbers.

Although there's also geoposition, xyz, isn't there? Which is not with respect to a datum. It's some absolute.

No, no, it is. It is also with respect to a datum. You need to know an ellipsoid. Well, a datum, the datum includes the orientation of the three axis. So different datums have slightly different orientations of the three axis.

Okay, yeah, so.

So there is a second argument in your position, XYZ too. Okay, but so the point is that we would have this astral displacement. And this ASTRO displacement is the thing you have in mind when you think of is this light like, is this space, like, is this time like. Right, it is. The numbers inside will be the vector that indicate how to start the geodesic in spacetime. Exactly as this geodisplacement.

It's a 4 vector.

In fact, it will be a 4 vector in our case. Yes. And so in Astro, we are interested in light observations, and so we focus on the case of light. But this could be generalized to an object that computes all these other kinds of geodesics in space times. So what did you want to make one.

I just want to make one comment here. I mean, in a sense, maybe what we're building here is a way of handling space time coordinates. I mean, you know, spatial coordinates are sort of trivial to handle. They're just what we handle in lists and, you know, all our linear algebra and all this kind of stuff. You know, spatial coordinates are straightforward, but the Minkowski metric, or something beyond Minkowski metric is not so easy to handle. And perhaps what we're doing here, I mean, you know, we're doing it in the astronomy case, but we could as well. You know, this could be, you know, somebody's Bose, Einstein, condensate You know, thing where there's. Where speed of light matters for some reason. I'm just. I'm making that comment. I. I think there's an argument that this notion of space time event and so on could be actually space time event, not astro event.

Yes, I agree with that. I mean, the one comment is that this purely spatial case can also be already complicated if the shape of the object you are working on is complicated.

Yes. Right.

So it's true that in relativity we have the added complication of Minkowski of the sign change for time. But so the thing. Now that we have seen this difference now, where is astroposition sitting here?

Sorry. I'm sorry, I'm sorry, I'm sorry, sorry. Just backing up to your comment about the essentially differential geometry comment that you made before. Y. You know, right now, you know, the datum is still on ellipsoid. But to do general differential geometry on an arbitrary surface, we've got something which is a generalization of a datum. And we could imagine. And we had that guy working for a while on that. On that problem of giving an arbitrary surface. I mean, given an arbitrary region object. So, Roger, this is a, you know, given a region object. And you want to know the distance on that weird shaped, you know, banana or something, right?

Yeah.

Between two points.

Yeah.

I mean, is that something we have right now?

We don't. But we, you know, it's been one of those. It's. I want. I'm curious to hear. I mean, it sounds like you're kind of relativity sort of interest in it. But it actually is useful in many other contexts for planning problems. For instance, to find sort of a shortest path. And there are many variations of it. But this thing of computing it on a surface, on a mesh, it's not that hard. So I don't know how far that guy got, but it's not that hard. We don't have it. But. But you know, I was thinking that the use case is kind of like path planning, basically.

Well, I mean, there are plenty of pure math use cases as well, defining judicial surfaces. Well, yeah, not completely uninteresting ones either. No, no. And so on.

Sure.

Yeah. Okay. All right. So. Okay, so keep going. Jose.

Yes. So. So the thing is, what is astroposition in. In. In the light of. Of this discussion? So what we are doing in astroposition is essentially what we do already in the opposition E and U, which is that we store a place and then we store a vector that communicates that place with the place you are interested in.

Yes.

Right. So in astroposition, we are storing the observation event. The. The base you were calling yesterday. Plus the numbers are how to start a light geodesic. That would take me to the place I'm interested in.

Well, hold on a second. What you were doing before was to say, here's the thing I'm looking at, and here's the place I'm at. Now, there's presumably a geodesic between those two. But rather than defining, you know, you're saying what the endpoints of the geodesic are. Right.

So the. The. So when I say astral position of Venus, I'm interested in two things. One is that I'm looking at Venus from a place on Earth right? Now, that's an event of observation. So I'm storing the event of observation so this date and this location. And I'm storing also the orientation of the frame with which I will define these three numbers. These three numbers are essentially the vector with which the light arrives at me. So you see, so it's a geodesic that comes from Venus to me. And I store the vector that would allow me to reconstruct the geodesic backwards in time and then discover where Venus was at that point. So that's what.

That's a nice clean description of what's going on. Okay, so now what do you think that means in terms of the design?

Well, I wanted to introduce this to find terminology and structure possible. Structure.

Right.

So.

Right.

Yeah.

Well, I mean. So. Really what you're saying is, first point is there's an observation point, an observation event.

Yes. So it's both position in space. So these are effectively 3. 3 numbers because we know we are on the surface of the Earth plus a date. These two dates are the same date. It's just that it's useful to store it in two forms to avoid converting from one to the other. But I might change that and cache it. It's the same date.

Okay, but. But. So the basic point here is we've got. It's just very strange to call it observation event.

Wasn't it observer? I mean, into geographics.

No, there's no analog in geographics. There's no.

No astrographics.

I mean, yeah, I know it was observer, which I don't like at all because an observer is like. I'm thinking of Arthur Eddington as an observer. Is know. Not, you know, 19. 19, you know, Princip island or whatever.

Perhaps this is the observation rather than the observer.

Yes, well, I think that's closer to what it is. But. But. Let's see some sort of setup. It's complicated because, I mean, you're right that, You know, observation event just sounds wrong. Because it's not. I mean, it's observer position in space and time.

Plus orientation of the frame in this case. And there is also the coordinate system. It's interesting to see that this object, your position E and U. It's assuming always the horizon frame.

Yeah.

With a given orientation ENU and cartesian coordinates. So what this is doing, it's generalizing to any frame. And then this specifying the equivalent of cartesian enu. So this is saying. No, I don't want cartesian. I want a spherical coordinates. And rather than enu, I want starting at the north azimuth. So this would be north eu.

Yeah.

So it's a different convention. So this. This all stored in. In these two things in this and this. Actually, we can say astro position of London from here. And we are going to use the horizontal frame as well. Well, I don't need to specify anything else. And I'm going to use Cartesian coordinates. And in the format enu. Okay, so those numbers are. Those numbers. But these are corrected for relativistic stuff. So they are very close to those.

Okay. What on earth does that mean? So astral position of London relative to. Where is our observer point? Where is our observer?

By default, it's here and now. So this is now and here. Those are the defaults observing from here.

Oh, I see. So here, wherever your geolocation was.

So now I can extract these. And these, of course, are in. So I have this notation which. So we could say quantity kilometers.

That's very weird.

This weird?

Yes.

No, sorry, doesn't work here.

Okay, so let's change these to. Okay, hold on, hold on, hold on. I'm still internalizing here.

What I mean here is that astroposition can work with things that are very close. Like London from us.

Yeah, I get it. Okay, So, all right. So basically what you're saying is. We need a word that's like. It's beyond frame. It's a combination of frame, position, location. Or maybe we don't need a rope. Maybe it's just the second argument. Astroposition. And that's. That's what it is. And we say astral position is this thing in the coordinate system. Is that the relativistic correction? What is that?

I can eliminate one by one. So, for example, first.

No, please.

Yes, yes.

Magnificent. But this is not what we should be doing right now. It's okay. I'm curious what that Does. But anyway, not allowed our physics moment here.

No, this is okay. ET so again, eliminated one by one.

By the way, you should. You should make aberration goes to none work. Just FYI.

Okay. Yeah.

Okay. So. All right, so let's go back again. So the first argument of astroposition is the thing you're looking at. And then. But it is. So geoposition by default is using absolute coordinates on the Earth with respect to a certain datum. Astroposition is necess. Is using. Let's see, because of the. Because of the light. You know, because of the relativity issue. You have to know where you're looking at it from. And also because these things are moving, which is not the case in, you know, on the Earth, you know, things don't move. Right. So I think it's the. Okay, so basically what it is, astroposition is the thing you're looking at and then sort of. And then you've got this bundle which is. I mean, I would feel more comfortable about having a wrapper Astro observer. That is that bundle of. Here, now frame. You see what I'm saying? It's not an option. It's a. It's a. It's an actual object.

An object that we can place in various places.

Yeah, right.

I see. I see.

Actually, that's not a bad idea.

Because.

Now you can store a bunch of observers.

Yes. Which is useful. And this is describing an observer, an astronomical observer, where they are, when they are, what frame they're using, whether they're dealing with refraction, blah, blah, blah.

Yeah.

Now it's a little weird that that refraction is in the eye of the observer, so to speak. Because refraction is either happening or it's not.

Well, we have parameters here like temperature, etc. So there are four parameters.

No, I understand that. I understand that. But. But that's. The observer is at the destination. The refraction is happening, not at the destination. I mean, here and now in Horizon. Those are all destination stories. Refraction is on the trip.

Refraction. Doesn't that seem to you like optic, like visual spectrum? Or does. Does that happen for X rays?

No, no. Refraction is. Is the question of how the. Yes, it is. It's.

It's actually, it's. It's referring to atmospheric refraction, which means.

Visible light in the atmosphere is bent. If it was an X ray, it would just go straight through.

Right. So this implicitly assumes visual light.

Yeah.

Which is.

You're right. And that's not really necessarily correct.

Well, we do have here. One of the four parameters is wavelength. And this has some models that work for several ranges of these four parameters. This thing is quite difficult to compute. And this is some approximation that gets more or less correctly what happens near the horizon. And then so we have basically two models. One for observations near the horizon, another one for the observations far from the horizon.

Okay, so if I'm on Mars.

It.

Doesn'T have much refraction going for it. Right? Right.

Yeah. The models we have are for the Earth. Indeed. But you can specify if you know the values of, of these things in Mars, then you can use them.

I see. I doubt that will work because it's got, you know, it's an atmosphere with different. No, why would that work? I mean, the, the refraction, the refractive index. Well, actually the refractive index of a gas. Right. It's Lorentz, Lorenz law or something. Gives refractive indices of gases, as I recall. And I don't know what it depends on.

You mean that this would also depend on the chemical composition?

Yeah, I don't know whether it does. I think it maybe doesn't, but I'm not sure.

I don't know either.

I mean, in the end, the refractive index does depend on that for a material like, but for, you know, it depends on atomic properties, but for a gas it's not.

So if you're worried about refraction, for example, there's another one which is the precession notation model. So these are all things that we need to know about the Earth. And again, it's not a property really of the observer. It's more of the setup of the observation.

Yeah, or maybe it's astro observation.

The last one is this one.

Okay, Okay, look, it's the position. I mean, maybe astroposition isn't the right concept. I don't know. Maybe the, the observation is a wrapper around the position that the position defines the position of the thing, the source object. You see what I'm saying? With its frame and you know, with it with its coordinate system and all that kind of thing. It's just that is where Venus is. That's the position of where Venus is. And now you have to observe that position from somewhere else. Am I making sense?

So.

Why don't you use docu tools?

I use the low level tools. So there are all these parameters in the observation.

I understand. So what I'm suggesting is maybe what we should do is astrop position really is the actual raw position as it is in geoposition. Yeah, yeah. Look, look, here's. Here's what I would suggest. Okay, let's imagine that Astroposition is the actual position. So astroposition of dated of Venus, blah blah, blah, could certainly give the position of Venus at that time. Right. In its. In whatever frame is our default frame. Okay. Then the question of where is Venus sort of projected onto our telescope. Where we are is a wrapper around that. It's an astro observation of this thing at a certain astral position. I see. The problem is the coordinate system that you quote the astral position in. Okay, here's the issue. Astral position of Venus is an absolute thing. You know, where Venus is in some coordinate system, right?

Yep.

And then, you know, wrapping as, excuse me, wrapping astro observation around that to say where does it appear in the sky? From me, it all makes sense. Okay. What that is not dealing with is I want to simply type the position of something in. You know, I've got this black hole merger just occurred at this, you know, galactic coordinate system position. So I don't understand what. Maybe what we need to do is the coordinate system. The problem is that a natural coordinate system in which to specify astral positions is the altitude, azimuth 1 or right ascension declination relative to where you are on the Earth. But in order to use that coordinate system, you have to back project from where you are, so to speak.

Right. So this has been very well developed for the solar system. So in the solar system there is this. This is called barycentric coordinate reference system. And so we can give coordinates everywhere in the solar system at any given time for a time that is defined by the. By essentially the time at the center of the solar system at the solar system body center. And then the same thing has been done for the Earth. There is the Geo Celeste, the geocentric celestial reference system.

Okay, now is that where you can give right ascensions and declinations?

No, rate ascensions and declinations are angles of a vector of observation. So this is what I was discussing before.

So if I know that the star Rigel is at this right ascension declination which, you know, Ptolemy had, you know who, whoever Hipparchus had tables that said that.

Yep.

Right. How do I type that in? Is that GCRS or is it close to GCRS or what?

So when you say I, I know that the altitude and.

No, no, I said, I said right ascension declaration.

Right ascension and declination of something. It means I used are in equatorial reference frame from the solar system barycenter or from the Earth. And I got these angles when I looked at it.

Yes, but not the solar system. I mean, you Know Ptolemy didn't use the solar system barycenter, he used the earth.

Exactly. Yeah.

And so if I type in his coordinates and I say my coordinate system is gcrs, will I get the right answer or not?

The most correct one for, for him would be what we call the true equatorial true equinox frame.

Okay, fine, but there is a. Okay, there is one. So, so basically what we're saying is a literal object like Venus just has some location. Okay. And a dated Venus or whatever has some location at a certain time. At the specified time. Yep. Now you know exactly what the dated means and how we back project the times. We have to talk about that, but in a first approximation. Right, so that this would be the.

Equivalent of, of what an astronomer would get.

No, I understand, but what I'm much more concerned about is if you say astral position, you type in a right ascension declination there.

Yes.

Right. Then it's all good. Right. You just can say. Okay, okay, so with the right ascension declination, and that's probably the default, is that correct? That if you don't give a second argument and you just give literal numbers.

The default is the horizon.

So altitude azimius, which I think may be a mistake.

Well, it's the default. It is the closest to you. So for an astronomer.

I know, but in order to do that, don't you have to have. Well, okay, maybe that's right. Okay, but that specifies. No, but isn't that just totally confusing everything again? Look, the whole point of astroposition is it is a literal space time point, not some back projected judiciary. But I mean, you know that astral position in a right of sanctum declination isn't a space time point, it's a direction some geodesic. Right.

This is a direction from which we can compute where something was. Because we know it was observed from some place.

Yeah, we don't know how far we knew how far away it was. But that's very different from saying Venus there, which is at a particular place at a certain time.

Well, this is assumed to be on the celestial sphere. If you don't specify distance, this is some sort of infinitely extended light ray.

Wait a second, wait a second. We're not talking light ray here.

Yes, everything that is is always a light ray. When it, when it's involved as an observation, when it's described as an observation. For example, when we get this information of where was these black hole merge, we get a direction which is very precise and relatively precise. And it may be not so Precise in distance. Or it may be that we don't know the distance. Even, for example, the distance to the Gamma rebursts in the 90s. In the early 90s, they didn't know whether they were in the galaxy or outside the galaxy.

Right, right, right.

So. But they still could give these numbers very precisely.

Right. Okay. So hold on. So I hate the fact that we're not defining whether it's array or a point. I think that's going to cause us trouble.

Yes. There is this. This parameter inside which perhaps this parameter is especially important to be broken into parts. So light time can have three values. And the observation value. So it means I'm looking at the light as it comes to me. Emission, which is I'm emitting myself the light. And I'm saying the light will arrive at this event at such a distance or geometric. Which means I'm using instantaneous propagation. And therefore I'm referring to where is.

Can we zoom out for a second? Okay.

Yep.

These issues which we really need to resolve. Is this the primary set of things we need to resolve for Astro stuff. Once we've nailed these, have we basically got the whole picture. Or is there a whole bunch of other design also to do?

I think this is the main thing for Astroposition.

Well, but what about the other Astro functionality?

Yes. Then Astro Graphics has the. These. The styling problems. Right. But I think these are things that are more the choice of projection colors. Things like that. Or I don't know.

Which we already discussed.

We have discussed yesterday. And we could bring Jeremy and discuss a bit about this. But I think this is more or less clear.

Okay. All right. So let's go back to Astroposition again. Okay. So let me just understand, Stephen.

It's not surprising that we get hung up on astroposition. This is the most complicated object there is.

Yeah, yeah, yeah, I know. I know.

Okay.

I'm not. I'm not complaining. I'm just trying to understand. No, no.

Okay.

Okay. Let's talk about a star. Rigel. Or something. Okay. When we give its astroposition, do we in fact have the distance? Do we have its point in space? In space. Or not? Or do we only have the ray?

For some of them we do. For others, we do not. For this one, I think we do. Yeah.

Yeah.

Okay.

But these some.

We literally don't know where they are. We only know the ray.

Yep.

Which is good enough for Astro Graphics. And it's good enough for Astro angular separation. It's not good enough for Astro Distance. Astro distance will fail.

Exactly.

If it's just the ray.

Exactly.

But we talked yesterday. Apparently there's quite a lot of them. We don't know the distance.

Yeah, yeah. Right, right, right. So listen, here's what I think we should do. I think we should have a symbolic thing that we give for the distance when we don't know the distance.

I see.

So that it's very clear in the astroposition. If we looked at astroposition, it would be something like indeterminate or something. Now, sometimes there may also be an interval that we can give. Like we know it's outside the galaxy or something like that. And that might be useful to give. But what I'm suggesting is that we always give what we need. We always give enough coordinates to. Quotes. Determine the position. Even if one of those coordinates is indeterminate. So it didn't determine the position. It effectively just defined array. Okay. So if we did that, then. And then, by the way, you know, astrodistance would just fail or give indeterminate or whatever else it does. Right.

Yes. For example, astroposition can understand directions too. So when I say astroposition, what is. I don't know, the. Through equinox. This is a direction. So it doesn't have a notion of distance. So.

Well, then we just call it indeterminate. I mean.

Yeah, go ahead. Right now I'm saying it's on the celestial sphere.

I know, but I don't think that's the right thing to do. I think that the position needs to be a position. And if it turns out it's a ray, that is. What do we do? Okay. In geometry. Okay. We have. What. How do we represent. You know, we have a position xyz. Or we have a line. We have the notion of a. Of a. Of a. You know, of array. Right, Roger. A symbolic representation of array. What does it look like?

Well, it has the similar parameterizations. Like, what is it called? Now? It's called. Not half space, half line.

Yeah, but how. What does half line have in it? It has. It has.

Look it up. It has basically a point of origin and a vector.

Right.

Actually, I think it has two parametrications in it. Very cool. Yeah. There's two of them. So if you look at the second one, there's a point of origin and a vector.

Okay. Okay. So the vector. Yeah, this is just a different parameterization where we're saying that because it's spherical coordinates, basically we're giving. You know, just the radius is indeterminate. I mean, not for the half line. But we could have a half line. We could have that Representation for a half line as well. Where the half line has, you know, altitude, has, you know, latitude, longitude or theta phi. And then R is indeterminate. We don't happen to have, you know, V is a vector, not is a, is a three vector. Is a normalized three vector. Presumably not a theta phi, but it could be a theta phi. Am I making sense? Roger. Am I making sense? Yeah, it's something we might consider adding to. Halfline is the, is the spherical version of half line.

But prismography, this works in, in multiple dimensions. So.

Yeah, this works in any.

Okay, but. So fine. But I mean, so, so what we don't have in the system.

Right.

And, and, you know, okay, okay, this is, this is where spherical position is relevant. Because spherical position could have the same issue. That is just like we have a, you know, we could define a theta phi with spherical position without giving a radius for the sphere. Or spherical position could give theta phi and a radius. Am I making sense?

Yep.

So, I mean, spherical position normally will just be on the unit sphere. Presumably that will be its default. But we could also have an indeterminate version which is on array and a version which is on a sphere of an arbitrary specified size. So effectively, what sphere position. Spherical position becomes. Is just a representation of a point in spherical coordinates. Right. Which seems to me to make quite a bit of sense. So we should take that little monologue there and clip it out and give it to Brad.

So, I mean, normally we think of, think of a point on the unit sphere in any dimension as generalization of angle.

Yeah. Okay, let's. Let's come back to this understanding because I think this is a decent understanding. So the proposal is that astroposition is always, you know, we can have short forms of how to input it with pairs of numbers that represent altitude, azimuth at your current point, things like that. But astroposition always simply represents an absolute space time event, basically. Well, okay. By event. Okay, now this is the other point. Just like its radial distance is indeterminate, so too its time could be indeterminate as well. Like the star Rigel.

Well, that's why it's important that we consider these things, observations. Imagine that we don't know the distance to Rigel, but we still get the light at a given point of very precise angles. So the way we handle this is by saying, okay, this is not where Rigel is now, this is where Rigel was when it emitted the light that we are receiving.

No, but then we've got to put. Look, the question is, what's in the source. Okay. Your point is? Who cares what the source information was of when the light was emitted? All we care about is when it was received.

Exactly. Exactly.

The problem is that astroposition seems like it is pinning things to the emitter.

No, no, no. To the observer, all these things.

It's not. No, that's this observer thing. That's different from astroposition. Look, we've got two concepts here. We've got the emitter, and we've got the observer.

Excellent.

Yep. Okay. So the problem is that there are cases. Where we have a raw emitter. Like Venus. At a certain date. That's a raw emitter. Something like Rigel. There are many aspects of the emitter. That we don't know or care about. Right. And the point that is at such and such an altitude. Azimuth is a ray. And if something is coming down that ray. We don't really care where it came from. All we care is how it's arriving.

Right.

Okay. So, yeah.

That's why we were also thinking. Here's another kind of use case. Which is not sort of far away observation. But actually sort of traveling around our own solar systems. With satellites, around Earth and nearby bodies. In which case the absolute. You know, I mean, to do orbital dynamics and all that stuff. We kind of want the absolute.

All right, let's go through this again. Okay. All right. So if astrop position represents the observed position. What do you actually say in the documentation does astroposition. Hold on. Let's. Let's just. Let's just look at the documentation.

Yep.

So astroposition really represents an observed astronomical position. Maybe we can write that statement down. Represents an observed astronomical position. I don't know whether you want to actually edit that. I wouldn't edit that. I would just put it in.

Okay. I'll put it here and then.

Okay. Astroposition represents an observed astronomical position. Okay. Now then we say. Okay, so one possibility is. It is an astronomical object. With a certain observer specification. So one possibility is astroposition of obj, comma, obs. If you write that down, ob beat J, comma, obs. Okay. That is of an object by an observer.

Yep.

Okay. Another possibility is that it is astral position of. Let's call them O cohorts, comma, obs. No, no. O chords. Not just cohorts. O cohorts. Because that's what it is. It's the observer's coordinate system. The coordinates that the observer is using to describe the object.

Yep.

Now, you know, much like other things. Like. Like, you know, I don't know. I'm thinking of inset or something. There is a way in which astral position might have raw coordinates. There in that first argument. Not the observers coordinates, the observers coordinates, things like altitude, azimuth. But you could also specify, you know, for the. Yes. That BCRS thing is a raw coordinates. Is that correct?

Exactly. So this is the case. So the BCRS is this raw coordinate system that is defined everywhere in the solar system. And when we do this, these coordinates are instantaneous to this date. So the VCRs automatically.

I get it, I get it, I get it. So I mean one, one case is. It's observer coordinates. So that's one case. So. So now you've also got ABS chords. And then really the next case, if you write it down over there, astral position comma, abs coords. Comma and then some kind of. I don't know what you call it. Coordinate system. You know, then it's a coordinate system which is a different thing from the observer because the coordinate system.

No, it doesn't. It's. It. It's a reference system. Again, it's. It's an observer situated at the center of the solar system. But now the point is that it's not following light rays. It's. It's kind of doing a space like.

Yeah.

Observation following that foliation that is preferred.

You know, at the end of all of this, we're actually going to viscerally understand relativity better than ever before. Before the. I don't like the term light time.

Yes, it's. It's standard terminology, but it's kind of. Yes. These are the so called light time correction. So the thing is that changing from one to the other for objects that are very close to us are tiny or. Tiny.

Yeah.

And so people consider them corrections rather than different objects. So I consider separating the three of them. The abstract observation, the position being instantaneous and then an asteroid emission, meaning that we are emitting the light towards them rather than vice versa. But then it gets more complicated. In the sense that you always have to think about which object you have.

Okay, let's zoom out for a second. I mean the thing that you currently have implemented, is there anything definitively wrong with it other than that we're slightly confused about exactly what the semantics are? You throw in a frame, you throw in the position, the observer position, you throw in the observer date.

And I don't think there is anything wrong. It's just that the design, and this is probably my style, is kind of compact in the sense that all the geoposition stuff is combined In a single powerful super function. But this doesn't prevent us from separating various parts in the future if needed. If we prefer something else.

No, no, I understand, but look, look, the issue is, I think it's important this statement represents an observed astronomical position. I think that's a useful statement to make it much less confusing. I mean, it doesn't, doesn't affect the design. It's just explaining what the heck is going on.

But it depends on the value of this option.

Okay, but. But it's still conceptually observed. I mean, observed where the speed of light is assumed to be infinite. Observed, blah, blah, blah. But it's basically observed. It's not.

Yes, exactly, I, I see what you mean. So it's observed in this sense. I was explaining before that everything is referred from these base point. That for us is. Is the second argument.

Yes.

Yeah.

All right. Well, I still do think that the astroposition altitude azimuth should have that R should be, well, presumably indeterminate. In other words, that first usage there is equivalent to the second usage with R being indeterminate.

I mean, is it indeterminate or so large that we don't know it?

Infinity. What do you want to call it?

I'm not using infinity because of the packing issue, but perhaps it, it will be closer. The physical meaning is closer to infinity.

You've got this hacky number, right? Yes, but I mean, so we could just put infinity. You know, we could put infinity and you can change it on, you know, on input.

Right, so something, something inconvenient of using something like indeterminate or infinity is that it doesn't work in Cartesian coordinates. In spherical coordinates you can isolate the infinity into one number, but not in Cartesian. That's another advantage of using a fake number.

Well, you can see the explicit scaling. Look, the fake number is going to get us in trouble. I guarantee the fake number is going to get us in trouble. But you know, it's a hack for now, but I think as much as possible we should remove it. What is the. Okay, the coordinate system does a. Cartesian coordinates. What is the cartesian. Which one is the cartesian coordinate system?

Xyz. You give the three numbers xyz, so this will be Cartesian.

But so if I want to convert to absolute XYZ in the BCRS frame. Yes, it can do that. Yeah. What do I do?

So for example, I can say I don't know again, if this is equatorial coordinates. And now I want them in Cartesian coordinates.

Right.

So now we have the XYZ Values.

That's frigging weird. Relative to what? Relative to the center of the Earth.

Equatorial coordinates. Yes.

The center of the Earth, say BCRS there.

In Teta or in icrs.

So bcrs, this is now from the center of the solar system?

Yeah.

Okay. What was 10? Really weird that the Z coordinate is the only one that's big. I don't understand that.

No, no, no. It's just that it.

It's.

It's switching these numbers out of the same order of these numbers. It's just using. You see, it's kiloparsecs.

Oh, it's kiloparsecs. Oh, yeah. Okay, so that's confusing.

It's the. The threshold is between these numbers. Precisely.

What is tt?

It means true equatorial. True equinox. Okay, so. So the equator of the Earth. The equator of the Earth is actually kind of vibrating due to something called mutation. And so people have two frames, the averaged one and the true one. So this is the true one. And then there is the average, which is called mean. Again, this is standard notation, but this is weird. Mean, equator, mean equinox.

Okay. All right, look, I think we're basically. I think basically the design you have is as reasonable as we're going to get. I mean, I think, you know. Right. Can you scroll down a bit? Oh, you misspelled light deflection, by the way. Left, left hand side.

Oh, yes. I. The D and D. Hi. Was good. Thank.

You. I heard there was a whole bunch of scuttleback about the Shapiro. Actually was the one behind the Shapiro time delay. But who's to know?

This is a super tiny effect. I put it there because it's very easy to add. But of all of them is the smallest one.

Polar motion. What does that mean?

Polar motion is an effect that considers the fact that the axis of rotation on the Earth does not coincide with the geographic or the rigid axis of the Earth.

That's relevant for coordinate system like equatorial. Is that right?

Exactly. If you want to convert from the coordinate systems inside the Earth to those outside the Earth, you need to go through these values.

Look, I think you should break that table into things that relate to the Earth and things that relate to. You know, because bcrs couldn't care less about polar motion. Right, Exactly.

Yes. Yeah. So some of these parameters do not affect some of the frames.

I think you should say Earth observation. Parameters relevant to Earth observation, like refraction is the same deal. Yep. Oh, so it does have a wavelength parameter in refraction?

Yes, it does. Therefore, pressure, temperature, relative humidity and wavelength.

Given as an association.

Yes. I mean, I think at the moment I'm just passing a list of four, but I, I can do that, too.

I think you should allow an association. I think it should be analogous to the things we do in thermodynamic data. In other words, it should be consistent with the, with the way we pass atmospheric information. And, and, and, I mean, I don't know, maybe we even have the data and thermodynamic data to be able to do a random methane ATM or something. I don't know. I don't. I doubt it, because we'd have to have the profile of the atmosphere and things. But, yeah, it should be consistent with the way it's done in thermodynamic data when we look up how it's done in thermodynamic data.

Yes, I will.

Okay. But epoch. I think it might be nice to qualify the word epoch slightly.

Yes. So this is the difference between data and epoch is that some people want to compare an observation now to an observation of 1950. And so there are two problems. One is that the thing might have moved, and the other thing is that the frame might have moved. So with these, you can say, I'm observing today, but I'm using the orientation of the frame as it was in 1950.

Yep. I know epoch is the standard term in astronomy for that, but it's a.

Word that is a bit abused in astronomy, but.

Well, can we qualify it there? Frame, epoch or something? Frame, date. What's date versus observation date?

It's the same. These two are observed are accepted as meaning the same thing.

Or.

I see. Yeah.

Okay. I wouldn't say instant of observation. I would say date, slash date, Date of observation. I mean, that's what it is.

Yep.

Okay, so then epoch is the date defined that defines the frame.

Yes. And the standard terminology here is of date, which means of today, of the observation date. Or some people say of J2000, for example, J2000 is a very important date in astronomy.

No, I understand, but I think that's the frame definition date or something. Or frame definition epoch would be a better name.

I see.

Well, And you can say J 2000, presumably quotes J 2000.

Yes, yes. We can say here. Where was Rachel in meme. In J2000? And that's this.

This sort of bag of things that you're giving there. I mean, you know, clearly many of those. So you need to. You need to. Then, you know, the epoch thing needs to be something because. Because other things, this Memmi thing, does it Also have a form where you can say something arrow, Memmi.

No.

Okay, so listen, listen, listen, listen. What I think should be the case with that second argument is there is a full form that is an association where everything in it is named. I see. And some of them you can just put as just free floating things in the way that you're doing it.

I see. We could have a property that extracts that as an association. So you see?

Yeah, that's fine. That's a canonicalization. But I think that the, the way you should document it is there is an association. You give all this stuff, but there is an elided form where some of those things can break out of the association and just be free floating.

Yep.

And that way. Yeah, you just mark the ones like epoch that can be out of the association.

Right?

Yes. So at the moment it's frame, date and location. Those are the three important ones.

I know, but, but, but, but, but you're not giving. Okay, so fine, but, but you didn't give loc. Oh, okay, okay. So you got to indicate, you gotta look, you gotta give a list of all of them that can be in the association, and then you gotta say, and these ones can be free floating.

Yes, that's missing. Indeed.

Okay. All right. Okay, now. And the coordinate system, you're saying is a separate argument to astroposition. I think that's right, yes.

Because it's very typical that you just want to change that. You just have Cartesian and you want cylindrical. You don't have to touch anything.

We are about to run out of time. But what, what other things do we have to cover? I mean, we're getting really close here. I think we should, you know, should redo this documentation and then we should look at it one more time. Time. What do we need to cover on this?

Okay, so yesterday we were discussing what's the default? So we wanted to have a default that looked the shape. And then there are several azimuthal projections. And Jeff and I have been looking at which ones are most used. And the main choices are typically stereographic, which has the advantage that is conformal. So angles are preserved. And you see how these are all equivalent spaces, but they get longer. So that's like a Mercator as you go farther away from the equator. So then asymmetric distance is very similar. But now these are always the same.

Okay, well, I mean, this is a question, I suppose, for Jeff. And so, I mean, those little things where you have a little circular slide ruley type thing that shows you the configuration of the Stars. What projections are those using?

You mean like planispheres?

Yes.

I don't know. Off the top of my head, I think stereographic is the most common. For example, astrolabes are based on. On stereographic projection.

Okay, well, that has a.

So from the geometric point of view, stereographic is probably the most well defined because circles and lines are preserved as circles. And what we should use.

I mean, astrolabes have been used for what, 2,000 years or something, right?

Yeah. So I tend to think the stereographic.

Is probably the best one by default. Okay.

Yeah.

Okay. And we got some coloring choices and things like that to make. And then if we specify. Okay, now in astrographics, we had that. Some of those additional parameters. So, I mean, you should be able to bank. Specify. Okay, you've got that astro observer option, which I don't like at all in astrographics, which is basically saying, given the astroposition, this is what you want to change. What are you trying to do with astro.

In a sense, imagine that you have a bunch of absolute positions. In the first argument, the observer is going to compute the observations for all of them and then put them all together here. So in a sense, Geographics is doing the same. It's selecting a point at the center. It's doing all the computations implicitly for displacement and then presenting them in a map.

I understand, but astroposition might have already done that. And now you want to. Now you want to convert to a different map. Like you want to change your position on the Earth, for example.

Yes.

And so it's kind of like a show in graphics with a different viewpoint or something.

But then you have to. You have to redo the computation. So it's not possible to say, I have an observation. What would be my observation from a different place based on this one.

I know, I know, I know. You've got all kinds of relativistic things and lots of stuff going on.

Right.

Because probably the object has moved and we don't know where he went. It went.

Yeah, right, I understand. So basically, the second argument of astroposition, the association that was given in the second argument of astroposition, everything that occurred in there, you want to be able to put into astro graphics.

Exactly.

With. And it will convert whatever the inferred actual astropositions of the objects were in the first argument. Not the observed astropositions, but the absolute astropositions, and then use the new observation specification to decide how to present those in the astrographics. Is that right?

Yes, effectively, if we have astropositions here already, what this is going to do is that it will take the orientation of the frame in the observer and reorient these ones. It's not going to recompute the observation because it cannot be done. Once we, I mean, if we have observed a star, or imagine that you observe Pluto from the Earth. Now you say what would be the same observation from Mars? Well, this cannot be done because from Mars the timing will be different and we don't know. Yeah, from an astroposition. Exactly what you want.

Wait a minute. So we can't change the astro observe observation that much. We can only change some things in it.

You can change the, the orientation, the, the coordinate system, et cetera. But the base point is, is essentially only informative to reconstruct the event.

Why do we need the base point in astrographics?

Well, because if you have objects here like Mars, etc. You have to use the base point to know the observation. But what I mean is that once you have performed an astro observation.

Wait, wait, wait, wait, wait, wait, wait, wait, wait, wait. The point is if the thing that is given as the first argument is a pure object like Mars that has not been resolved into coordinates. You're saying you have to know more things in order to know how to resolve it into coordinates?

Exactly. Yep.

So that's a somewhat. I mean, it might be in it. Whereas if it's already been resolved, then what are you going to do with the, with the specification of coordinates that are given in the second argument? Sometimes you won't be able to do anything because it will have already been resolved. And you can't change that resolution as, as you say.

But there might be in different coordinate systems. So I have to kind of conform them to the one that is specified by the observer.

I know, but what if you've been given an absolute position in astroposition in the first argument, astrographics, you've given one absolute astroposition and one object specification like Mars. What do you do?

Well, I will use the observer to observe Mars. And then I will reorient the astral position given to conform so that.

I know.

But you can't do more with the astroposition than that.

Exactly. So imagine that you want to present one of these. Although I'm talking of positions of Mars.

Right, I understand. If the astral position. Oh, I see what you're saying. You see, you don't even want to do that. But if the astral position actually did have a space time event encoded in it, you could make a correction.

Well, if you had a trajectory, if you have A world line. You can observe the world line from different events and you always intersect the world line with a light ray. But if you give just a point observed from another one and you go to another observation point, most probably you will not intersect the original event.

Yeah. By the way, I mean given what we're doing here, we probably should. I mean, presumably we could stick a black hole in. I mean given that we actually have gravitational lensing built into this, we could. Presumably. I mean, does the gravitational lensing computation that we have here work if you stick a black hole in it?

Well, the system is prepared to follow exactly what we know the physics of the solar system is. We could change the physics and say and this is the solar system plus a black hole that has appeared instantaneously here. But we are not providing a way to do that yet.

Okay, fine. But I mean we still need to get the outside the solar system coordinates so that we can do lensing around galaxies and stuff like this.

Right, exactly.

I think it's going to be quite useful to do that. I think people are going to really like it.

Somehow that would need some sort of environment physics variable which is specify my physics is the solar system or my physics is a black hole somewhere.

And then so you guys are all focused on these very far away events. I think it's way more exciting the fact that we can travel around our solar system and become multi planetary.

That's, you know, I understand, I understand both things are relevant. I mean there's both, you know, notice that a very big expensive telescope just got launched that's about to produce tons and tons of data on things.

Well aware, absolutely.

So people are going to care about that just as they're going to care about, you know, space operations, so to speak, where you know, you have whatever transfer orbits going to wherever it is.

Exactly, yes.

RBS on our livestream is asking can we do an asteroid simulation? Yes, we can do an asteroid. We know where lots of minor planets are. We know the ephemerides, we know lots of stuff for this.

You were trying yesterday Sirius.

Yeah, That is, yeah.

Or moons. It's also fun to do Callisto.

You know, I really do think that the, that the icon there should be a position of the altitude azimuth if we know it. Right. Given that this is altitude azimuth, why not just put up, why not just.

Use that telescope when we don't know the, you know, when we only know it array?

It's horrifying. I mean I think we should put up the planisphere Type thing. You know, put up the stereographic projection with a dot in it.

Oh, I see. Like a little version of this one.

Yeah. With just a dot.

That's a very small graphic. I mean, maybe it'll translate. I don't know.

No, you don't understand. I'm just saying you can put the plane of the ecliptic in there if you want, but nothing else. You're just putting one dot that represents the altitude azimuth.

I see. Yeah. It's doable.

Yeah. I mean, you might as well. You can give the plane of the ecliptic and you give the one dot. But I think.

I see that would have the advantage that it's generalizable to when we have several points, because we have this.

Yes, yes. That's nice. Right. Just like the geoposition case.

Yep.

All right, we've got a wrap for now. Why don't you. You know, there's some redocument, you know, there's some documentation. Tune up and a little bit of other stuff here. And then let's take a look at this one more time. Let's bring Jeremy in. Let's look at. Okay, but this is really lovely. I mean, it's really lovely. It's great. It's. And it's fascinating to see. I mean, I guess this is what people spent the 1700s and 1800s worrying about, getting all this stuff. Right.

And they did it all on paper.

Well, yes, they did. I have a bunch of those books from people like Adams and Le Verrier and all these. All these. And Discovering Neptune. Yeah, yeah. But they have all. All these hand calculations of all these power series expansions and so on. It's all quite impressive. And I mean, it's. I mean, I do think in terms.

Of a killer app that drove resources into it, which was navigation, except that.

Neptune wasn't that relevant to that.

I mean, but. So they can spend a bit free time on, you know, the hobby.

The moons of Jupiter almost made, you know, a killer navigation timekeeping mechanism, but they didn't quite make it.

Oh, I've never heard that story.

Oh, yeah, absolutely. Yeah. People were going to use that for.

But they perturb each other. So over the long term, it doesn't behave.

I know, but locally, I mean, they had tables. Right. So locally, that was a way of figuring out. I'm now forgetting. But that was. That was a scheme for longitude, wasn't it, using the transit times of the moons of Jupiter.

It must have. I mean, the way you describe it, it sounds like it.

Yeah. Anyway, well, very nice. Very, very nice. I. I do think, given that we've gotten this far in getting all the physics. We should go further and, you know, we should do the. The, you know, deep, deep space of, you know, I mean, within the galaxy, outside the solar system. Within the galaxy. Can we do stuff there? We have galactic coordinates, but we don't have. We don't have enough to be able to do everything properly. Is that true?

Right. Yeah. So perhaps we have to start by going a bit outside the solar system and getting. Because we know the distance to many of the stars around us. So perhaps we can start.

Yeah. I mean, obviously, the thing that we should be able to do. Which I know we've been able to do for years in some form. Is just to make the 3D picture of the local stars. Which should be easy for us right now because we just take Cartesian. We're just using astroposition with Cartesian. And then we're getting out the three coordinates. Right. And one thing we need to look at next time is. Is the accessor functions. To get things like RAW coordinates out of astroposition.

Right. Yeah. So it would be basically this star. We have the XYZ coordinates.

Right. Yeah.

So then the first argument would be these numbers in au.

Right. All right. I gotta go. Excellent work. See? Let's see it one more time. Hopefully in the next week or so and take it from there.

Okay, thank you.

See you all soon.