NavList:

Peter, you wrote:
"Here's an image of the Hubble Space Telescope passing through Sagittarius Friday evening."

Thanks. Looks good. :)

And:
"It was a lucky shot, the best of about a dozen. Still, with enough exposures, lucky things happen."

Right. And for an automated system, this is part of the equation. A robot doesn't care if it's taking photos continuously, so one could design a system that fires off a hundred shots and then search for the good ones. This also would generally solve the problem of motion. While many shots would be spoiled by motion, some would be taken just by luck of the draw when the mounting system is nearly non-rotating.

And you wrote:
"As for internal astrometric consistency, I think it's better than the 6 arcsec I mentioned before."

Yes, that makes sense. I have wondered how much the "plate correction" model changes from one shot to the next with these handheld cameras. The detector array can be tilted slightly skewing the image in a variable way. If there are enough stars in the field, it can all be calculated. But if we have a short exposure and just a handful of stars, that may limit the accuracy.

You added:
"I think it's now taking out the last remaining bits of barrel distortion from the lens system."

I've only used astrometry.net for a handful of images and mostly for the entertainment value. It sounds like you've experimented in much more detail. Are you able to extract the so-called "plate constants" or "lens-distortion model" from the results when it's done? If we can get at the model derived from a field of stars, and if it's relatively stable, then we can turn a camera into an accurate sextant. So far, most attempts to do this that we've discussed in NavList messages have used a a very simple model for converting pixels to angles. It's a fair start, but clearly if we could get at this distortion model without having to build new software for it, that would be terrific.

And:
"So, bottom line: suppose we have a system capable of 3 arcsecond accuracy using, say, half a dozen selected handheld photos. That's the equivalent of 5 or 10 meters on the ground for objects in LEO and a couple of hundred meters for objects in MEO."

I know you know this, Peter, but I think it's worth mentioning that the distance that counts here is the range to the satellite at the time of the photo (or visual observation). Consider the ISS. As it climbs above 10° altitude, it is just about 800 nautical miles away. When it's at the zenith, its distance is around 225 nautical miles. Also there are timing and angular factors. By the way, ISS passes come in cycles, and we've got a set that's just ending here in the northeast. After tonight (which I won't see given clouds), there's not a single evening pass of the ISS until October 6. There is a substantial orbit boost scheduled for Sunday, if I remember correctly, so the details may change after that.

You wrote:
"The problem seems to be that the published orbits (and the orbit models themselves) are not nearly that good. The Spacetrack report says that TLEs degrade to hundreds or even thousands of meters before the next update, and that's with objects that get frequent updates. (The reference-frame situation is also confusing.) I didn't see data on how much error is typically cross-track and how much along-track."

Well, some TLEs are better than others, so we pick and choose. We're not required to make a system that would work with each and every satellite (for anyone unfamiliar with the terminology, a "TLE" is "two line element" set, a standardized, very simple text-based format for satellite orbital data used since the early Space Age. Here's a page showing the orbit of the ISS, and near the bottom you can see the TLE: http://www.heavens-above.com/orbit.aspx?satid=25544). There are many satellites whose behavior matches the orbital data, so we just need a little vetting here. That's not too complicated. The positional error in most cases is "along-track" and therefore it's equivalent to a timing error. The satellite will turn up at the right spot but maybe five or ten seconds late or early. Since timing observations to the nearest seconds may be difficult or suspect for other reasons, I think it's preferable to treat it as uncertain for every satellite observation. When the satellite is unusually late/early on its orbit (let's say a minute or more), then you do get some cross-track error, but those satellites would be avoided in any case.

You wrote:
"If we abandon the SGP and SDP models, estimate our own state vectors for all objects of interest, and do full-bore numerical integration with a current gravity model, what is the inherent unpredictability of typical LEO objects assuming no maneuvers?"

I don't know... The standard SGP/SDP models are awfully good! Plus they're tied very tightly to the TLE data. It's possible to do what you suggest, and people do run such integrations, of course, but mostly I've seen it done for critical cases like satellites near re-entry. Do you follow Seesat-L (http://satobs.org/seesat/)?

So just how unpredictable are "normal" satellites? A satellite can end up early or late on its orbit when the air resistance, small though it is, is greater or less than expected (there are other factors, but this is the most basic). For example, if a satellite experiences just slightly greater drag, its orbit will become very slightly smaller. If the orbital altitude (from the Earth's center) decreases by some small percentage, then the orbital period decrease by 3/2 of that percentage (take Kepler's Third Law, differentiate, and you'll find (dT/T)=(3/2)(da/a)). From that relationship, if a satellite in low orbit is 100 feet lower than predicted, then its orbital period will be shorter by about 0.04 seconds if I've done my numbers right. Not much, but it adds up over time. That satellite would be early in its orbit by ten seconds after just 400 hours or about 17 days. Given that the decay rate for the ISS is around 200 feet in orbital altitude every single day right now, it's not hard to imagine substantial timing differences from slight variations in the decay rate. But again, this amounts to a timing error, nearly identical to a watch error for that specific satellite. We can plan around this.

You concluded:
"If the game is to have a system usable onboard ship, autonomously, for a duration of several weeks or months, then we need to pick objects for which this predictability is better than our accuracy goal."

It's a good question: just what is the 'game' here? What kind of system are we describing? Something just for fun? Or something with real, practical value? I think there is practical value here, but it exists along a spectrum of options. First, though, I think we can drop the issue of worrying about a system that can work "months" into the future. There's no need for that --at least that I can imagine. We could probably limit ourselves to a maximum of ten days without Internet access and TLE updates. We could build a highly accurate, automated system, but that takes money and time, and I think there are some groups working on these already. For another 'game', there's pure visual observation, requiring nothing more than binoculars (and in many cases even they would not be necessary). The positioning accuracy is lower, on the order of five miles, but certainly useful to ocean sailors. And for this use, we might even be able to dispense with the big SGP/SDP models and use simple precessing Keplerian ellipses. Like I say, there is a spectrum of options. I'm trying to resist the urge to imagine the biggest and best system possible, and instead, for the time being, I'm focusing on a system that can be fielded now and easily employed by average observers.

-FER

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