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    Re: Satellite photo for navigation
    From: Frank Reed
    Date: 2013 Aug 24, 13:55 -0700

    Peter, you wrote:
    " Attached is a kmz with the GPS position and the estimates you give. About 380 meters from the LOP and about 415 meters from your fix."

    Well, that's pretty darn close! In our usual navigational units, that's an error of just 0.22 nautical miles (100km is almost dead-on equal to 54 nautical miles). For anyone who would like to see Peter's .kmz file data and see just how close my LOP and position estimate were to his actual position, visit this link (see PS):
    http://goo.gl/maps/kQri8

    In terms of the input data, this was an image that was known to be ISS and Polaris, and it was stamped with the date and UTC. Nothing unusual there. But Peter also provided one other critical piece of information: he identified that fifth magnitude star in the field of view. This helped by providing an angular scale, though we could have gotten that from other means potentially. More importantly, that identification gave us the local apparent time for the date in question. Just as if we had an old-fashioned "nocturnal", the orientation of stars around the North Star tells us the local sidereal time and since the date was known, also the local time. This depends on the assumption that Peter's camera was relatively level when he took the photo (that turned out to be the case but it's really an unknown here). Given the local time and the Univeral Time, I could estimate the longitude. This matters because passes of satellites are dramatically different if we move just a hundred miles, and because I had forgotten that Peter had informed us he was in the SF Bay area. Once the longitude was relatively well determined as somewhere on the Pacific coast, I started guessing latitudes. I started near Seattle, then moved to near Eugene, Oregon, and then to San Francisco. At each step I simply looked at heaven-above.com for ISS passes with approximately the right time passing near Polaris. Once I hit San Francisco and found a close match, it was just a matter of adjusting latitude and longitude up and down to get the beginning of the path in the right location. For a practical method of navigation using this technique, we need some software that allows us to adjust lat/lon with a quick up/down, left/right interface. That would not be difficult to create. And of course in a real navigational circumstance, we would use an estimated position as a starting point so there would be much less initial guesswork.

    Peter: last January I bought myself a new digital camera. While the camera in my cell phone (Samsung Galaxy S3) is stunningly good, it has no zoom and no controllable time exposure function. The camera I bought is the Canon SX260. This is basically identical to the one you've been using, right? I've taken some very nice handheld Moon photos with it, but no other astronomical photos yet. I will have to try for an ISS photo soon. This is also the camera I used for those photos that demonstrated rather dramatic changes in terrestrial refraction which I posted back in April.

    I wrote previously: "Then I realized that this motion is the composite of the actual motion and the motion of your camera during the exposure."
    And you replied: "It would be nice for the camera to remove this ambiguity by
    interrupting the exposure for a few milliseconds near the end of the
    500-ms main exposure."

    That would work. It dawned on me while I was driving yesterday that it doesn't matter. I could have used the average of the start and end points on all three objects. That seems obvious now. :)

    Also a little jitter might actually be useful. I remember a few years ago reading a description of the star-finding software aboard a little spacecraft navigating in the asteroid belt. The images of the stars were jittery, looking like melted pretzels. But this was considered a benefit since it distinguished actual star and asteroid images from noise and cosmic ray impacts on the detector array, and it also provided a simple means for determining the average center of each star image.

    You also wrote:
    "the ISS orbit would be determined from the space radars. Now, no doubt ISS carries GPS receivers; is that data available anywhere, so that a truly precise orbit can be used?"

    I've checked a few times, and the TLE data for the ISS used by heavens-above.com is the standard up-to-date set of orbital elements provided by the USAF, but their source in any specific case is not available. While most of their satellite data is derived from radar observations, they may well be using the position data supplied by NASA for the ISS and a handful of other satellites. That's one other advantage of using the ISS for visual satellite navigation despite the rarity of useful passes. As long as we know that the orbit is current, it has a good chance of being extremely accurate since this is such an important satellite. Derelict satellites sometimes have orbital data weeks out of date.

    If we could improve the accuracy of this system by just a factor of five or ten, which seems within reach, we would run into an interesting problem with ISS observations: it's 100 meters across! The orbital data probably refers to a location close to the physical center, but the visual center could easily be fifty meters away.

    I've been working on two options on this visual satellite navigation system in the past few weeks. First, of course, there are the brighter satellites, especially the ISS, but there are also a few dozen that are routinely brighter than magnitude 2.5. As another option, I've been considering the Iridium satellites since they have a very nice global pattern almost ideal for visual navigation. The Iridium satellites are famous for their brilliant flares, but for the most part, we can ignore those, except as an easy means of identifying the satellites. The key factor for the Iridium satellites is that the active ones are arranged in nice neat bands of longitude. The satellites fly on six equally-spaced nearly polar orbits with orbital periods of just about 100 minutes. Each orbit has 10 to 12 satellites evenly spaced along it (so a satellite passes overhead every ten minutes or better). Since the orbits are nearly polar, the bands are separated by 30 degrees of longitude. It's a lot like those polar "rings" in Hale's short story from 150 years ago (except that, as Sean pointed out, the orbits are relatively fixed while the Earth turns beneath them, so it is as if the rings are rotating in longitude at 15°/hour). The magnitudes of these satellites when they are not flaring but relatively high in the sky are around 6.0, so this would almost always require binoculars for observations, but that's not a serious problem if we have an approximate position to work from. The fact that there would always be one satellite within about 30 degrees from the zenith, anytime after twilight as long as they are not in shadow, and from any location on Earth would be a big plus. Since they are used actively for communications, their orbits are well-determined and relatively reliable. They do maneuver but very rarely.

    -FER
    PS: Suppose you have a .kmz file that you have found online, e.g. the one that Peter posted which is linked in his previous message. You take the url for that file and drop it into Google Maps and then click the usual search button. Google Maps will then display the information contained in that file. Next you click on the "link" button, located usually just below the search box. The icon on this link button looks either link a couple of links in a chain or maybe more like a pair of eyeglasses looking at you. Click that and it makes a link or, as here, select "Short URL" and you get a shortened link. Then copy and paste the result where you want it.
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