On 12/28/2009 06:09 PM, Rick Monteverde wrote: > > Saw an orange fire colored UFO last night just after nightfall. The > path was that of an object flying in a curved path at high altitude (a > u-turn, basically), definitely not a satellite, and a bit brighter > than a good space station sighting. Even through 8x binoculars it > appeared as a point source. The time of day, the sighting angle, and > the variable characteristics of the light over the two minutes or so > the object was visible suggests it was reflected light from the > setting sun on the lower surface of a solid object, but given that the > sky was almost completely dark at my location at that point, my guess > is that its altitude could have been above the atmosphere. I’ve seen > conventional aircraft reflecting sunset’s light after local sunset, > and though the appearance was similar, in those cases it was much > closer to sunset and sky was still quite light. Once it gets dark, I > think such reflections tend to be in satellite territory. > > Anyway, since I can find the sight angle because of its passage near > identifiable stars, the time, and my location on that date, it should > be possible to calculate the earth’s shadow line from the setting sun > and see where my sight line crosses it. That would tell me if it was > just an airplane at very high altitude, or something maneuvering up a > bit higher than conventional aircraft can reach. Anybody have an idea > how I would go about that (umbra?) line? >
Finding the exact time of sunset at your location should be possible by using Google or an astronomy program, such as Starry Night (or you may already know it). What you need, of course, is the elapsed time from sunset to the time of the sighting; I assume you know the time of the sighting so knowing sunset time gives you this. Call that elapsed time Ts. Now at this point it starts to get messy. To start, you need the distance from the sunset line in radians, which we'll call Ds (for Distance from Sunset). On a world without seasons, or at the equinox, you could find that distance just by taking Ds = 2 pi Ts/24 (assuming Ts is in hours) Now this is *NOT* the great circle angular distance from the terminator; rather, it's the angle along a parallel (a latitude line). Note, however, that the parallels intersect the terminator at a right angle (at the equinox). Unfortunately we're not at the equinox, we're at the solstice, and you need to throw in a correction. I *think* the correction term for any date near 21 December is going to be very close to cos(23.5 degrees), and we'll actually have Ds = cos(23.5 deg) * 2 pi Ts/24 This is probably not exact but it should be pretty close. With that in hand, you can find the surface distance from the shadow line by taking the radius of the latitude circle at your location and multiplying by Ds. If Re is the radius of the Earth, then the radius of the latitude circle at your location should be something like Rl = Re * cos(Latitude) and so the surface distance from the shadow line, which we'll call Df (for Flat Distance), should have been Df = Re * cos(Latitude) * cos(23.5 deg) * 2 pi Ts/24 That should be pretty close unless you're very far north. Now what we want isn't actually the flat distance, nor is it the angular distance along a parallel; it's the great circle angular distance, and that should be Dc = Df/Re Finally, what you want is the altitude of a sunbeam at your location. If the Sun's light traveled in a straight line, then that would be Altitude = (Re / cos(Dc)) - Re = Re * (1/cos(Dc) - 1) Last, there is one more correction which I haven't any idea how to make, which is for the fact that sunlight bends traveling through the air. It bends down as it hits the atmosphere, and it bends down again as it streams up from its point of contact at the terminator. The former affects the time of sunset, and the latter results in the sunlight going over at a /lower/ altitude than you might expect just after the sun has set. What I wrote *may* give you enough to go on to get some approximate numbers out, if you plug in the appropriate times and locations for the sighting. But you'd want to check them, or get someone who knows what they're talking about to look over what I said and see if it really makes sense. > Thanks, > > - Rick >
