## Saturday, October 16, 2010

### Using Iridium Flares for Parallax Measurements

Iridium flare captured simultaneously at a) Largs North, SA and b) Black wood SA. You may need to click on the image to embiggen and see that the flare trail is shifted with regard to the stars.

Back on October 8 I and some other people were fortunate to witness a bright Iridium flare near Jupiter. I got a nice shot from my camera (mounted on my telescope with the drive going to stop star trailing), and Dean Male from Blackwood kindly sent me his image captured at the same time.

One thing that I noticed was that the image of the flare was slightly shifted with regard to the background stars. This represented a great opportunity to measure parallax in these images and do ... something.

Parallax is the slight shift in a nearer object against a simultaneously viewed distant background object. Parallax is used to measure the distance to the Moon, the planets and the stars. Amateur photographers have used their images of the Moon and nearby stars to measure the distance of the Moon to within 3%. So could I use the parallax shift in the images of the flare to measure the height of the satellite?

Highly sophisticated parallax measuring system.

Well, I measured the separation of the trails, using the sophisticated method of scaling SkyMap charts to the same scale as the images at full resolution, and using a bit of paper to plot the flare location.

I came up with 36' 57"
separation, or 0.6158 degrees (about a Lunar Diameter). Using the formula used for Lunar parallax:
$\mathrm{distance}_{\textrm{moon}} = \frac {\mathrm{distance}_{\mathrm{observerbase}}} {\tan (\mathrm{angle})}$
and estimating that Largs and Blackwood are roughly 25 km apart as the crow flies I get .... the iridium satellite was 2,326 Km up.

Which, as they orbit around 800 Km up, is a 300% error. I tried the formula out on the lunar separation measured here, and got the right result. Using the more complex formula:
Where D is the distance to the object, b is the separation between observers and Theta is the angular separation between the two images with respect to the background stars gives the same result.

Either Dean and I were 8 Km apart or the flare images separation was 3 times larger than I measured (not likely) or I'm doing something very wrong, or the formula is not appropriate for small separations of observers (The amateur Moon calculation was done from observers over 2000 Km apart, this won't work fro iridium flares which are only observed in a small area).

Anyone have any ideas? UPDATE: There is at least a partial solution to the Puzzle. In my original posting I had estimated that Dean and I were 25 Km apart, based on my rough measurements from Google maps. But that was from points that Google decided were Largs North and Blackwood. Dean sent me the flare information from his site, and from that I could calculate that we were 13 Km apart, not 25.

This gives a distance of 1209 Km, within 20% of the distance to the satellite from my site (1022 Km given by CalSky), still not the orbital distance (790 Km) but a heck of a lot better than 200%. JupiterIsBig (see comments) sent me the following diagram:

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which illustrates the sorts of correction we need to fix our calculations. I'm waiting for JIB to give this math's challenged biologist explicit instruction on how convert Altitude and Azimuthal data into correction factors.