ARISSat-1 Analysis - Eclipses and Elevations

2012-02-15T23:25:00.003-05:00

Tonight, I spent some time analyzing ARISSat-1 eclipses and elevations. I derived the location of ARISSat-1 and eclipse state from the Keplerian Elements. I did this at five second intervals over the entire lifetime of the satellite. I outputted the results of these calculations to a text file using the following format:

[start | finish]: DATE TIME LON LAT ELEV SEQ ECLIPSE_STATE

This is a snapshot of what the first and last few records of my output file look like:

finish: 2011/8/4 18:21:17 113.762852 49.033371 371964.468750 12 0
start: 2011/8/4 19:20:37 -7.871781 -39.483602 391577.468750 12 1
finish: 2011/8/4 19:53:32 90.504473 49.075380 371938.281250 12 0
start: 2011/8/4 20:52:57 -30.867104 -39.211426 391519.281250 12 1
finish: 2011/8/4 21:25:47 67.247877 49.117396 371912.218750 12 0
start: 2011/8/4 22:25:12 -54.178058 -39.131865 391518.687500 12 1
finish: 2011/8/4 22:58:02 43.993081 49.159412 371886.250000 12 0
start: 2011/8/4 23:57:32 -77.176042 -38.856010 391459.843750 12 1
finish: 2011/8/5 00:30:27 21.651420 49.400924 371882.750000 12 0
start: 2011/8/5 01:30:07 -99.258447 -37.981538 391225.031250 12 1
...

finish: 2012/1/4 18:17:25 121.704409 -49.697238 117080.125000 4794 0
start: 2012/1/4 19:16:30 -10.982721 8.533542 106730.476562 4794 1
finish: 2012/1/4 19:44:15 101.065455 -49.408605 113319.164062 4794 0
start: 2012/1/4 20:43:10 -32.699206 8.090581 102507.820312 4794 1
finish: 2012/1/4 21:11:05 80.918078 -48.988825 109536.718750 4794 0
start: 2012/1/4 22:09:40 -54.591120 7.913555 98236.382812 4794 1
finish: 2012/1/4 22:37:45 60.295578 -48.652503 105764.578125 4794 0
start: 2012/1/4 23:36:05 -76.460252 7.733447 93970.554688 4794 1
finish: 2012/1/5 00:04:50 42.428476 -47.516509 101850.984375 4794 0
start: 2012/1/5 01:03:25 -95.938934 4.290120 90538.757812 4794 1

By doing a quick search through my output file (grep and wc for linux users :-), I was able to determine that ARISSat-1 eclipsed somewhere in the ballpark of 2415 times.

The satellites elevation changed over time, gradually diminishing towards Earths surface until it finally re-entered. But what does this difference in elevation look like? First, let us disregard the fact that ARISSat-1 re-entered and strictly examine the elevation data that we can derive from the Keplerian elements (using specific date/times). To accomplish this, I chose two different transits periods, one in the early life of ARISSat and one near (or after?) it's re-entry, specifically:

2011/8/6 - 13:24:43

2012/1/4 - 00:22:30

I rendered the orbits realized after these times and then examined a common geographic location above the Equator. You can observe these plots in the images below. The orbit with the higher elevation occurred earlier in the life of ARISSat-1 slightly after 2011/8/6 13:24:43. The orbit with the lower elevation may have occurred later in the life of ARISSat-1, slightly after 2012/1/4 00:22:30. The images below provide a clear illustration of just how different the elevations were over time.

The elevation of ARISSat-1 as it passed over the Equator slightly after 13:24:43 on 2011/8/6 was approximately 381km.

The elevation of ARISSat-1 could have been roughly 166km as it passed over the Equator slightly after 00:22:30 on 2012/1/4.

The images above clearly illustrate the difference in elevation but they do not provide a good view of the overall orbit differences. The image below provides a top-down view of the two orbits.

This final image provides a good feel for the direction ARISSat-1 was heading at these two different spans of time.

If you would like to obtain my calculated eclipse data or if you have any questions or comments, please let me know.

ARISSat-1 Keplerian Element Analysis - First Shot

2012-02-14T00:03:00.001-05:00

Here are the preliminary results of my code that will ingest ARISSat-1 Keplerian Elements and output KML. I generated a plot of the position of ARISSat-1 over the lifetime of its mission. I accomplished this by examining the satellites position at one minute intervals in-between keplerian element epochs. If you plot each position over every minute of the satellites lifetime, you end up with an image that looks like this. Yes, that is quite a few lines! Each colored line represents the trajectory defined by an individual Keplerian element (from its own epoch until the next Keplerian elements epoch).

Update: I posted the image above and received many comments referring to how the orbits transit-over the south poll. This would be incorrect for an orbit with an inclination of 51deg. The reason the image above looks like this is because of where I have the eye-point set. We are really looking over the top of the Earth, from far north of the equator. The two images below will clarify what is taking place around the north and south polls. Here is a shot of our South Poll.

And here is a clear shot of our North Poll. Hopefully this clarifies the situation :-)

Now back to business. The first Keplerian element results in the following trajectory over time. Specifically, this is a plot from 2011/08/04 18:02:17 until 2011/08/05 05:05:17. This is an image of the starting point.

This is an image of the ending point for the first Keplerian Element. Notice where the line ends right over Nova Scotia, the satellite passed this point at approximately: 2011/08/05 : 05:05:17.

The next plot illustrates the first and second ARISSat-1 keplerian elements. The blue line still represents Keplerian Element 1 and the green line represents Keplerian Element 2. You can clearly see how the green line picks up from where the blue line leaves off.

Each of these plots is being rendered via Google Earth using a KML file that I am generating in my code. Besides trajectory at any minute, I am also calculating when the satellite was and was not eclipsed. Here you can see a brief view of when ARISSat-1 left eclipse for the first time.

What if we are interested in other eclipses? With my generated KML, it is trivial to plot them. Here is another shot that shows the first three times ARISSat-1 eclipsed.

I just made a couple of quick updates to my tool and this is what the data looks like now. The left hand side of the image shows what the layer looks like within Google Earth. The names are the satellite sequence numbers. You will have multiple entries for each Kelperian sequence, depending on whether or not the satellite is eclipsed. The color is black if eclipsed and orange if not eclipsed. The descriptions contain the epoch for the starting point of the segment.

Let me know if you have any questions about these plots. At this point in time, I have the following values being calculated and dumped to a table: TIME, LAT, LON, ELEVATION, SEQUENCE#, ECLIPSED. I post-process these values from the table into a KML file for visualization.

libJoe

ARISSat-1 Analysis - Eclipses and Elevations

ARISSat-1 Keplerian Element Analysis - First Shot