LightSail-A: Post-Sail Deployment Orbital Elements
Ted Molczan
The orbital decay analysis described in the update of Jun 14 20:40 UTC has been extended to include the final three passes for which Doppler-shifted radio observations are available. Updated space weather data has been used. The probable time of disintegration is estimated to have been on Jun 14, between 17:21 UTC and 17:24 UTC. Plots showing the evolution of altitude and deceleration during the final hours in orbit are provided.
304 X 419 km
1 40661U 15025L 15164.98442663 .12253905 00000-0 83486-1 0 09
2 40661 54.9934 233.7871 0085530 258.9801 100.1611 15.69159281 05
Arc 20150613.54-0613.99 WRMS resid 0.057 totl 0.018 xtrk
The quality of the Doppler observations is evident in the following TLE, that Cees produced using 2,315 measurements, made on six passes between Jun 13 23:52 UTC and Jun 14 07:46 UTC, which he used to correct a preliminary optical/visual TLE of the same epoch, by adjusting mean anomaly, mean motion and rate of decay:
304 X 418 km
1 40661U 15025L 15164.98442276 .12897728 00000-0 88268-1 0 09
2 40661 54.9934 233.7749 0084684 258.0841 101.0696 15.69153991 08
# 20150613.99-20150614.33, 2315 measurements, 0.024 kHz rms
Our two TLEs share the same epoch and are otherwise nearly identical, despite having no data in common. Mine is at the end of a nearly 12 hour arc, and Cees' is at the start of an 8 hour arc. It was fairly easy to derive my TLE from the available precise optical/visual observations. It was much more challenging to rely on Doppler data, but Cees produced an excellent result.
TCA Pred. minus Obs
Date UTC Observer s
2015-06-13 23:52:48 C. Bassa
2015-06-14 01:27:27 C. Bassa +1.5
2015-06-14 03:02:34 C. Bassa
2015-06-14 04:37:48 C. Bassa +1.5
2015-06-14 07:27:45 S. Tilley
2015-06-14 07:46:25 C. Bassa
2015-06-14 09:01:31 S. Tilley +0.5
2015-06-14 10:35:47 S. Tilley +1
2015-06-14 12:10:19 S. Tilley
2015-06-14 13:44:32 S. Tilley +1
2015-06-14 15:17:49 S. Tilley
2015-06-14 16:52:51 Cal Poly +1
Cees determined all of the above TCA times through analysis of the frequency vs. time radio observations.
Each of the comparisons is based on a TLE derived from a GMAT Cartesian state vector close to the observed TCA. The difference between the TCA predicted by the GMAT-propagated trajectory and the observed TCA averaged about 1 s, with little discernible trend. This small difference was of no consequence, and could easily have been eliminated by adjusting the mean anomaly of the starting TLE. Cees further verified the GMAT trajectory, by comparing each TLE to the nearest Doppler curve, which revealed RMS residuals less than 0.1 to 0.05 kHz. With the accuracy of the GMAT trajectory confirmed, the propagation was allowed to continue to decay.
The following TLE derived from the GMAT analysis is for the final ascending node prior to decay. GMAT does not output rates of decay, so the decay terms were estimated using Satevo, to match the time of decay of the GMAT propagation.
215 X 233 km
1 40661U 15025L 15165.67891751 1.20000005 00000-0 67377-1 0 04
2 40661 54.9777 230.4462 0013559 249.6061 110.4963 16.18352355 03
This TLE was not used for the analysis, but it is an accurate representation of the orbit near decay, for use with the SGP4 propagator.
Figure 1 (below) compares the deceleration vs. altitude of LightSail-A with that of 1965-099C, the BOZ ullage motor assembly of the Luna 8 probe, which was available from an unrelated study. LightSail-A's A/m (1.413 m2/kg) was more than 200 times that of 1965-099C (0.00618 m2/kg), which Fig.1 reveals to have resulted in a profoundly different deceleration profile.
![[LightSail-A re-entry Fig.1]](seesat_ref/LightSail-A/LightSail-A_Fig1.jpg)
Due to its much greater A/m, LightSail-A's period of high-g deceleration occurred at a significantly greater altitude than that of 1965-099C. It's peak deceleration, about 8.4 g, occurred at about 87 km altitude. This would have been the approximate altitude of peak heating. 1965-099C reached a peak of 7 g, at 50 km altitude. It seems reasonable to assume that LightSail-A's onset of self-luminosity and its main-break-up would also have occurred at a much greater altitude than for a typical object, like 1965-099C. If, as I suspect, the heating experienced during those events is associated with deceleration, then that could provide the basis to estimate the altitudes at which they occurred for LightSail-A.
For a typical object like 1965-099C, the rule of thumb altitude of self-luminosity of 96 km corresponded to approximately 0.035 g. For LightSail-A, this occurred at about 132 km altitude, near 17:21 UTC, at which point the spacecraft was near 53 S, 45 W.
For 1965-099C, the rule of thumb altitude of main-breakup of 78 km corresponded to about 0.68 g. For LightSail-A, this occurred at about 108 km altitude, near 17:24 UTC, at which point the spacecraft was near 55 S, 25 W.
Due to its low mass, it seems likely that LightSail-A disintegrated sometime between the onset of self-luminosity near 17:21 UTC and main-break-up at 17:24 UTC. If the solar sail separated early in this period, then the spacecraft bus might have survived for perhaps another 2 or 3 minutes, due to its much lower A/m, which would have resulted in a decreased rate of descent. It would be interesting to see the results of simulations using satellite re-entry fragmentation models.
LightSail-A deployed its solar sail on Jun 7, while in a 357 X 699 km orbit. In just under a week, atmospheric drag whittled away most of its altitude. Figure 2 (below) depicts the dramatic final hours of the descent, plotting altitude and deceleration vs. time. Shortly after Jun 14 15:00 UTC, it briefly circularized at about 240 km altitude, from which it quickly spiralled out of orbit. It was down to about 208 km when last heard by Cal Poly just before 16:56 UTC. The deceleration spike just after 17:20 UTC roughly marks the point of disintegration.
![[LightSail-A re-entry Fig.2]](seesat_ref/LightSail-A/LightSail-A_Fig2.jpg)
Figure 3 (below) plots a subset of the altitude and deceleration vs. time data of Fig.2 for the 10 minutes centred on the peak deceleration. Disintegration most likely occurred sometime between the estimated onset of self-luminosity near 17:21 UTC and main break-up near 17:24 UTC.
![[LightSail-A re-entry Fig.4]](seesat_ref/LightSail-A/LightSail-A_Fig3.jpg)
Figure 4 (below) plots the ground track on Jun 14 from 15:00 UTC until the estimated time of disintegration between 17:21 UTC and 17:24 UTC.
![[LightSail-A re-entry Fig.4]](seesat_ref/LightSail-A/LightSail-A_Fig4.jpg)
An updated official USAF TLE has been issued via Cal Poly:
LightSail-A 216 X 248 km 1 40661U 15165.67889456 +.99999999 +11333-4 +98645-1 0 00405 2 40661 054.9754 230.4257 0024090 251.5155 108.3598 16.15412206003819The orbit represented by this TLE is a bit higher in altitude, but more rapidly decaying, than the one we determined for the same epoch from Doppler-shifted radio observations, reported on Jun 14, in the 20:40 UTC update.
I believe that the USAF's ndot/2 term (.99999999 rev/d2) was truncated; therefore, too low to obtain accurate results with the Satevo decay propagator, that relies on this element. I estimated 1.46660733 rev/d2, using a formula that relates ndot/2 and B*, which causes Satevo to propagate the TLE to decay on Jun 14 near 17:19 h UTC, within a few minutes of the GMAT propagation of our orbit.
Date UTC Site 2015-06-14 13:44:32 8049 2015-06-14 15:17:49 8049The contemporaneous GMAT-propagated state vector agrees with the first of the above to the nearest second, and is about 2.5 s early relative the second one. Justin Foley, CubeSat Systems Engineer, Cal Poly, reported that on the 15:17 UTC pass, the object was about 45 s early relative the USAF TLE of epoch 15164.53699814, which works out to about 5.5 s early relative the GMAT state vector - within about 3 s of the measured TCA on the same pass. This new data tends to confirm that the 7.16 m2 drag area is sufficient to account for the rate of decay during LightSail-A's final 18 h in orbit.
Below is probably my final TLE from visual or optical observations. It is a fit to a synthetic observation generated from the USAF TLE of epoch 15164.53699814 (at epoch), Andriy Makeyev's observations on Jun 13 near 22:23 UTC and 23:55 UTC, and observations by Alberto Rango and the Astronomical Observatory of Odessa University (via Nikolay Koshkin) on Jun 13 near 23:55 UTC.
LightSail-A 304 X 419 km 1 40661U 15025L 15164.98442663 .12253905 00000-0 83486-1 0 09 2 40661 54.9934 233.7871 0085530 258.9801 100.1611 15.69159281 05 Arc 20150613.54-06131 WRMS resid 0.057 totl 0.018 xtrkSubsequent to the epoch of this TLE, Cees Bassa and Scott Tilley made observations of the Doppler shift on nine passes, from Jun 14 01:27 UTC to 12:10 UTC, during which LightSail-A passed progressively early relative the elements. Below are the observed times of closest approach (TCA), provided by Cees Bassa:
Date UTC Site 2015-06-13 23:52:48 4071 2015-06-14 01:27:27 4071 2015-06-14 03:02:34 4071 2015-06-14 04:37:48 4071 2015-06-14 07:27:45 8049 2015-06-14 07:46:25 4071 2015-06-14 09:01:31 8049 2015-06-14 10:35:47 8049 2015-06-14 12:10:19 8049 Site 4071 52.8344 N, 6.3785 E, 10 m, Cees Bassa Site 8049 49.43488 N, 123.66854 W, 40 m, Scott TilleyI took advantage of this data to fit the following orbit, which closely matches the TCA of Scott's 12:10 UTC pass, and is my latest TLE derived from observation.
LightSail-A 266 X 334 km 1 40661U 15025L 15165.50719572 .00000000 00000-0 00000-0 0 63 2 40661 54.9883 231.2921 0051203 264.6596 185.5882 15.90837413 03I used the numerical integrator in GMAT 2014a (General Mission Analysis Tool) to propagate the epoch 15164.98442663 TLE, adjusting the drag area by trial and error to produce a state vector that closely matched the TCA of Scott's 12:10 UTC pass. For assumed Cd=2.2 and known mass=4.93 kg, the required drag area was found to be 7.16 m2. The above TLE was converted from a GMAT state vector close to the time of Scott's observation.
As a further check of the reliability of the drag area, I also converted a GMAT state vector close to the time of Scott's and Cees' respective observations near 07:28 UTC and 07:46 UTC, and found that the TCA agreed to within a second or two.
Cal Poly heard LightSail-A on Jun 14, from about 16:51:37 UTC to 16:55:37 UTC. The GMAT propagation yields this TLE near the most recent ascending node (decay terms approximate), which shows that the pass culminated 7 deg above the southwestern horizon.
LightSail-A 214 X 231 km 1 40661U 15025L 15165.67891370 1.30191243 00000-0 70000-1 0 15 2 40661 54.9774 230.4458 0012663 247.8987 112.3918 16.18952000 01
Allowing the GMAT propagation to continue to decay revealed that it would have reached the altitude at which decaying objects typically become self-luminous (96 km) on Jun 14 near 17:22 UTC, and would have passed through the typical altitude of "main-break-up" (78 km) near 17:23 UTC. Given its low mass, I doubt it could have survived much longer. If this is correct, then it survived less than half an hour after the Cal Poly pass.
If Doppler shifted data for the Cal Poly pass, that is suitable for analysis becomes available, then I may produce an additional GMAT analysis to fit that data, which could improve our knowledge of the rate of decay during the final few hours in orbit, and possibly result in a different estimated time of decay.
For those who wish to use our epoch 15165.50719572 TLE for predictions, here is a version with decay terms chosen to yield Satevo decay near 17:23 UTC:
266 X 334 km
1 40661U 15025L 15165.50719572 .39500001 00000-0 10920 0 0 62
2 40661 54.9883 231.2921 0051203 264.6596 185.5882 15.90837413 03
The positional data of the Astronomical Observatory of Odessa University for Jun 13 near 23:55 UTC is available as received here, and converted by me to IOD format here (I used a subset at 15 s intervals for the orbit determination). Photometric data is here. The photometric plot is here (regular variation in brightness is evident).
The following TLE is fit to a synthetic observation generated from the USAF TLE of epoch 15164.53699814 (at epoch), a synthetic observation based on Andriy Makeyev's report that LightSail-A was 3 s late relative this TLE on Jun 13 at 22:22:55 UTC, and observations by Alberto Rango and the Astronomical Observatory of Odessa University (via Nikolay Koshkin) on Jun 13 near 23:55 UTC.
LightSail-A 305 X 419 km 1 40661U 15025L 15164.98442276 .11526967 00000-0 79765-1 0 04 2 40661 54.9934 233.7749 0084684 258.0841 101.0696 15.68909366 02 Arc 20150613.54-06131 WRMS resid 0.009 totl 0.009 xtrkOn tonight's N. American passes, I estimate that the object will pass within +/-20 s of this TLE.
Satevo propagates this TLE to decay on Jun 14 near 20:39 h UTC; uncertainty is 4 h, based on the rule of thumb of 20% of time from epoch to decay. I am not as confident in this estimate as in others, because complete observations were available for only one of the passes upon which the TLE was based.
This is the subset of the of the Astronomical Observatory of Odessa University data that I used.
40661 15 025L 1086 G 20150613235424846 37 15 1413189+423114 37 40661 15 025L 1086 G 20150613235445006 37 15 1402579+544141 37 40661 15 025L 1086 G 20150613235502587 37 15 1342279+662619 37 40661 15 025L 1086 G 20150613235515068 37 15 1307413+744543 37 40661 15 025L 1086 G 20150613235530189 37 15 1042486+825402 37 40661 15 025L 1086 G 20150613235545189 37 15 0546236+812558 37 40661 15 025L 1086 G 20150613235600070 37 15 0416031+742445 37 40661 15 025L 1086 G 20150613235615010 37 15 0347093+673438 37 40661 15 025L 1086 G 20150613235630011 37 15 0333580+613441 37 40661 15 025L 1086 G 20150613235645011 37 15 0326501+562609 37 40661 15 025L 1086 G 20150613235700432 37 15 0322317+515528 37 40661 15 025L 1086 G 20150613235715013 37 15 0320012+481527 37 40661 15 025L 1086 G 20150613235730133 37 15 0318239+445724 37 40661 15 025L 1086 G 20150613235745034 37 15 0317265+420650 37 40661 15 025L 1086 G 20150613235800075 37 15 0316553+393456 37 40661 15 025L 1086 G 20150613235808535 37 15 0316471+381660 37 Observatory coordinates: [086] Odessa, Ukraine: Lon=30.75564, lat=46.47778, h=56I will post the complete positional and photometric data of the Astronomical Observatory of Odessa University later today.
An updated official USAF TLE has been issued via Cal Poly:
LightSail-A 315 X 459 km 1 40661U 15025L 15164.53699814 .10886989 00000-0 81622-1 0 385 2 40661 54.9934 235.8636 0106041 252.3637 105.8215 15.60164534 3635I recommend using this TLE for predictions tonight.
I believe that the USAF's ndot/2 term (.10886989 rev/d2) is too high for use with Satevo. I estimate .08950441 rev/d2, based on the B* term, which causes Satevo to propagate the TLE to decay on Jun 14 near 18 h UTC; uncertainty is 6 h, based on the rule of thumb of 20% of time from epoch to decay.
I am unlikely to be available to make additional updates prior to tonight's European passes. Look for updated USAF TLEs at the Cal Poly page. Look for new observation reports and TLEs from visual, optical and radar observers at the SeeSat-L archive.
I have revised the TLE reported at 01:30 UTC to take advantage of newly reported observations by the Astronomical Observatory of Odessa University (via Nikolay Koshkin) on Jun 12 near 23:17 UTC.
LightSail-A 324 X 494 km 1 40661U 15025L 15164.02321799 .06638464 00000-0 75209-1 0 04 2 40661 54.9908 238.2353 0125135 250.6527 108.0943 15.52608638 03 Arc 201506111-0613.04 WRMS resid 0.098 totl 0.018 xtrkThis result appears to be in reasonable agreement with Doppler measurements by Cees Bassa, especially near TCA of his pass near 05:39 UTC.
Satevo propagates this TLE to decay on Jun 14 near 19 h UTC; uncertainty is 8 h, based on the rule of thumb of 20% of time from epoch to decay.
I am unlikely to be available to make additional updates prior to tonight's European passes. Look for updated USAF TLEs at the Cal Poly page. Look for new observation reports and TLEs from visual, optical and radar observers at the SeeSat-L archive.
The positional data of the Astronomical Observatory of Odessa University for Jun 12 near 23:17 UTC is available as received here, and converted by me to IOD format here (I used a subset at 15 s intervals for the orbit determination). Photometric data is here. The photometric plot is here (a well-defined periodic variation in brightness is evident).
Cees Bassa has reported new optical observations. LightSail-A was 10-30 s late, depending on the TLE. The following TLE is based on Cees' new observations, and previously reported ones made last night by the Astronomical Observatory of Odessa University, Alberto Rango and Cees.
LightSail-A 324 X 493 km 1 40661U 15025L 15164.02321742 .06860311 00000-0 77534-1 0 03 2 40661 54.9961 238.2507 0124429 247.3969 111.3864 15.52760368 09 Arc 201506111-0613.04 WRMS resid 0.015 totl 0.008 xtrk
Satevo propagates this TLE to decay on Jun 14 near 17 h UTC; uncertainty is 8 h, based on the rule of thumb of 20% of time from epoch to decay.
An updated official USAF TLE has been issued via Cal Poly:
LightSail-A 330 X 523 km 1 40661U 15025L 15163.50698574 .06533945 00000-0 73484-1 0 364 2 40661 54.9944 240.6029 0141897 243.9136 114.1430 15.46659033 3475This TLE appears to confirm a small increase in rate of decay after last night's European passes, roughly consistent with Ron Dantowitz's observation that it was running early at 6:12 UTC. (Note: Ron Dantowitz later sent a correction stating that the pass was 1.1 s late, not early; therefore, there was no increase in rate of decay.) We may have Doppler TCA (time of closest approach) data for several passes later today, which could help evaluate this new TLE, and enable prediction time uncertainty to be estimated for tonight's passes.
I believe that the USAF's ndot/2 term is too high. I estimate .05575645 rev/d2, based on the B* term, which causes Satevo to propagate the TLE to decay on Jun 14 near 17 h UTC; uncertainty is 11 h, based on the rule of thumb of 20% of time from epoch to decay. Since early June 10 UTC, the Satevo estimates have agreed on decay on Jun 14, ranging between 13 h and 21 h UTC; median 17 h UTC.
Based on newly reported observations by the Astronomical Observatory of Odessa University (via Nikolay Koshkin) on Jun 12 near 00:00 UTC, I have decided to produce a TLE that ends with last night's European passes:
LightSail-A 336 X 544 km 1 40661U 15025L 15163.05397602 .04745179 00000-0 70734-1 0 00 2 40661 54.9918 242.6501 0152989 240.6002 117.9681 15.42042563 08 Arc 20150611.28-0612.07 WRMS resid 0.036 totl 0.011 xtrkIt is similar to the one I issued earlier today at 02:30 for the same epoch, but more reliable due to a greater number of underlying observations. I now suspect that Ron Dantowitz observed it running a bit early on his pass hour later, because the rate of decay increased in the interim. Therefore, the above TLE probably best documents the orbit as of the European passes, and the epoch 15163.24831584 TLE I posted at 13:50 UTC, probably will be more accurate for later passes. (Note: Ron Dantowitz later sent a correction stating that the pass was 1.1 s late, not early; therefore, there was no increase in rate of decay, and the epoch 15163.24831584 TLE is invalidated.)
Satevo propagates this TLE to decay on Jun 14 near 18 h UTC; uncertainty is 13 h, based on the rule of thumb of 20% of time from epoch to decay.
The positional data of the Astronomical Observatory of Odessa University is available as received is here, and converted by me to IOD format here (I used a subset at 15 s intervals for the orbit determination). Photometric data is here. The photometric plot is here (it shows a well-defined periodic variation in brightness).
I have added observations reported by Alberto Rango. Ron Dantowitz of the Clay Center Observatory reported that LightSail-A was 1.1 s early on Jun 12 near 06:12 UTC, relative the epoch 15163.05397193 TLE. That is the only observation received so far of this morning's pass of the N. American east coast. Adding Alberto's and Ron's observations yields the following elements:
LightSail-A 333 X 535 km 1 40661U 15025L 15163.24831584 .05238559 00000-0 73838-1 0 01 2 40661 54.9903 241.7701 0148263 243.8928 114.6783 15.44108482 08 Arc 20150611.28-0612.26 WRMS resid 0.049 totl 0.015 xtrkIn the event additional observations are reported that fall within the arc of this TLE, I may issue a revision.
Satevo propagates this TLE to decay on Jun 14 near 15 h UTC; uncertainty is 12 h, based on the rule of thumb of 20% of time from epoch to decay.
Note: Ron Dantowitz later sent a correction stating that the pass was 1.1 s late, not early. This invalidates the above TLE.
Cees Bassa has reported new optical observations. LightSail-A was about 2 s late relative the USAF TLE of epoch 15162.46941668, and about 6 s late relative the hobbyist TLE of epoch 15162.40455211. Both TLEs produced similar cross-track errors, roughly 0.1 deg. Adding Cees Bassa's observations to those previously reported by Kevin Fetter, Scott Tilley and myself, yields the following elements.
LightSail-A 335 X 545 km 1 40661U 15025L 15163.05397193 .04783963 00000-0 70785-1 0 04 2 40661 54.9926 242.6541 0154101 239.6699 118.9014 15.42066823 05 Arc 20150611.28-0612.07 WRMS resid 0.018 totl 0.014 xtrkIn the event additional observations are reported that fall within the arc of this TLE, I may issue a revision.
An updated official USAF TLE has been issued via Cal Poly:
LightSail-A 341 X 569 km 1 40661U 15025L 15162.46941668 .04707738 00000-0 69278-1 0 348 2 40661 54.9952 245.2896 0167199 240.3376 117.1030 15.36955075 3313This TLE yields predictions similar to those of the epoch 15162.40455211 TLE in my previous update, generated from hobbyist observations.
The following TLE is derived from the same observations as the epoch 15162.33948982 TLE, plus newly reported observations by the Astronomical Observatory of Odessa University (via Nikolay Koshkin) on Jun 11 near 00:36 UTC, and by Scott Tilley on Jun 11 near 09:59 UTC:
LightSail-A 341 X 572 km 1 40661U 15025L 15162.40455211 .04174871 00000-0 70655-1 0 06 2 40661 55.0032 245.6011 0169371 241.0418 117.3538 15.36446209 08 Arc 20150611.02-0611.42 WRMS resid 0.032 totl 0.012 xtrk
Satevo propagates this TLE to decay on Jun 14 near 15 h UTC; uncertainty is 16 h, based on the rule of thumb of 20% of time from epoch to decay.
The positional data of the Astronomical Observatory of Odessa University is available as received is here, and converted by me to IOD format here (I used a subset at 15 s intervals for the orbit determination). Photometric data is here. The photometric plot is here.
Scott Tilley's observations:
40661 15 025L 8049 G 20150611095833384 17 25 2059145+063319 37 S 40661 15 025L 8049 G 20150611095836083 17 25 2104145+070728 37 S 40661 15 025L 8049 G 20150611095841123 17 25 2113209+080983 37 S 40661 15 025L 8049 G 20150611095845623 17 25 2121473+090434 37 S ROBERTS CREEK 1: 8049 ST 49.4348 -123.6685 40.
The following TLE is based on observations reported by Leo Barhorst, Cees Bassa here and here, a video by Kevin Fetter, from which Cees Bassa reduced observations posted here and here, Andriy Makeyev, Alberto Rango, and myself.
LightSail-A 341 X 576 km 1 40661U 15025L 15162.33948982 .03837174 00000-0 65724-1 0 02 2 40661 54.9923 245.8728 0171523 243.1553 115.1848 15.35818682 04 Arc 20150611.02-0611.35 WRMS resid 0.040 totl 0.015 xtrk
Satevo propagates this TLE to decay on Jun 14 near 21 h UTC; uncertainty is 17 h, based on the rule of thumb of 20% of time from epoch to decay.
Ron Dantowitz of the Clay Center Observatory reports that LightSail-A was 0.7 s late, with no detectable cross track error relative the epoch 15162.07897262 TLE that I posted in my previous update. That was on a pass that culminated 63 deg above the northwest horizon on Jun 11 near 06:50 UTC.
Cees Bassa has reported observations from his second pass. Adding them to previously reported observations by Scott Tilley and myself, yields the following elements.
LightSail-A 343 X 585 km 1 40661U 15025L 15162.07897262 .03726413 00000-0 66814-1 0 01 2 40661 54.9917 247.0285 0176484 238.9270 119.4332 15.33904503 09 Arc 20150610.31-0611.09 WRMS resid 0.021 totl 0.008 xtrkIn the event additional observations are reported that fall within the arc of this TLE, I may issue a revision. They will certainly be used when the arc is extended forward.
Satevo propagates this TLE to decay on Jun 14 near 19 h UTC; uncertainty is 18 h, based on the rule of thumb of 20% of time from epoch to decay.
Cees Bassa has reported new optical observations. Adding them to previously reported observations by Alberto Rango, Scott Tilley and myself, yields the following elements.
LightSail-A 343 X 587 km 1 40661U 15025L 15162.01380545 .03900529 00000-0 70198-1 0 08 2 40661 55.0145 247.3565 0178072 239.9319 118.3945 15.33568053 02 Arc 20150610.04-0611.03 WRMS resid 0.014 totl 0.008 xtrkIn the event additional observations are reported that fall within the arc of this TLE, I may issue a revision.
Satevo propagates this TLE to decay on Jun 14 near 14 h UTC; uncertainty is 17 h, based on the rule of thumb of 20% of time from epoch to decay.
An updated official USAF TLE has been issued via Cal Poly:
LightSail-A 346 X 607 km 1 40661U 15025L 15161.49169160 .04014814 00000-0 68169-1 0 332 2 40661 55.0009 249.6588 0190634 236.0707 122.2387 15.29783738 3166This TLE yields predictions similar to those of the epoch 15161.42634807 TLE that I generated earlier from hobbyist observations.
The following note is relevant to users of the Satevo decay propagator, and anyone else who relies on the old SGP decay terms in TLEs. It can be ignored by anyone who uses software based exclusively on the SGP4 model (which is almost everyone).
Modern TLEs are based on the SGP4 orbital model, which employs the B* decay term. For backward compatibility, TLEs also include the two decay terms of the old SGP model, that SGP4 replaced. SGP4 ignores the SGP decay terms, but some software, including Satevo, makes use of them. Both the USAF and hobbyist TLEs have been generated using SGP4, but their SGP decay terms may differ considerably due to different methods used to compute them. I do not know how the USAF computes those terms. Normally, only SGP's ndot/2 decay term is non-zero. I derived a formula relating ndot/2 and B*, which I and a few other hobbyists use to convert between the two. That is the formula used to estimate ndot/2 in my TLEs. Usually, this formula yields results similar to the USAF ndot/2, but not always. In the case of LightSail-A, the USAF's ndot/2 is somewhat greater than the hobbyist values, despite fairly similar B*. As a result, Satevo and other programs that rely on ndot/2, will produce significantly different results, depending on the source of the TLE. For example, Satevo propagates our epoch 15161.42634807 TLE to decay on Jun 14 near 13 h UTC, but propagates the USAF's epoch 15161.49169160 TLE to decay 11 h earlier. I have no opinion as to which is more accurate.
Scott Tilley has reported optical observations made on Jun 10 at 10:30 UTC. Using them to extend the arc upon which the epoch 15161.29558274 TLE was based, yields the following result:
LightSail-A 346 X 609 km 1 40661U 15025L 15161.42634807 .03503735 00000-0 68491-1 0 06 2 40661 54.9923 249.9426 0191654 239.6095 118.5864 15.29348197 09 Arc 20150609.39-0610.44 WRMS resid 0.030 totl 0.013 xtrkIn the event that additional observations within the arc of this solution are reported, I may issue a revision incorporating them.
Satevo propagates this TLE to decay on Jun 14 near 13 h UTC; uncertainty is 20 h, based on 20% of time from epoch to decay rule of thumb.
The rate of decay decreased significantly after Brad Young's observation of Jun 09 at 09:20 UTC. Alberto Rango observed it running approx. 30 s late relative the epoch 15160.37823939 TLE on Jun 10 at 01:02 UTC. I observed it running 59 s late on Jun 10 at 07:19 UTC. Below are approximate updated elements based on Brad's, Alberto's and my observations:
LightSail-A 346 X 616 km 1 40661U 15025L 15161.29558274 .03349743 00000-0 65851-1 0 08 2 40661 55.0165 250.5705 0196826 235.6816 122.5444 15.28388351 04 Arc 20150609.39-0610.31 WRMS resid 0.036 totl 0.021 xtrkSatevo propagates this TLE to decay on Jun 14 near 16 h UTC; uncertainty 21 h, based on 20% of time from epoch to decay rule of thumb. This exceeds the uncertainty range of the earlier estimate based on the epoch 15160.37823939 TLE. Clearly a very difficult decay to predict with any confidence.
Nikolay Koshkin has kindly granted permission to share the positional and photometric data observed by the Astronomical Observatory of Odessa University on Jun 08 near 23:53 UTC. The positional data is here; photometric data is here; photometric plot is here.
Observatory coordinates: [086] Odessa, Ukraine: Lon=30.75564, lat=46.47778, h=56
Tracking telescope KT-50: 0.5 m diameter, Focal length 3 m, CCD Wat-902H2 FOV = 12x9'.
Professionally measured satellite coordinates and photometry at optical wavelengths without a filter.
The following TLE is based on optical and visual observations spanning 2015 Jun 08 08:01 UTC through Jun 09 09:20 UTC:
LightSail-A 350 X 645 km 1 40661U 15025L 15160.37823939 .03856298 00000-0 84492-1 0 09 2 40661 55.0165 254.6080 0214087 233.7415 124.3658 15.22810628 07 Arc 20150608.33-0609.39 WRMS resid 0.027 totl 0.014 xtrkNew data in this arc consists of four positions and time that I extracted from a NASA/MSFC meteor camera video, taken by Aaron Kingery, Bill Cooke and Robert Suggs on Jun 08 08:01 UTC, and visual observations by Brad Young on Jun 09 on passes at 07:43 UTC and 09:20 UTC. Data received earlier from Andriy Makeyev and Nikolay Koshkin also is in the arc.
Satevo propagates this TLE to decay on Jun 13 near 9 h UTC; uncertainty 19 h, based on 20% of time from epoch to decay rule of thumb.
An updated official USAF TLE has been issued via Cal Poly:
LightSail-A 346 X 642 km 1 40661U 15025L 15160.50936430 .04437127 00000-0 82492-1 0 303 2 40661 54.9987 254.0125 0215427 231.6648 125.8930 15.23779744 3012Satevo propagates this to decay on Jun 13 near 0 h UTC; uncertainty 18 h, based on 20% of time from epoch to decay rule of thumb.
The following TLE is derived from optical observations by Cees Bassa on Jun 08 near 01:45 UTC, the Astronomical Observatory of Odessa University on Jun 08 near 23:53 UTC (thank you Nikolay Koshkin for sharing this data), and by Andriy Makeyev on Jun 09 near 01:30 UTC:
LightSail-A 353 X 657 km 1 40661U 15025L 15160.04976882 .03614314 00000-0 83570-1 0 06 2 40661 54.9977 256.0073 0220525 232.9009 125.1677 15.20352458 08 Arc 20150608.07-0609.06 WRMS resid 0.015 totl 0.007 xtrkSatevo propagates this to decay on Jun 13 near 10 h UTC; uncertainty 21 h, based on 20% of time from epoch to decay rule of thumb.
Andriy Makeyev has observed LightSail-A running 2.5 s late and less than 0.03 deg from the track predicted by the epoch 15159.59005712 issued by the USAF. It was 3.8 s early, and 0.15 deg from the track of our epoch 15159.75000000 TLE.
The first official USAF TLE has been issued via Cal Poly:
1 40661U 15025L 15159.59005712 .03473181 00000-0 83705-1 0 273 2 40661 55.0067 258.0312 0232820 229.0835 134.4435 15.17229817 2873As expected, it has very small residuals compared with our Doppler and optical observations. For tonight, it yields predictions about 10 s earlier than our epoch 15159.75000000 TLE.
Scott Tilley has revised the elements using 857 Doppler measurements taken during the 8.4 h period ended Jun 08 18:00 UTC. Scott's TLE was stated for the start of the arc. I have propagated it to the end:
1 40661U 15025L 15159.75000000 .02993987 00000-0 69200-1 0 01 2 40661 55.0136 257.3619 0233514 228.9444 288.9061 15.18205779 02This TLE predicts passes over N. America tonight, approximately 10 s earlier than the epoch 15159.06218063 TLE.
The 71002 TLE that I posted at 03:00 UTC, derived from Cees Bassa's optical observations Jun 08 01:45 UTC, remained accurate on half a dozen passes through 14:34 UTC. Most of the observations were Doppler TCA (time of closest approach), by Cees and Scott Tilley. Since the orbit has proven accurate, I am re-issuing it with the correct identifiers:
1 40661U 15025L 15159.06218063 .02648498 00000-0 67226-1 0 94 2 40661 55.0136 260.3261 0243391 227.2228 135.1229 15.14087982 04The Satevo decay propagator estimates re-entry mid-day of Jun 14 UTC. Uncertainty is at least 1 day.
We may post an updated TLE later today, but for now the above should be plenty accurate for preliminary planning of observations tonight.
Heavens-Above now has the TLE that I posted at 03:00 UTC, so it will yield fairly accurate observations for the remaining passes this morning. Specify your observing location, then click on the special LightSail entry on the main page:
Ron Dantowitz of the Clay Center Observatory reports that LightSail-A was 2.9 s late relative the 71002 TLE that I posted in my previous update. That was on a pass that culminated 29 deg above the southeast horizon on Jun 08 near 06:26 UTC.
The 2.9 s lateness was about 3 revs after the epoch of the TLE, so it is reasonable to expect that it will trend approx. 0.9 s later per rev. That should not pose any challenge for most observers.
Ron did not have any comparison stars by which to judge, but his impression was that it was approximately mag 4, and mostly stable in brightness. That would be consistent with my standard magnitude estimate of 4.4 (1000 km, 90 deg phase angle).
Cees Bassa has reported the first optical observations post-sail deployment. It passed much less early than expected, relative the pre-sail deployment orbit. The rate of decay appears to have increased by a factor of more than 100, but that would be about 30 percent of my earlier estimate.
Below is a preliminary estimate of the orbit that fits the observations reported by Cees.
1 71002U 15159.06218063 .02648498 00000-0 67226-1 0 94 2 71002 55.0136 260.3261 0243391 227.2228 135.1229 15.14087982 07Please use the above TLE for predictions for the remainder of the night, or until further notice. I intend to update upon receipt of additional observations.
Thank you, Rex Ridenoure, CEO of Ecliptic Enterprises Corporation, for informing me that the correct mass of LightSail-A is 4.93 kg. I have incorporated that into the above estimate. The mass is nearly 10 percent greater than I used in my earlier estimates. That accounts about one third of the lower than expected rate of decay. The remainder could easily be due to drag modelling errors, arising from the uncertainty in the atmospheric density model and in the spacecraft's drag area (the area presented into the direction of motion). I caution against attempting to draw any conclusions about the state of the sail from the lower than expected decay rate.
LightSail-A (2015-025L / 40661) deployed its solar sail on 2015 Jun 7 near 19:55 UTC.
These were its orbital elements prior to sail deployment:
1 90726U 15157.54176440 +.00024677 +00000-0 +65506-3 0 00277 2 90726 055.0115 266.9142 0247634 223.3078 134.8095 15.12700107002561Deployment of its solar sail will greatly increase LightSail's rate of orbital decay; therefore, the above elements will become progressively and rapidly less accurate. I estimate that it will re-enter early on June 10 UTC. In the meantime, its large, highly reflective sail will be observable visually and optically from certain ranges of latitude.
Observers between about 20 N and 56 N will have morning visibility of the orbit. Those south of about 43 S will have evening visibility.
I estimate that with its sail deployed, LightSail-A's standard visual magnitude will be about 4.4 (1000 km range, 90 deg phase angle), resulting in mag 2 to 3 on high-elevation, well illuminated passes. Its brightness may vary considerably from one pass to another. It could be much fainter than expected, or flare to negative magnitudes. I suspect it will begin tumbling during its first pass through perigee, which could cause it to appear to flash periodically.
I have estimated the following TLEs to assist in visual, optical and radio tracking during the first 15 h post-sail deployment, which spans the passes visible on the night of Jun 7/8 UTC, from Europe, Africa, and North and South America.
1 70001U 15158.86308014 .07672137 00000-0 19593 0 0 00 2 70001 55.0102 261.1869 0244236 226.5489 130.5327 15.13784762 08 1 70002U 15158.92986525 .07923140 00000-0 19899 0 0 76 2 70002 55.0109 260.8972 0240777 226.9370 134.3416 15.14809531 00 1 70003U 15158.99607738 .08337582 00000-0 20584 0 0 17 2 70003 55.0115 260.6104 0237223 227.2983 135.3057 15.15858747 05 1 70004U 15159.06146780 .08678894 00000-0 21023 0 0 60 2 70004 55.0127 260.3263 0233702 227.6489 132.0504 15.16949143 08 1 70005U 15159.12706861 .08636904 00000-0 20491 0 0 64 2 70005 55.0125 260.0406 0230147 228.0123 130.1929 15.18087828 08 1 70006U 15159.19334589 .09012408 00000-0 20962 0 0 89 2 70006 55.0102 259.7502 0226383 228.3817 132.2958 15.19232689 09 1 70007U 15159.25915494 .09660876 00000-0 21997 0 0 62 2 70007 55.0077 259.4608 0222568 228.7128 132.1507 15.20418885 00 1 70008U 15159.32397867 .09708942 00000-0 21612 0 0 37 2 70008 55.0080 259.1752 0218535 229.0014 126.9342 15.21671393 03 1 70009U 15159.38996897 .10032923 00000-0 21810 0 0 88 2 70009 55.0094 258.8851 0214471 229.4062 128.2943 15.22952785 07 1 70010U 15159.45527671 .10400000 00000-0 22077 0 0 89 2 70010 55.0104 258.5983 0210198 229.8433 126.1871 15.24263240 02Any of the 700XX TLEs will be adequate to determine whether you have a visible pass on the night of Jun 7/8 UTC. For best accuracy, use the TLE closest in epoch to the pass you intend to observe.
To cope with the uncertainty in the rate of decay, I recommend comparing predictions against the pre-sail deployment TLE, and taking 50% of the difference in prediction time as the uncertainty, e.g. if a 700XX TLE predicts a pass 5 min. earlier than the 90726 TLE, then allow 2.5 min. prediction time uncertainty.
I estimated the TLEs using the following procedure. I used SGP4 to propagate the 90726 TLE to the time of deployment, which I took to be Jun 07 at 19:55 UTC. TLE Analyzer 2.12 converted the result to a state vector type compatible with GMAT 2014a (General Mission Analysis Tool).
I used GMAT to numerically propagate the orbit, based on the mass of the spacecraft (4.5 kg), the dimensions of its sail (~5.66 x 5.66 m2), my guess that it will be tumbling, and the current space weather.
GMAT produced Cartesian state vectors at close time intervals. I selected state vectors near successive ascending nodes and converted them to TLEs. I computed the mean ndot/2 and corresponding B* decay terms between successive TLEs, and inserted them into the TLEs.
I intend to revise in the event I receive visual, optical or radio tracking data that reveals a significantly different rate of decay, in time to be to useful to observers on the night of Jun 7/8 UTC. Updates will be posted on this page, so please check back from time to time.
I also intend to produce TLEs for the night of Jun 8/9, if I have sufficient data.
Link to the VSO Home Page.
