Orbital Analysis for matched events on 20211103_050525.033_UK

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Summary for Event
-----------------
shower ID 13 LEO
Lg 137.63° Bg 18.78° Vg 64.08km/s
mass 0.00538g, abs. mag 0.7
best visual mag 1.8
Path Details
------------
start -1.22° 52.94° 108.12km
end   -1.28° 52.97° 98.42km

Orbit Details
-------------
Semimajor axis 2.20A.U., eccentricity 0.57, inclination 145.65°, Period 3.26Y, LA Sun 220.70°, last Perihelion 2021-10-11

Full details below
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Input measurement type: Azimuth +east of due north for meas1, Elevation angle above the horizon for meas2

Uncertainties type:
 Purely geometric uncertainties

Reference JD: 2459521.712095292751
Time: 2021-11-03 05:05:25.033294 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0035 and UK003X
 Convergence angle = 83.32612 deg
 R.A. = 147.57515  Dec = +33.52668 deg

Best intersection: Stations UK0035 and UK003X with Qconv = 83.33 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =  -1828088.74 +/- 63.83 m
 Y =   3464399.40 +/- 38.64 m
 Z =   5152929.02 +/- 49.23 m
 Vx =   -45544.87 +/- 180.73 m/s
 Vy =    29586.81 +/- 483.46 m/s
 Vz =    35781.04 +/- 341.84 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+4.246587e+03, -1.030662e+03, -2.249501e+03, +1.081803e+04, +1.103379e+04, -1.133894e+03
-1.030662e+03, +1.607504e+03, -8.645442e+01, +3.941406e+03, +4.767174e+03, -6.322495e+03
-2.249501e+03, -8.645442e+01, +2.589235e+03, -3.939522e+03, -5.553292e+03, +8.942175e+03
+1.081803e+04, +3.941406e+03, -3.939522e+03, +1.324277e+05, +1.277894e+05, +2.425253e+03
+1.103379e+04, +4.767174e+03, -5.553292e+03, +1.277894e+05, +1.285792e+05, -2.086955e+04
-1.133894e+03, -6.322495e+03, +8.942175e+03, +2.425253e+03, -2.086955e+04, +1.081722e+05

Timing offsets (from input data):
    UK0035: 0.000217 s
    UK003X: 0.000000 s

Reference point on the trajectory:
  Time: 2021-11-03 05:05:25.033294 UTC
  Lon     = +-1.216341 +/- 0.0008 deg
  Lat     = +52.940889 +/- 0.0004 deg
  Lat geo = +52.758738 +/- 0.0004 deg
  Ht      =  108153.33 +/- 59.11 m

  JD dynamic   = 2459521.712896033656 
  LST apparent = 117.8196428554 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      = 146.99149 +/- 0.5040 deg
  Dec       = +33.37746 +/- 0.2597 deg
  Azimuth   = 121.59140 +/- 0.7156 deg
  Elevation = +61.45487 +/- 0.3508 deg
  Vavg      =  64.77992 +/- 0.0784 km/s
  Vinit     =  65.03843 +/- 0.1743 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      = 147.25393 +/- 0.5040 deg
  Dec       = +33.30983 +/- 0.2597 deg
  Azimuth   = 121.31768 +/- 0.7156 deg
  Elevation = +61.26664 +/- 0.3508 deg
  Vavg      =  64.89671 +/- 0.0784 km/s
  Vinit     =  65.15522 +/- 0.1743 km/s
Radiant (geocentric, J2000):
  R.A.   = 146.82702 +/- 0.5067 deg
  Dec    = +33.31082 +/- 0.2623 deg
  Vg     =  64.08462 +/- 0.1769 km/s
  Vinf   =  65.03843 +/- 0.1743 km/s
  Zc     =  28.45009 +/- 0.3517 deg
  Zg     =  28.66468 +/- 0.3544 deg
Radiant (ecliptic geocentric, J2000):
  Lg     = 137.63368 +/- 0.4422 deg
  Bg     = +18.78327 +/- 0.2715 deg
  Vh     =  37.21641 +/- 0.2686 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     = 143.55185 +/- 0.8441 deg
  Bh     = +33.67291 +/- 0.3755 deg
  Vh_x   =  24.91380 +/- 0.3527 km/s
  Vh_y   = -18.40037 +/- 0.3185 km/s
  Vh_z   = -20.63467 +/- 0.3445 km/s
Orbit:
  La Sun = 220.698741 +/- -0.0000 deg
  a      =   2.199361 +/- 0.1291 AU
  e      =   0.570313 +/- 0.0221
  i      = 145.653327 +/- 0.4002 deg
  peri   = 150.394282 +/- 1.5877 deg
  node   = 220.701875 +/- 0.0000 deg
  Pi     =  11.096157 +/- 1.5877 deg
  q      =   0.945037 +/- 0.0058 AU
  f      =  29.607105 +/- 1.5877 deg
  M      =   6.876536 +/- 0.6243 deg
  Q      =   3.453685 +/- 0.2598 AU
  n      =   0.302176 +/- 0.0219 deg/day
  T      =   3.261710 +/- 0.2992 years
  Last perihelion JD = 2459498.956137 (2021-10-11 10:56:50.227557) +/- 1.0679 days
  Tj     =   1.484488 +/- 0.1196
Shower association:
  IAU No.  =   13
  IAU code =  LEO

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (deg) ,   peri (deg) ,    i (deg)
e   , +5.211444e-04, -5.251034e-05, +5.358560e-04, -3.742148e-07, -6.019477e-03, -8.909095e-03
q   , -5.251034e-05, +3.604899e-05, +6.020628e-03, +7.657395e-09, +9.528023e-03, +1.748191e-04
Tp  , +5.358560e-04, +6.020628e-03, +1.203394e+00, -6.346896e-06, +1.759053e+00, -1.525641e-01
node, -3.742148e-07, +7.657395e-09, -6.346896e-06, +2.990686e-10, -4.422346e-06, +7.127747e-06
peri, -6.019477e-03, +9.528023e-03, +1.759053e+00, -4.422346e-06, +2.660681e+00, -1.074419e-01
i   , -8.909095e-03, +1.748191e-04, -1.525641e-01, +7.127747e-06, -1.074419e-01, +1.698938e-01

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.000000
 a2 = 0.000000

Mean time residuals from time vs. length:
  Station with reference time: UK003X
  Avg. res. = 9.446e-06 s
  Stddev    = 3.07e-03 s

Begin point on the trajectory:
  Lon =    -1.216550 +/- 0.0005 deg
  Lat =    52.940967 +/- 0.0003 deg
  Ht  = 108122.48 +/- 28.52 m
End point on the trajectory:
  Lon =    -1.283232 +/- 0.0008 deg
  Lat =    52.965428 +/- 0.0003 deg
  Ht  = 98416.89 +/- 32.03 m

Stations
--------
        ID, Ignored, Lon +E (deg), Lat +N (deg),  Ht (m), Jacchia a1, Jacchia a2,  Beg Ht (m),  End Ht (m), +/- Obs ang (deg), +/- V (m), +/- H (m), Persp. angle (deg), Weight, FOV Beg, FOV End, Comment
    UK0035,   False,     1.010397,    52.949859,   25.00, 151.973336,   0.000000,   107928.59,    98416.89,          0.013957,     30.95,     32.43,              79.74, 1.0000,    True,    True, {"ff_name": "FF_UK0035_20211103_050518_030_1088000.fits"}
    UK003X,   False,    -2.362458,    51.684814,  132.00,   0.000000,   0.000000,   108122.48,    99177.03,          0.021711,     46.18,     55.92,              60.46, 1.0000,    True,    True, {"ff_name": "FF_UK003X_20211103_050517_252_1063936.fits"}

Points
------
 No, Station ID,  Ignore,  Time (s),                   JD,     meas1,     meas2, Azim +E of due N (deg), Alt (deg), Azim line (deg), Alt line (deg), RA obs (deg), Dec obs (deg), RA line (deg), Dec line (deg),       X (m),       Y (m),       Z (m), Latitude (deg), Longitude (deg), Height (m),  Range (m), Length (m), State vect dist (m),  Lag (m), Vel (m/s), Vel prev avg (m/s), H res (m), V res (m), Ang res (asec), AppMag, AbsMag
  0,     UK0035,       0,  0.017942, 2459521.712095497642,  52.45611,  27.44657,              270.53758,  34.86925,       270.53153,       34.86789,     52.45611,     +27.44657,      52.45924,      +27.44220, -1827909.58,  3464283.01,  5152788.27,      52.941455,       -1.217938,  107928.59,  185631.36,       0.00,              255.84,  -599.65,      0.00,           69584.71,     12.04,     11.50,          18.50,  +4.65,  +3.31
  1,     UK0035,       0,  0.058698, 2459521.712095969357,  51.48941,  26.90218,              270.85755,  33.88630,       270.85487,       33.88569,     51.48941,     +26.90218,      51.49104,      +26.90023, -1825567.87,  3462761.80,  5150948.57,      52.948854,       -1.238032,  104991.27,  185017.92,    3343.97,             3599.81,    93.61,  82048.62,           69584.71,      5.39,      5.15,           8.31,  +2.50,  +1.16
  2,     UK0035,       0,  0.099258, 2459521.712096438743,  50.75988,  26.49748,              271.10747,  33.14797,       271.09354,       33.14484,     50.75988,     +26.49748,      50.76759,      +26.48731, -1823813.87,  3461622.36,  5149570.59,      52.954398,       -1.253141,  102791.37,  184599.24,    5848.71,             6104.55,   -39.61,  61753.76,           69584.71,     28.13,     26.89,          43.48,  +1.83,  +0.50
  3,     UK0035,       0,  0.139886, 2459521.712096909061,  49.97651,  26.03055,              271.35329,  32.33019,       271.35140,       32.32977,     49.97651,     +26.03055,      49.97810,      +26.02917, -1821893.67,  3460374.96,  5148062.04,      52.960469,       -1.269681,  100383.26,  184178.09,    8590.77,             8846.61,    60.07,  67492.00,           69584.71,      3.84,      3.67,           5.94,  +1.95,  +0.62
  4,     UK0035,       0,  0.180414, 2459521.712097377982,  49.35159,  25.62656,              271.52738,  31.65358,       271.55938,       31.66075,     49.35159,     +25.62656,      49.33518,      +25.65010, -1820325.57,  3459356.30,  5146830.10,      52.965428,       -1.283232,   98416.89,  183865.63,   10830.03,            11085.87,  -336.55,  55252.15,           66255.64,    -65.40,    -62.41,         101.42,  +3.23,  +1.91
  0,     UK003X,       0,  0.000000, 2459521.712095292751, 237.25565,  62.04616,               28.77666,  33.03872,        28.75634,       33.04981,    237.25565,     +62.04616,     237.26860,      +62.06555, -1828064.14,  3464383.42,  5152909.69,      52.940967,       -1.216550,  108122.48,  194265.46,       0.00,               35.13,   346.53,      0.00,           61523.37,    -53.17,     43.82,          73.16,  +4.24,  +2.80
  1,     UK003X,       0,  0.040416, 2459521.712095760740, 238.47464,  61.88965,               28.36539,  32.55585,        28.36921,       32.55377,    238.47464,     +61.88965,     238.47224,      +61.88601, -1826465.67,  3463345.03,  5151653.90,      52.946017,       -1.230315,  106117.38,  193165.95,    2282.62,             2317.75,     0.56,  56478.12,           61523.37,      9.97,     -8.22,          13.79,  +2.83,  +1.40
  2,     UK003X,       0,  0.080856, 2459521.712096228730, 239.72683,  61.70283,               27.95242,  32.04276,        27.96903,       32.03373,    239.72683,     +61.70283,     239.71537,      +61.68707, -1824813.11,  3462271.49,  5150355.61,      52.951239,       -1.244552,  104044.60,  192051.41,    4642.50,             4677.63,  -269.72,  58355.09,           61523.37,     43.23,    -35.69,          60.21,  +2.28,  +0.86
  3,     UK003X,       0,  0.121392, 2459521.712096697651, 241.24946,  61.46114,               27.44658,  31.41161,        27.48337,       31.39167,    241.24946,     +61.46114,     241.22228,      +61.42638, -1822804.48,  3460966.64,  5148777.59,      52.957589,       -1.261838,  101525.46,  190728.41,    7510.84,             7545.97,   -37.78,  70760.36,           61523.37,     95.45,    -78.87,         133.91,  +2.14,  +0.74
  4,     UK003X,       0,  0.161920, 2459521.712097167037, 242.63462,  61.18033,               27.01431,  30.79216,        27.03037,       30.78348,    242.63462,     +61.18033,     242.62259,      +61.16522, -1820931.76,  3459750.09,  5147306.34,      52.963511,       -1.277982,   99177.03,  189525.54,   10185.09,            10220.22,     0.60,  65985.30,           63236.68,     41.59,    -34.34,          58.70,  +1.96,  +0.57

Notes
-----
- Points that have not been taken into consideration when computing the trajectory have '1' in the 'Ignore' column.
- The time already has time offsets applied to it.
- 'meas1' and 'meas2' are given input points.
- X, Y, Z are ECI (Earth-Centered Inertial) positions of projected lines of sight on the radiant line.
- Zc is the observed zenith distance of the entry angle, while the Zg is the entry zenith distance corrected for Earth's gravity.
- Latitude (deg) and Longitude (deg) are in WGS84 coordinates, while Height (m) is in the EGM96 datum. There values are coordinates of each point on the radiant line.
- Jacchia (1955) deceleration equation fit was done on the lag.
- Right ascension and declination in the table are given in the epoch of date for the corresponding JD, per every point.
- 'RA and Dec obs' are the right ascension and declination calculated from the observed values, while the 'RA and Dec line' are coordinates of the lines of sight projected on the fitted radiant line. The coordinates are in the epoch of date, and NOT J2000!. 'Azim and alt line' are thus corresponding azimuthal coordinates.
- 'Vel prev avg' is the average velocity including all previous points up to the given point. For the first 4 points this velocity is computed as the average velocity of those 4 points.