Orbital Analysis for matched events on 20210810_030738.677_UK

Summary for Event
-----------------
shower ID 872 ETR
Lg 38.77° Bg 21.69° Vg 66.41km/s
mass 0.18373g, abs. mag -3.0
Path Details
------------
start -4.42° 53.69° 109.43km
end   -4.52° 53.73° 94.82km

Orbit Details
-------------
Semimajor axis 15.59A.U., eccentricity 0.94, inclination 142.17°, Period 61.57Y, LA Sun 137.43°, last Perihelion 1960-02-01

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: 2459436.630308771506
Time: 2021-08-10 03:07:38.689164 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK001Z and UK003F
 Convergence angle = 15.70449 deg
 R.A. =  28.24224  Dec = +37.37093 deg

Best intersection: Stations UK001Z and UK003F with Qconv = 15.70 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3849548.04 +/- 249.24 m
 Y =     88270.25 +/- 160.01 m
 Z =   5205129.95 +/- 379.09 m
 Vx =    48540.39 +/- 1974.33 m/s
 Vy =    26117.52 +/- 1262.10 m/s
 Vz =    38659.01 +/- 2696.10 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+4.424740e+03, +2.075992e+03, -7.111731e+03, +4.197517e+04, +2.697939e+04, -6.157108e+04
+2.075992e+03, +1.379133e+03, -3.204500e+03, +2.767093e+04, +2.270609e+04, -4.276347e+04
-7.111731e+03, -3.204500e+03, +1.165108e+04, -6.305731e+04, -3.967401e+04, +9.234919e+04
+4.197517e+04, +2.767093e+04, -6.305731e+04, +5.736307e+05, +4.579679e+05, -8.785157e+05
+2.697939e+04, +2.270609e+04, -3.967401e+04, +4.579679e+05, +4.146665e+05, -7.243963e+05
-6.157108e+04, -4.276347e+04, +9.234919e+04, -8.785157e+05, -7.243963e+05, +1.356508e+06

Timing offsets (from input data):
    UK001Z: -0.000201 s
    UK003F: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-10 03:07:38.689164 UTC
  Lon     = +-4.419274 +/- 0.0023 deg
  Lat     = +53.688048 +/- 0.0037 deg
  Lat geo = +53.507353 +/- 0.0037 deg
  Ht      =  110233.59 +/- 171.23 m

  JD dynamic   = 2459436.631109643262 
  LST apparent = 1.3135637697 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  28.28281 +/- 0.2933 deg
  Dec       = +35.04396 +/- 2.9274 deg
  Azimuth   = 123.73421 +/- 5.1668 deg
  Elevation = +63.48249 +/- 2.1995 deg
  Vavg      =  64.91611 +/- 0.0877 km/s
  Vinit     =  67.32617 +/- 0.1282 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  28.54233 +/- 0.2933 deg
  Dec       = +34.98155 +/- 2.9274 deg
  Azimuth   = 123.43928 +/- 5.1668 deg
  Elevation = +63.30464 +/- 2.1995 deg
  Vavg      =  65.02087 +/- 0.0877 km/s
  Vinit     =  67.43093 +/- 0.1282 km/s
Radiant (geocentric, J2000):
  R.A.   =  28.10318 +/- 0.2945 deg
  Dec    = +34.79067 +/- 2.9479 deg
  Vg     =  66.40549 +/- 0.1300 km/s
  Vinf   =  67.32617 +/- 0.1282 km/s
  Zc     =  26.41756 +/- 2.1850 deg
  Zg     =  26.60273 +/- 2.2010 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  38.77302 +/- 1.1516 deg
  Bg     = +21.69286 +/- 2.7724 deg
  Vh     =  41.15034 +/- 0.9790 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  30.57695 +/- 1.9256 deg
  Bh     = +36.62041 +/- 4.2016 deg
  Vh_x   = -28.43489 +/- 1.7989 km/s
  Vh_y   = -16.80091 +/- 0.1570 km/s
  Vh_z   = -24.54662 +/- 2.9128 km/s
Orbit:
  La Sun = 137.434156 +/- -0.0000 deg
  a      =  15.593178 +/- 68.4937 AU
  e      =   0.938628 +/- 0.0939
  i      = 142.167914 +/- 3.9748 deg
  peri   = 207.817155 +/- 4.7604 deg
  node   = 137.431430 +/- 0.0005 deg
  Pi     = 345.248585 +/- 4.7599 deg
  q      =   0.956980 +/- 0.0133 AU
  f      = 332.177398 +/- 4.7607 deg
  M      = 359.684153 +/- nan deg
  Q      =  30.229375 +/- 136.9903 AU
  n      =   0.016007 +/- 0.0385 deg/day
  T      =  61.574738 +/- 442216272.6257 years
  Last perihelion JD = 2436965.798404 (1960-02-01 07:09:42.093188) +/- 281822.6616 days
  Tj     =  -0.609379 +/- 0.4556
Shower association:
  IAU No.  =  872
  IAU code =  ETR

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +6.225838e-04, +1.608855e-04, -5.987362e+03, +1.208638e-07, -8.199816e-04, -8.509972e-04
q   , +1.608855e-04, +4.493920e-05, -1.770907e+03, +3.119286e-08, -2.282339e-04, -2.197773e-04
Tp  , -5.987362e+03, -1.770907e+03, +1.049692e+11, -1.119843e+00, +9.060637e+03, +8.022113e+03
node, +1.208638e-07, +3.119286e-08, -1.119843e+00, +2.351284e-11, -1.588812e-07, -1.653952e-07
peri, -8.199816e-04, -2.282339e-04, +9.060637e+03, -1.588812e-07, +1.159557e-03, +1.119750e-03
i   , -8.509972e-04, -2.197773e-04, +8.022113e+03, -1.653952e-07, +1.119750e-03, +1.163936e-03

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.070506
 a2 = 35.197185

Mean time residuals from time vs. length:
  Station with reference time: UK003F
  Avg. res. = 2.049e-05 s
  Stddev    = 4.53e-03 s

Begin point on the trajectory:
  Lon =    -4.424242 +/- 0.0021 deg
  Lat =    53.690017 +/- 0.0034 deg
  Ht  = 109429.27 +/- 148.74 m
End point on the trajectory:
  Lon =    -4.515813 +/- 0.0025 deg
  Lat =    53.725840 +/- 0.0036 deg
  Ht  = 94816.64 +/- 141.32 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
    UK001Z,   False,    -2.949729,    50.877448,   82.00, 115.777662,   0.000000,   109429.27,    94816.64,          0.007091,     42.45,      8.47,              86.61, 1.0000,    True,    True, {"ff_name": "FF_UK001Z_20210810_030732_782_0609024.fits"}
    UK003F,   False,    -1.802002,    51.351948,  130.00,   0.000000,   0.000000,   107009.05,    95758.89,          0.018842,    103.52,     39.30,              89.62, 1.0000,    True,    True, {"ff_name": "FF_UK003F_20210810_030736_861_0612864.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,     UK001Z,       0,  0.011109, 2459436.630308902357, 211.07838,  53.21287,              342.75389,  16.77411,       342.75766,       16.77309,    211.07838,     +53.21287,     211.07217,      +53.21302,  3848899.96,    87921.55,  5204613.80,      53.690017,       -4.424242,  109429.27,  349068.56,       0.00,              898.89,  -394.63,      0.00,           71671.50,      4.47,     22.40,          13.50,  +3.75,  +1.04
  1,     UK001Z,       0,  0.051441, 2459436.630309369415, 211.03192,  52.73392,              342.62585,  16.31031,       342.61896,       16.31219,    211.03192,     +52.73392,     211.04347,      +52.73365,  3846794.40,    86788.64,  5202936.87,      53.696414,       -4.440559,  106816.26,  349171.29,    2920.44,             3819.33,  -189.59,  72409.96,           71671.50,     -8.19,    -41.04,          24.72,  +1.49,  -1.23
  2,     UK001Z,       0,  0.091761, 2459436.630309836008, 211.00747,  52.25750,              342.48653,  15.85284,       342.48179,       15.85413,    211.00747,     +52.25750,     211.01558,      +52.25731,  3844700.82,    85662.17,  5201269.48,      53.702779,       -4.456803,  104218.35,  349297.71,    5824.26,             6723.15,    -0.35,  72019.47,           71671.50,     -5.65,    -28.30,          17.04,  +0.97,  -1.75
  3,     UK001Z,       0,  0.132073, 2459436.630310302600, 210.97997,  51.79187,              342.35348,  15.40486,       342.34827,       15.40629,    210.97997,     +51.79187,     210.98896,      +51.79166,  3842652.73,    84560.18,  5199638.32,      53.709007,       -4.472715,  101677.14,  349444.81,    8664.99,             9563.88,   126.32,  70468.48,           71671.50,     -6.24,    -31.25,          18.81,  +0.74,  -1.98
  4,     UK001Z,       0,  0.172349, 2459436.630310768727, 210.96906,  51.37515,              342.22677,  15.00644,       342.22918,       15.00578,    210.96906,     +51.37515,     210.96590,      +51.37525,  3840819.96,    83574.04,  5198178.65,      53.714584,       -4.486985,   99403.26,  349596.39,   11207.07,            12105.96,   -43.23,  63116.52,           69853.74,      2.90,     14.50,           8.72,  +0.53,  -2.19
  5,     UK001Z,       0,  0.212653, 2459436.630311235320, 210.93926,  50.92412,              342.10143,  14.57159,       342.10080,       14.57176,    210.93926,     +50.92412,     210.94116,      +50.92410,  3838832.17,    82504.50,  5196595.51,      53.720634,       -4.502464,   96937.28,  349781.37,   13964.16,            14863.06,     0.35,  68407.47,           69127.45,     -0.76,     -3.79,           2.28,  +0.18,  -2.54
  6,     UK001Z,       0,  0.252917, 2459436.630311700981, 210.89550,  50.53697,              342.00588,  14.19465,       341.99067,       14.19880,    210.89550,     +50.53697,     210.92065,      +50.53640,  3837122.62,    81584.66,  5195233.98,      53.725840,       -4.515813,   94816.64,  349958.30,   16335.33,            17234.22,  -339.30,  58890.54,           67772.47,    -18.32,    -91.78,          55.16,  +1.37,  -1.35
  0,     UK003F,       1,  0.000000, 2459436.630308771506, 234.40221,  47.27964,              326.68190,  17.70463,       326.68378,       17.70434,    234.40221,     +47.27964,     234.39971,      +47.28029,  3849534.43,    88262.93,  5205119.11,      53.688089,       -4.419331,  110216.71,  336048.12,       0.00,               18.87,  -526.71,      0.00,           70330.04,      3.78,      9.95,           6.53,  +4.24,  +1.61
  1,     UK003F,       0,  0.040560, 2459436.630309240893, 234.03003,  46.72420,              326.61867,  17.09694,       326.58046,       17.10283,    234.03003,     +46.72420,     234.08059,      +46.71098,  3846949.76,    86872.23,  5203060.60,      53.695942,       -4.439321,  107009.05,  336348.85,    3584.98,             3603.85,   327.52,  88387.12,           70330.04,    -77.02,   -203.03,         133.16,  +1.63,  -1.00
  2,     UK003F,       0,  0.080936, 2459436.630309708416, 233.86367,  46.32932,              326.51586,  16.69775,       326.51088,       16.69851,    233.86367,     +46.32932,     233.87054,      +46.32760,  3845210.33,    85936.32,  5201675.27,      53.701229,       -4.452843,  104850.58,  336574.64,    5997.59,             6016.46,    21.77,  59753.54,           70330.04,    -10.06,    -26.49,          17.37,  +0.55,  -2.09
  3,     UK003F,       0,  0.121352, 2459436.630310175940, 233.63966,  45.90244,              326.43481,  16.25020,       326.43427,       16.25028,    233.63966,     +45.90244,     233.64087,      +45.90225,  3843279.09,    84897.20,  5200137.17,      53.707102,       -4.467852,  102454.28,  336844.77,    8676.24,             8695.11,   -20.64,  66277.02,           70330.04,     -1.09,     -2.87,           1.88,  +0.24,  -2.40
  4,     UK003F,       0,  0.161768, 2459436.630310643930, 233.43024,  45.46788,              326.34334,  15.80018,       326.35735,       15.79803,    233.43024,     +45.46788,     233.41268,      +45.47266,  3841327.36,    83847.05,  5198582.75,      53.713040,       -4.483035,  100032.76,  337139.17,   11383.33,            11402.19,   -34.61,  66980.48,           68902.61,     28.53,     75.07,          49.13,  -0.27,  -2.91
  5,     UK003F,       0,  0.202200, 2459436.630311111920, 233.21053,  45.02131,              326.25496,  15.33531,       326.27844,       15.33170,    233.21053,     +45.02131,     233.18095,      +45.02928,  3839311.24,    82762.27,  5196977.06,      53.719176,       -4.498728,   97531.59,  337465.67,   14179.70,            14198.57,    39.64,  69162.47,           68531.58,     48.00,    126.26,          82.56,  -0.32,  -2.96
  6,     UK003F,       0,  0.242508, 2459436.630311578512, 233.02540,  44.71320,              326.21715,  15.00242,       326.22237,       15.00162,    233.02540,     +44.71320,     233.01967,      +44.71496,  3837882.24,    81993.38,  5195838.96,      53.723527,       -4.509910,   95758.89,  337712.78,   16161.75,            16180.62,  -692.10,  49172.47,           66331.61,     10.68,     28.11,          18.36,  +1.37,  -1.27

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.