Orbital Analysis for matched events on 20210813_210345.562_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 64.73° Bg 38.38° Vg 59.47km/s
mass 0.01517g, abs. mag -0.7
Path Details
------------
start -4.25° 52.71° 112.69km
end   -4.49° 52.38° 91.61km

Orbit Details
-------------
Semimajor axis 43.05A.U., eccentricity 0.98, inclination 113.29°, Period 282.42Y, LA Sun 141.03°, last Perihelion 2021-07-23

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: 2459440.377610671800
Time: 2021-08-13 21:03:45.643153 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002H and UK002Z
 Convergence angle = 17.69012 deg
 R.A. =  49.78127  Dec = +58.81601 deg

Best intersection: Stations UK002H and UK002Z with Qconv = 17.69 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =    290378.47 +/- 286.04 m
 Y =  -3928127.39 +/- 349.39 m
 Z =   5144597.21 +/- 122.33 m
 Vx =    19946.30 +/- 1233.57 m/s
 Vy =    23948.49 +/- 1519.26 m/s
 Vz =    51849.61 +/- 1408.09 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.532013e+04, +1.956644e+04, -5.613110e+03, +6.290912e+04, +7.671678e+04, -1.441801e+04
+1.956644e+04, +2.519337e+04, -7.436963e+03, +8.331017e+04, +1.018117e+05, -1.870270e+04
-5.613110e+03, -7.436963e+03, +2.658203e+03, -2.938197e+04, -3.621345e+04, +5.945679e+03
+6.290912e+04, +8.331017e+04, -2.938197e+04, +3.464591e+05, +4.258956e+05, -6.816051e+04
+7.671678e+04, +1.018117e+05, -3.621345e+04, +4.258956e+05, +5.238132e+05, -8.346767e+04
-1.441801e+04, -1.870270e+04, +5.945679e+03, -6.816051e+04, -8.346767e+04, +1.448868e+04

Timing offsets (from input data):
    UK002H: 0.000000 s
    UK002Z: 0.000029 s

Reference point on the trajectory:
  Time: 2021-08-13 21:03:45.643153 UTC
  Lon     = +-4.227464 +/- 0.0045 deg
  Lat     = +52.743653 +/- 0.0017 deg
  Lat geo = +52.561335 +/- 0.0017 deg
  Ht      =  114619.19 +/- 294.83 m

  JD dynamic   = 2459440.378412351478 
  LST apparent = 274.2277788417 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  50.20965 +/- 0.0736 deg
  Dec       = +58.98972 +/- 1.7241 deg
  Azimuth   =  23.74679 +/- 0.9539 deg
  Elevation = +27.25110 +/- 1.5144 deg
  Vavg      =  60.34127 +/- 0.7015 km/s
  Vinit     =  60.49601 +/- 0.6634 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  49.83237 +/- 0.0736 deg
  Dec       = +58.82743 +/- 1.7241 deg
  Azimuth   =  24.02627 +/- 0.9539 deg
  Elevation = +27.20075 +/- 1.5144 deg
  Vavg      =  60.44469 +/- 0.7015 km/s
  Vinit     =  60.59943 +/- 0.6634 km/s
Radiant (geocentric, J2000):
  R.A.   =  50.32513 +/- 0.0539 deg
  Dec    = +58.38451 +/- 1.7307 deg
  Vg     =  59.47043 +/- 0.6754 km/s
  Vinf   =  60.49601 +/- 0.6634 km/s
  Zc     =  62.91581 +/- 1.5133 deg
  Zg     =  63.51513 +/- 1.5179 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  64.72801 +/- 0.7758 deg
  Bg     = +38.37746 +/- 1.6315 deg
  Vh     =  41.60247 +/- 0.2649 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  85.03485 +/- 4.3274 deg
  Bh     = +62.55981 +/- 1.8835 deg
  Vh_x   =  -1.65928 +/- 1.1798 km/s
  Vh_y   = -19.09941 +/- 1.2306 km/s
  Vh_z   = -36.92187 +/- 0.7853 km/s
Orbit:
  La Sun = 141.031270 +/- nan deg
  a      =  43.046107 +/- 241.6988 AU
  e      =   0.978046 +/- 0.0237
  i      = 113.289064 +/- 2.6240 deg
  peri   = 149.790586 +/- 0.1847 deg
  node   = 141.029225 +/- 0.0002 deg
  Pi     = 290.819811 +/- 0.1848 deg
  q      =   0.945056 +/- 0.0005 AU
  f      =  30.205234 +/- 0.1846 deg
  M      =   0.073224 +/- nan deg
  Q      =  85.147158 +/- 483.3975 AU
  n      =   0.003490 +/- 0.0047 deg/day
  T      = 282.423904 +/- 489897453.3896 years
  Last perihelion JD = 2459419.396284 (2021-07-23 21:30:38.972604) +/- 0.0440 days
  Tj     =  -0.353016 +/- 0.0826
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +4.725841e-05, -2.632935e-06, +1.454524e-04, +1.054201e-08, -3.834345e-06, -1.363156e-04
q   , -2.632935e-06, +2.448125e-07, +5.508752e-06, -8.614487e-10, +6.008474e-07, +1.110453e-05
Tp  , +1.454524e-04, +5.508752e-06, +2.336149e-03, -5.625995e-09, +4.191821e-05, +6.793699e-05
node, +1.054201e-08, -8.614487e-10, -5.625995e-09, +3.186708e-12, -1.937854e-09, -4.109347e-08
peri, -3.834345e-06, +6.008474e-07, +4.191821e-05, -1.937854e-09, +1.839217e-06, +2.492106e-05
i   , -1.363156e-04, +1.110453e-05, +6.793699e-05, -4.109347e-08, +2.492106e-05, +5.299242e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.248283
 a2 = 8.152232

Mean time residuals from time vs. length:
  Station with reference time: UK002H
  Avg. res. = 2.758e-06 s
  Stddev    = 1.66e-03 s

Begin point on the trajectory:
  Lon =    -4.249423 +/- 0.0033 deg
  Lat =    52.713340 +/- 0.0012 deg
  Ht  = 112688.73 +/- 212.56 m
End point on the trajectory:
  Lon =    -4.492866 +/- 0.0114 deg
  Lat =    52.378684 +/- 0.0058 deg
  Ht  = 91609.65 +/- 538.71 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
    UK002H,   False,    -2.412630,    53.386080,   20.00,   0.209822,   8.358738,   112688.73,    91609.65,          0.006803,      2.51,     22.51,             102.56, 1.0000,    True,    True, {"ff_name": "FF_UK002H_20210813_210344_430_0063744.fits"}
    UK002Z,   False,    -0.382830,    53.537790,   34.00,   0.000000,   0.000000,   111206.53,   106762.97,          0.015577,     33.02,     74.87,             109.51, 1.0000,    True,   False, {"ff_name": "FF_UK002Z_20210813_210345_229_0075520.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,     UK002H,       1,  0.000000, 2459440.377610671800, 230.98264,  15.31703,              240.30699,  38.19665,       240.28517,       38.20740,    230.98264,     +15.31703,     231.00363,      +15.31688,   290385.37, -3928119.10,  5144615.16,      52.743803,       -4.227016,  114628.78,  182739.25,       0.00,               20.95,   735.53,      0.00,           56198.34,    -64.16,     -7.16,          72.87,  +3.88,  +2.57
  1,     UK002H,       1,  0.040392, 2459440.377611139324, 230.96054,  14.86700,              240.02383,  37.80524,       239.98549,       37.82409,    230.96054,     +14.86700,     230.99761,      +14.86674,   289893.27, -3928709.93,  5143335.97,      52.733081,       -4.234956,  113945.51,  183156.20,    1492.51,             1471.56,  -257.42,  36950.51,           56198.34,   -113.33,    -12.68,         128.42,  +1.93,  +0.62
  2,     UK002H,       0,  0.081104, 2459440.377611610573, 230.98956,  14.04424,              239.44242,  37.12351,       239.44356,       37.12295,    230.98956,     +14.04424,     230.98880,      +14.04425,   288987.62, -3929797.30,  5140981.77,      52.713340,       -4.249423,  112688.73,  183946.48,    4239.29,             4218.35,    26.46,  67468.75,           56198.34,      3.40,      0.38,           3.84,  +1.11,  -0.21
  3,     UK002H,       0,  0.121740, 2459440.377612080891, 230.98372,  13.31723,              238.96961,  36.50279,       238.97317,       36.50105,    230.98372,     +13.31723,     230.98079,      +13.31726,   288180.52, -3930766.35,  5138883.73,      52.695739,       -4.262327,  111569.46,  184683.28,    6687.20,             6666.25,    16.05,  60239.83,           56198.34,     10.72,      1.19,          12.05,  +0.42,  -0.91
  4,     UK002H,       0,  0.162348, 2459440.377612550743, 230.96102,  12.61809,              238.53962,  35.89543,       238.52790,       35.90114,    230.96102,     +12.61809,     230.97305,      +12.61801,   287398.00, -3931705.89,  5136849.60,      52.678668,       -4.274838,  110484.96,  185426.03,    9060.54,             9039.60,   -67.23,  58445.24,           57427.46,    -35.63,     -3.97,          39.88,  -0.06,  -1.40
  5,     UK002H,       0,  0.203000, 2459440.377613021526, 230.96969,  11.87371,              238.05547,  35.26365,       238.06113,       35.26091,    230.96969,     +11.87371,     230.96504,      +11.87374,   286557.96, -3932714.47,  5134665.96,      52.660334,       -4.288250,  109321.51,  186253.27,   11608.32,            11587.37,    21.26,  62672.75,           58528.65,     17.37,      1.93,          19.36,  -0.12,  -1.47
  6,     UK002H,       0,  0.243624, 2459440.377613491379, 230.95470,  11.16268,              237.62380,  34.64672,       237.62213,       34.64753,    230.95470,     +11.16268,     230.95735,      +11.16267,   285748.25, -3933686.65,  5132561.15,      52.642654,       -4.301178,  108200.79,  187080.41,   14064.13,            14043.18,    19.48,  60452.22,           59127.79,     -5.19,     -0.58,           5.76,  -0.36,  -1.72
  7,     UK002H,       0,  0.284244, 2459440.377613961697, 230.96070,  10.45379,              237.17848,  34.04061,       237.19094,       34.03459,    230.96070,     +10.45379,     230.94973,      +10.45388,   284933.82, -3934664.49,  5130444.07,      52.624863,       -4.314174,  107074.26,  187941.13,   16534.25,            16513.30,    32.26,  60810.49,           59517.58,     38.97,      4.34,          43.03,  -0.69,  -2.06
  8,     UK002H,       0,  0.324836, 2459440.377614431549, 230.95043,   9.77967,              236.77711,  33.45481,       236.78670,       33.45019,    230.95043,      +9.77967,     230.94242,       +9.77974,   284152.13, -3935603.03,  5128412.10,      52.607780,       -4.326649,  105993.70,  188794.36,   18905.07,            18884.12,   -52.58,  58406.02,           59625.39,     30.25,      3.37,          33.25,  -0.68,  -2.06
  9,     UK002H,       0,  0.365436, 2459440.377614901401, 230.92797,   9.10003,              236.39026,  32.85689,       236.38453,       32.85965,    230.92797,      +9.10003,     230.93512,       +9.10000,   283356.61, -3936558.17,  5126344.16,      52.590388,       -4.339336,  104894.71,  189689.14,   21317.85,            21296.91,   -95.93,  59428.25,           59669.53,    -18.25,     -2.04,          19.97,  -0.81,  -2.20
 10,     UK002H,       0,  0.406052, 2459440.377615371253, 230.93434,   8.39944,              235.96710,  32.25385,       235.97556,       32.24979,    230.93434,      +8.39944,     230.92772,       +8.39950,   282528.73, -3937552.17,  5124192.12,      52.572281,       -4.352526,  103751.76,  190648.07,   23828.76,            23807.82,   -42.13,  61820.77,           59791.39,     27.20,      3.03,          29.61,  -0.84,  -2.24
 11,     UK002H,       0,  0.446656, 2459440.377615841571, 230.93248,   7.71474,              235.56708,  31.65918,       235.58114,       31.65245,    230.93248,      +7.71474,     230.92049,       +7.71484,   281711.31, -3938533.60,  5122067.28,      52.554395,       -4.365545,  102624.01,  191622.65,   26307.94,            26286.99,   -19.33,  61057.44,           59910.37,     45.64,      5.08,          49.44,  -0.92,  -2.33
 12,     UK002H,       0,  0.487252, 2459440.377616311423, 230.91650,   7.03731,              235.19058,  31.06269,       235.19582,       31.06018,    230.91650,      +7.03731,     230.91335,       +7.03735,   280894.08, -3939514.81,  5119942.92,      52.536505,       -4.378556,  101497.24,  192624.08,   28786.56,            28765.61,     3.40,  61055.78,           60020.02,     17.20,      1.92,          18.53,  -1.01,  -2.43
 13,     UK002H,       0,  0.527840, 2459440.377616781276, 230.90090,   6.37359,              234.82624,  30.47722,       234.82296,       30.47879,    230.90090,      +6.37359,     230.90636,       +6.37356,   280084.94, -3940486.29,  5117839.60,      52.518785,       -4.391433,  100382.35,  193641.93,   31240.63,            31219.68,     2.05,  60462.90,           60101.59,    -10.86,     -1.21,          11.64,  -0.86,  -2.29
 14,     UK002H,       0,  0.568420, 2459440.377617250662, 230.88648,   5.71676,              234.46900,  29.89733,       234.45833,       29.90242,    230.88648,      +5.71676,     230.89946,       +5.71669,   279275.66, -3941457.96,  5115735.90,      52.501054,       -4.404307,   99267.98,  194685.67,   33695.14,            33674.20,     1.64,  60485.81,           60164.22,    -35.62,     -3.99,          37.98,  -0.99,  -2.44
 15,     UK002H,       0,  0.608984, 2459440.377617720049, 230.89292,   5.08117,              234.10690,  29.34512,       234.10963,       29.34383,    230.89292,      +5.08117,     230.89275,       +5.08119,   278484.26, -3942408.15,  5113678.70,      52.483708,       -4.416894,   98178.95,  195730.99,   36095.40,            36074.45,   -52.07,  59172.04,           60184.27,      9.21,      1.03,           9.76,  -0.89,  -2.35
 16,     UK002H,       0,  0.649544, 2459440.377618189901, 230.88257,   4.44565,              233.76548,  28.78394,       233.76469,       28.78431,    230.88257,      +4.44565,     230.88607,       +4.44565,   277684.17, -3943368.78,  5111598.89,      52.466163,       -4.429613,   97078.64,  196811.94,   38522.04,            38501.09,   -79.15,  59828.32,           60191.06,     -2.69,     -0.30,           2.83,  -0.98,  -2.45
 17,     UK002H,       0,  0.690132, 2459440.377618659288, 230.88345,   3.78095,              233.40066,  28.20168,       233.40774,       28.19832,    230.88345,      +3.78095,     230.87924,       +3.78100,   276837.81, -3944384.96,  5109398.80,      52.447597,       -4.443050,   95915.49,  197981.00,   41089.01,            41068.06,    32.41,  63244.63,           60249.36,     24.33,      2.72,          25.51,  -0.95,  -2.43
 18,     UK002H,       0,  0.730652, 2459440.377619128209, 230.87421,   3.19294,              233.09117,  27.68101,       233.09545,       27.67898,    230.87421,      +3.19294,     230.87296,       +3.19297,   276080.50, -3945294.22,  5107430.21,      52.430977,       -4.455086,   94875.37,  199050.20,   43385.88,            43364.93,  -122.01,  56684.85,           60234.95,     14.84,      1.66,          15.48,  -0.87,  -2.36
 19,     UK002H,       0,  0.771192, 2459440.377619597595, 230.86480,   2.58672,              232.77507,  27.14357,       232.77649,       27.14289,    230.86480,      +2.58672,     230.86659,       +2.58673,   275291.05, -3946242.08,  5105378.06,      52.413644,       -4.467620,   93791.79,  200186.52,   45780.24,            45759.29,  -180.16,  59061.71,           60207.72,      4.97,      0.56,           5.15,  -0.80,  -2.31
 20,     UK002H,       0,  0.811736, 2459440.377620066982, 230.85621,   1.96991,              232.45560,  26.59646,       232.45502,       26.59674,    230.85621,      +1.96991,     230.86018,       +1.96990,   274478.40, -3947217.78,  5103265.62,      52.395795,       -4.480512,   92677.09,  201379.15,   48244.96,            48224.01,  -168.20,  60791.13,           60195.12,     -2.04,     -0.23,           2.11,  -0.77,  -2.29
 21,     UK002H,       0,  0.852256, 2459440.377620535903, 230.85456,   1.38570,              232.14945,  26.08069,       232.15348,       26.07879,    230.85456,      +1.38570,     230.85403,       +1.38573,   273699.72, -3948152.71,  5101241.46,      52.378684,       -4.492866,   91609.65,  202543.89,   50606.67,            50585.72,  -257.78,  58285.05,           60163.06,     14.36,      1.61,          14.72,  -0.76,  -2.29
  0,     UK002Z,       1,  0.096072, 2459440.377611784730, 214.62568,   6.47521,              251.91715,  20.77338,       251.91282,       20.77720,    214.62568,      +6.47521,     214.63162,       +6.47605,   288675.25, -3930172.36,  5140169.76,      52.706529,       -4.254415,  112255.45,  299383.78,       0.00,             5165.77,    68.40,      0.00,           60309.58,    -26.60,    -11.75,          20.04,  +4.80,  +2.42
  1,     UK002Z,       0,  0.136224, 2459440.377612249460, 214.72083,   6.08302,              251.59599,  20.50426,       251.61933,       20.48372,    214.72083,      +6.08302,     214.69158,       +6.07851,   287918.70, -3931080.70,  5138203.15,      52.690028,       -4.266518,  111206.53,  300310.68,    2294.56,             7460.33,   -66.07,  57146.86,           60309.58,    143.89,     63.43,         108.00,  +3.39,  +1.00
  2,     UK002Z,       0,  0.176452, 2459440.377612714656, 214.76429,   5.61978,              251.27822,  20.14693,       251.28145,       20.14410,    214.76429,      +5.61978,     214.76091,       +5.61915,   287038.55, -3932137.46,  5135915.22,      52.670824,       -4.280564,  109987.03,  301405.89,    4964.02,            10129.78,   169.75,  66358.12,           60309.58,     19.95,      8.80,          14.92,  +1.82,  -0.58
  3,     UK002Z,       0,  0.216636, 2459440.377613179851, 214.80324,   5.23652,              251.01376,  19.85261,       251.00284,       19.86219,    214.80324,      +5.23652,     214.81809,       +5.23864,   286304.62, -3933018.65,  5134007.40,      52.654803,       -4.292300,  108970.77,  302335.82,    7189.99,            12355.75,   -35.25,  55394.45,           60309.58,    -67.78,    -29.95,          50.56,  +1.54,  -0.86
  4,     UK002Z,       0,  0.256816, 2459440.377613645047, 214.87593,   4.81941,              250.70053,  19.54886,       250.69738,       19.55162,    214.87593,      +4.81941,     214.88102,       +4.82002,   285491.88, -3933994.46,  5131894.73,      52.637054,       -4.305271,  107846.10,  303380.35,    9654.96,            14820.73,    -1.00,  61348.37,           60227.57,    -19.60,     -8.66,          14.57,  +0.99,  -1.42
  5,     UK002Z,       0,  0.297000, 2459440.377614110243, 214.93091,   4.41797,              250.41320,  19.24769,       250.40615,       19.25386,    214.93091,      +4.41797,     214.94115,       +4.41934,   284708.68, -3934934.81,  5129858.83,      52.619944,       -4.317772,  106762.97,  304402.84,   12030.37,            17196.14,   -56.57,  59113.27,           60044.98,    -44.10,    -19.48,          32.67,  +0.63,  -1.79

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.