Orbital Analysis for matched events on 20210813_013815.111_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 61.97° Bg 39.31° Vg 58.01km/s
mass 0.10927g, abs. mag -1.4
Path Details
------------
start -1.17° 53.97° 116.29km
end   -1.38° 53.89° 90.61km

Orbit Details
-------------
Semimajor axis 7.98A.U., eccentricity 0.88, inclination 111.59°, Period 22.52Y, LA Sun 140.25°, last Perihelion 2021-07-24

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: 2459439.568230462261
Time: 2021-08-13 01:38:15.111939 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000Y and UK002Z
 Convergence angle = 57.07555 deg
 R.A. =  45.96210  Dec = +58.66117 deg

Best intersection: Stations UK000Y and UK002Z with Qconv = 57.08 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3699613.74 +/- 40.23 m
 Y =   -983674.41 +/- 35.80 m
 Z =   5229161.15 +/- 94.90 m
 Vx =    21415.02 +/- 136.45 m/s
 Vy =    21958.27 +/- 175.48 m/s
 Vz =    50471.12 +/- 183.08 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.784786e+03, +6.988950e+02, +2.920020e+03, +2.030291e+03, -1.565345e+03, +1.115543e+03
+6.988950e+02, +1.322501e+03, +1.179439e+03, -4.268626e+01, +1.941894e+03, -1.769246e+03
+2.920020e+03, +1.179439e+03, +9.266416e+03, +1.613236e+03, -4.267348e+03, +9.808430e+03
+2.030291e+03, -4.268626e+01, +1.613236e+03, +5.447149e+03, -2.357968e+03, -3.056088e+03
-1.565345e+03, +1.941894e+03, -4.267348e+03, -2.357968e+03, +9.811925e+03, -1.245222e+04
+1.115543e+03, -1.769246e+03, +9.808430e+03, -3.056088e+03, -1.245222e+04, +3.340472e+04

Timing offsets (from input data):
    UK000Y: 0.000000 s
    UK002Z: 0.000755 s

Reference point on the trajectory:
  Time: 2021-08-13 01:38:15.111939 UTC
  Lon     = +-1.169914 +/- 0.0006 deg
  Lat     = +53.972925 +/- 0.0004 deg
  Lat geo = +53.792967 +/- 0.0004 deg
  Ht      =  116415.77 +/- 92.38 m

  JD dynamic   = 2459439.569031203166 
  LST apparent = 345.1103659916 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  45.71760 +/- 0.1840 deg
  Dec       = +58.71241 +/- 0.1379 deg
  Azimuth   =  56.76472 +/- 0.2292 deg
  Elevation = +57.25020 +/- 0.1124 deg
  Vavg      =  58.34922 +/- 0.1580 km/s
  Vinit     =  59.06016 +/- 0.1285 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  45.97151 +/- 0.1840 deg
  Dec       = +58.51095 +/- 0.1379 deg
  Azimuth   =  57.03710 +/- 0.2292 deg
  Elevation = +57.05980 +/- 0.1124 deg
  Vavg      =  58.47605 +/- 0.1580 km/s
  Vinit     =  59.18699 +/- 0.1285 km/s
Radiant (geocentric, J2000):
  R.A.   =  45.85122 +/- 0.1852 deg
  Dec    = +58.53198 +/- 0.1396 deg
  Vg     =  58.00942 +/- 0.1308 km/s
  Vinf   =  59.06016 +/- 0.1285 km/s
  Zc     =  32.84874 +/- 0.1121 deg
  Zg     =  33.15192 +/- 0.1141 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  61.96818 +/- 0.1116 deg
  Bg     = +39.31428 +/- 0.1459 deg
  Vh     =  40.49535 +/- 0.1803 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  81.42947 +/- 0.2561 deg
  Bh     = +65.17608 +/- 0.1287 deg
  Vh_x   =  -2.53364 +/- 0.0693 km/s
  Vh_y   = -16.81136 +/- 0.0674 km/s
  Vh_z   = -36.75367 +/- 0.1931 km/s
Orbit:
  La Sun = 140.254015 +/- -0.0000 deg
  a      =   7.975162 +/- 1.7405 AU
  e      =   0.879363 +/- 0.0159
  i      = 111.592140 +/- 0.1077 deg
  peri   = 153.143268 +/- 0.4126 deg
  node   = 140.253884 +/- 0.0000 deg
  Pi     = 293.397152 +/- 0.4126 deg
  q      =   0.962096 +/- 0.0012 AU
  f      =  26.853033 +/- 0.4126 deg
  M      =   0.849883 +/- 0.1603 deg
  Q      =  14.988229 +/- 3.4803 AU
  n      =   0.043762 +/- 0.0078 deg/day
  T      =  22.522155 +/- 8.5712 years
  Last perihelion JD = 2459420.148357 (2021-07-24 15:33:38.039547) +/- 0.3427 days
  Tj     =   0.218740 +/- 0.0864
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.563094e-04, +1.167881e-05, +4.812339e-03, +1.974290e-09, +8.989438e-05, -2.853179e-05
q   , +1.167881e-05, +1.583838e-06, +4.039881e-04, +1.084247e-10, +8.986853e-06, -1.566741e-06
Tp  , +4.812339e-03, +4.039881e-04, +1.228135e-01, +4.040023e-08, +2.547073e-03, -5.838106e-04
node, +1.974290e-09, +1.084247e-10, +4.040023e-08, +2.093431e-14, +7.798269e-10, -3.025864e-10
peri, +8.989438e-05, +8.986853e-06, +2.547073e-03, +7.798269e-10, +5.427678e-05, -1.126884e-05
i   , -2.853179e-05, -1.566741e-06, -5.838106e-04, -3.025864e-10, -1.126884e-05, +4.373628e-06

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.000000
 a2 = 57.383403

Mean time residuals from time vs. length:
  Station with reference time: UK000Y
  Avg. res. = 4.908e-06 s
  Stddev    = 2.22e-03 s

Begin point on the trajectory:
  Lon =    -1.170947 +/- 0.0004 deg
  Lat =    53.972525 +/- 0.0004 deg
  Ht  = 116287.42 +/- 73.19 m
End point on the trajectory:
  Lon =    -1.380479 +/- 0.0003 deg
  Lat =    53.892094 +/- 0.0005 deg
  Ht  = 90609.97 +/- 77.90 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
    UK000Y,   False,    -1.740490,    53.069201,  230.00,   0.000000,   0.000000,   116287.42,    90609.97,          0.019398,     35.24,     35.32,              23.55, 1.0000,    True,    True, {"ff_name": "FF_UK000Y_20210813_013814_686_0478208.fits"}
    UK002Z,   False,    -0.382830,    53.537790,   34.00,   0.000000,   0.000000,   113160.82,    91171.65,          0.020833,      9.82,     43.02,              49.47, 1.0000,    True,    True, {"ff_name": "FF_UK002Z_20210813_013809_145_0483328.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,     UK000Y,       0,  0.000000, 2459439.568230462261,  93.09831,  75.35227,               20.36943,  46.47077,        20.36386,       46.47572,     93.09831,     +75.35227,      93.09066,      +75.35822,  3699558.41,  -983731.15,  5229030.73,      53.972525,       -1.170947,  116287.42,  158788.86,       0.00,              152.61,   257.55,      0.00,           57119.65,    -12.26,    -12.27,          22.53,  +3.12,  +2.12
  1,     UK000Y,       0,  0.040208, 2459439.568230927456,  94.20831,  75.49345,               19.97094,  46.32096,        20.00775,       46.28837,     94.20831,     +75.49345,      94.25669,      +75.45392,  3698800.97,  -984507.80,  5227245.60,      53.967058,       -1.185264,  114530.61,  156875.57,    2088.92,             2241.52,   -28.22,  51952.79,           57119.65,     80.18,     79.88,         148.81,  +1.84,  +0.86
  2,     UK000Y,       0,  0.080496, 2459439.568231394049,  95.67528,  75.58208,               19.55903,  46.07442,        19.57759,       46.05812,     95.67528,     +75.58208,      95.69800,      +75.56206,  3697901.16,  -985430.44,  5225124.92,      53.960557,       -1.202246,  112443.83,  154609.20,    4570.49,             4723.10,    73.93,  61595.83,           57119.65,     39.70,     39.61,          74.82,  +1.60,  +0.65
  3,     UK000Y,       0,  0.120764, 2459439.568231860176,  97.06040,  75.66619,               19.16670,  45.84869,        19.17620,       45.84040,     97.06040,     +75.66619,      97.07142,      +75.65590,  3697079.05,  -986273.41,  5223187.35,      53.954612,       -1.217781,  110537.44,  152544.30,    6837.79,             6990.40,   -37.00,  56305.28,           57119.65,     20.00,     19.96,          38.20,  +0.95,  +0.03
  4,     UK000Y,       0,  0.161040, 2459439.568232326303,  98.50143,  75.75119,               18.75856,  45.61934,        18.76478,       45.61395,     98.50143,     +75.75119,      98.50834,      +75.74444,  3696252.27,  -987121.15,  5221238.81,      53.948627,       -1.233408,  108620.48,  150473.73,    9117.94,             9270.54,  -135.56,  56612.98,           57086.01,     12.86,     12.84,          24.92,  +0.56,  -0.33
  5,     UK000Y,       0,  0.201348, 2459439.568232792895, 100.15499,  75.83926,               18.29726,  45.35894,        18.30203,       45.35483,    100.15499,     +75.83926,     100.16004,      +75.83406,  3695339.85,  -988056.72,  5219088.40,      53.942016,       -1.250642,  106505.20,  148196.24,   11634.29,            11786.90,     0.19,  62428.16,           57840.46,      9.70,      9.69,          19.08,  +0.42,  -0.43
  6,     UK000Y,       0,  0.241652, 2459439.568233259022, 101.73555,  75.88339,               17.89576,  45.09241,        17.87348,       45.11144,    101.73555,     +75.88339,     101.71960,      +75.90773,  3694512.92,  -988904.64,  5217139.47,      53.936018,       -1.266282,  104588.32,  146138.82,   13914.88,            14067.49,   -99.57,  56584.75,           57975.10,    -44.52,    -44.53,          88.88,  +0.25,  -0.57
  7,     UK000Y,       0,  0.281940, 2459439.568233725615, 103.30901,  75.94896,               17.46829,  44.84863,        17.44772,       44.86609,    103.30901,     +75.94896,     103.29694,      +75.97148,  3693707.29,  -989730.70,  5215240.76,      53.930170,       -1.281528,  102721.04,  144140.95,   16136.71,            16289.32,  -257.16,  55148.71,           57795.56,    -40.48,    -40.47,          81.90,  +0.11,  -0.68
  8,     UK000Y,       0,  0.322300, 2459439.568234192673, 105.28749,  76.02413,               16.93284,  44.54814,        16.92216,       44.55714,    105.28749,     +76.02413,     105.28354,      +76.03584,  3692731.14,  -990731.61,  5212940.16,      53.923077,       -1.299971,  100458.84,  141729.86,   18828.82,            18981.42,    51.28,  66702.31,           58306.86,    -20.63,    -20.60,          42.43,  -0.07,  -0.83
  9,     UK000Y,       0,  0.362624, 2459439.568234659266, 107.05314,  76.05456,               16.48617,  44.26434,        16.46337,       44.28342,    107.05314,     +76.05456,     107.04648,      +76.07959,  3691898.67,  -991585.20,  5210978.20,      53.917022,       -1.315729,   98529.85,  139681.58,   21124.66,            21277.27,   -34.42,  56934.97,           58492.11,    -43.30,    -43.27,          90.39,  -0.27,  -1.00
 10,     UK000Y,       0,  0.403000, 2459439.568235126790, 109.14323,  76.11007,               15.93045,  43.95358,        15.92655,       43.95682,    109.14323,     +76.11007,     109.14413,      +76.11436,  3690943.48,  -992564.62,  5208726.99,      53.910067,       -1.333792,   96316.76,  137341.51,   23758.99,            23911.59,   215.29,  65244.72,           58900.79,     -7.28,     -7.26,          15.44,  -0.26,  -0.95
 11,     UK000Y,       0,  0.443312, 2459439.568235593382, 110.92972,  76.14644,               15.45993,  43.68992,        15.47450,       43.67787,    110.92972,     +76.14644,     110.93253,      +76.13043,  3690157.58,  -993370.46,  5206874.77,      53.904339,       -1.348687,   94496.11,  135424.05,   25926.40,            26079.01,     1.87,  53766.06,           58938.84,     26.81,     26.69,          57.62,  -0.55,  -1.21
 12,     UK000Y,       0,  0.483724, 2459439.568236060906, 113.11752,  76.10866,               14.94921,  43.31667,        14.92817,       43.33392,    113.11752,     +76.10866,     113.12183,      +76.13171,  3689225.08,  -994326.62,  5204677.04,      53.897536,       -1.366336,   92336.12,  133159.45,   28498.14,            28650.75,   186.88,  63638.05,           59117.22,    -37.93,    -37.86,          83.02,  -0.50,  -1.12
 13,     UK000Y,       0,  0.524040, 2459439.568236527499, 114.92759,  76.13287,               14.46857,  43.05920,        14.48137,       43.04875,    114.92759,     +76.13287,     114.92667,      +76.11887,  3688479.80,  -995090.80,  5202920.56,      53.892094,       -1.380479,   90609.97,  131357.38,   30553.53,            30706.14,  -138.80,  50982.01,           58996.75,     22.78,     22.67,          50.47,  +1.61,  +1.02
  0,     UK002Z,       1,  0.026610, 2459439.568230761215, 284.30557,  63.58199,              312.76942,  57.78525,       312.80117,       57.76932,    284.30557,     +63.58199,     284.26310,      +63.59546,  3699155.94,  -984143.83,  5228082.20,      53.969621,       -1.178573,  115353.92,  135851.84,       0.00,             1262.55,  -204.08,      0.00,           61195.12,     53.73,    -12.25,          83.68,  +3.19,  +2.52
  1,     UK002Z,       0,  0.067314, 2459439.568231232464, 283.15096,  62.90153,              311.73867,  57.13269,       311.72052,       57.14166,    283.15096,     +62.90153,     283.17535,      +62.89399,  3698210.34,  -985113.42,  5225853.59,      53.962792,       -1.196410,  113160.82,  134189.37,    2607.87,             3870.42,    -0.19,  64069.12,           61195.12,    -30.42,      6.91,          47.95,  +2.13,  +1.49
  2,     UK002Z,       0,  0.107998, 2459439.568231703248, 282.16209,  62.18410,              310.67018,  56.51564,       310.68309,       56.50935,    282.16209,     +62.18410,     282.14555,      +62.18935,  3697293.69,  -986053.32,  5223693.23,      53.956164,       -1.213712,  111035.16,  132607.19,    5135.87,             6398.43,   125.01,  62137.57,           61195.12,     21.45,     -4.88,          34.22,  +1.11,  +0.50
  3,     UK002Z,       0,  0.148650, 2459439.568232174031, 281.23129,  61.51788,              309.73225,  55.91180,       309.74014,       55.90800,    281.23129,     +61.51788,     281.22162,      +61.52103,  3696452.64,  -986915.71,  5221711.02,      53.950078,       -1.229607,  109085.03,  131182.11,    7455.41,             8717.96,    43.63,  57058.34,           61195.12,     13.02,     -2.96,          20.99,  +0.47,  -0.12
  4,     UK002Z,       0,  0.189346, 2459439.568232644815, 280.29409,  60.79864,              308.75710,  55.26528,       308.76801,       55.26008,    280.29409,     +60.79864,     280.28077,      +60.80292,  3695576.45,  -987814.13,  5219646.01,      53.943731,       -1.246163,  107053.67,  129724.95,    9871.84,            11134.40,    56.55,  59377.66,           60449.44,     17.89,     -4.07,          29.17,  +0.14,  -0.43
  5,     UK002Z,       0,  0.230030, 2459439.568233115599, 279.40753,  60.09090,              307.83949,  54.62159,       307.84641,       54.61833,    279.40753,     +60.09090,     279.39962,      +60.09357,  3694737.06,  -988674.80,  5217667.74,      53.937645,       -1.262036,  105107.88,  128356.53,   12186.76,            13449.32,   -31.33,  56900.06,           59729.30,     11.28,     -2.57,          18.60,  -0.00,  -0.54
  6,     UK002Z,       0,  0.270754, 2459439.568233586848, 278.49980,  59.34531,              306.91803,  53.93169,       306.90835,       53.93621,    278.49980,     +59.34531,     278.51323,      +59.34163,  3693873.01,  -989560.78,  5215631.34,      53.931374,       -1.278376,  103105.14,  126976.61,   14569.72,            15832.28,   -53.54,  58514.81,           59341.83,    -15.71,      3.57,          26.17,  -0.30,  -0.82
  7,     UK002Z,       0,  0.311478, 2459439.568234058563, 277.64184,  58.59472,              306.02471,  53.24048,       306.00432,       53.24989,    277.64184,     +58.59472,     277.66883,      +58.58710,  3693030.73,  -990424.42,  5213646.25,      53.925255,       -1.294313,  101153.10,  125660.69,   16892.63,            18155.18,  -135.80,  57040.23,           58988.43,    -32.95,      7.48,          55.46,  -0.39,  -0.89
  8,     UK002Z,       0,  0.352310, 2459439.568234531209, 276.74162,  57.70393,              304.98628,  52.44940,       304.99275,       52.44644,    276.74162,     +57.70393,     276.73502,      +57.70631,  3692075.62,  -991403.76,  5211395.24,      53.918309,       -1.312369,   98939.86,  124203.68,   19526.71,            20789.27,    86.74,  64510.28,           59193.06,     10.41,     -2.37,          17.73,  -0.42,  -0.89
  9,     UK002Z,       0,  0.393094, 2459439.568235002924, 275.93813,  56.86395,              304.04682,  51.70056,       304.07829,       51.68634,    275.93813,     +56.86395,     275.90082,      +56.87534,  3691200.96,  -992300.61,  5209333.82,      53.911942,       -1.328923,   96913.29,  122904.43,   21938.93,            23201.48,    90.25,  59146.18,           59294.59,     50.49,    -11.51,          86.91,  -0.38,  -0.83
 10,     UK002Z,       0,  0.433862, 2459439.568235475104, 275.11819,  56.07253,              303.23461,  50.94304,       303.22550,       50.94713,    275.11819,     +56.07253,     275.13120,      +56.06928,  3690374.99,  -993147.54,  5207387.16,      53.905924,       -1.344570,   94999.74,  121709.17,   24216.87,            25479.42,   -39.58,  55875.65,           59194.25,    -14.60,      3.32,          25.37,  -0.69,  -1.12
 11,     UK002Z,       0,  0.474690, 2459439.568235947285, 274.35982,  55.17064,              302.29191,  50.14436,       302.32242,       50.13079,    274.35982,     +55.17064,     274.32461,      +55.18139,  3689488.23,  -994056.79,  5205297.25,      53.899457,       -1.361362,   92945.64,  120460.46,   26662.44,            27924.99,    -5.32,  59899.34,           59163.60,     48.79,    -11.12,          85.68,  -0.70,  -1.10
 12,     UK002Z,       0,  0.515418, 2459439.568236419000, 273.72973,  54.36951,              301.47899,  49.43831,       301.55207,       49.40604,    273.72973,     +54.36951,     273.64343,      +54.39496,  3688722.32,  -994842.13,  5203492.14,      53.893866,       -1.375892,   91171.65,  119412.73,   28774.73,            30037.28,  -298.43,  51863.37,           58904.35,    116.72,    -26.70,         206.83,  -0.06,  -0.45

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.