Orbital Analysis for matched events on 20210813_002836.210_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 65.61° Bg 38.37° Vg 57.78km/s
mass 0.07887g, abs. mag -1.5
Path Details
------------
start 2.62° 53.00° 111.36km
end   2.48° 52.93° 97.17km

Orbit Details
-------------
Semimajor axis 7.17A.U., eccentricity 0.87, inclination 111.70°, Period 19.20Y, LA Sun 140.21°, last Perihelion 2021-07-18

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: 2459439.519863544963
Time: 2021-08-13 00:28:36.210285 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002F and UK002K
 Convergence angle = 54.71319 deg
 R.A. =  51.15707  Dec = +58.55735 deg
Intersection 2 - Stations: UK002F and UK0032
 Convergence angle = 44.94947 deg
 R.A. =  51.02144  Dec = +58.69514 deg
Intersection 3 - Stations: UK002K and UK0032
 Convergence angle = 9.76443 deg
 R.A. =  50.59271  Dec = +57.98472 deg

Best intersection: Stations UK002F and UK002K with Qconv = 54.71 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3437446.37 +/- 122.24 m
 Y =  -1870801.96 +/- 95.72 m
 Z =   5159650.14 +/- 84.10 m
 Vx =    19006.69 +/- 625.19 m/s
 Vy =    23749.67 +/- 483.42 m/s
 Vz =    50359.20 +/- 878.44 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+8.177392e+03, +5.902463e+03, +5.995447e+03, +3.724300e+04, +2.495562e+04, +2.373121e+04
+5.902463e+03, +5.126387e+03, +4.884385e+03, +2.407876e+04, +1.970502e+04, +1.677117e+04
+5.995447e+03, +4.884385e+03, +5.866626e+03, +2.763469e+04, +1.942777e+04, +1.805405e+04
+3.724300e+04, +2.407876e+04, +2.763469e+04, +2.289098e+05, +1.535133e+05, +1.602301e+05
+2.495562e+04, +1.970502e+04, +1.942777e+04, +1.535133e+05, +1.281264e+05, +1.297801e+05
+2.373121e+04, +1.677117e+04, +1.805405e+04, +1.602301e+05, +1.297801e+05, +1.516949e+05

Timing offsets (from input data):
    UK002F: 0.000138 s
    UK002K: 0.000727 s
    UK0032: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 00:28:36.210285 UTC
  Lon     = ++2.622603 +/- 0.0021 deg
  Lat     = +53.001892 +/- 0.0003 deg
  Lat geo = +52.819940 +/- 0.0003 deg
  Ht      =  111368.66 +/- 102.02 m

  JD dynamic   = 2459439.520664285868 
  LST apparent = 331.4431203893 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  51.32996 +/- 0.3892 deg
  Dec       = +58.86651 +/- 0.4130 deg
  Azimuth   =  48.99135 +/- 0.6675 deg
  Elevation = +47.58306 +/- 0.1014 deg
  Vavg      =  58.17598 +/- 0.5183 km/s
  Vinit     =  58.83324 +/- 0.7635 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  51.42349 +/- 0.3892 deg
  Dec       = +58.63286 +/- 0.4130 deg
  Azimuth   =  49.26026 +/- 0.6675 deg
  Elevation = +47.42830 +/- 0.1014 deg
  Vavg      =  58.32175 +/- 0.5183 km/s
  Vinit     =  58.97901 +/- 0.7635 km/s
Radiant (geocentric, J2000):
  R.A.   =  51.58133 +/- 0.4063 deg
  Dec    = +58.59850 +/- 0.4104 deg
  Vg     =  57.77760 +/- 0.7767 km/s
  Vinf   =  58.83324 +/- 0.7635 km/s
  Zc     =  42.53651 +/- 0.1009 deg
  Zg     =  42.94030 +/- 0.0981 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  65.60873 +/- 0.4116 deg
  Bg     = +38.37040 +/- 0.3306 deg
  Vh     =  40.34052 +/- 0.5084 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  89.59865 +/- 1.7093 deg
  Bh     = +62.75636 +/- 0.6571 deg
  Vh_x   =  -0.12936 +/- 0.6389 km/s
  Vh_y   = -18.46644 +/- 0.6099 km/s
  Vh_z   = -35.86547 +/- 0.2374 km/s
Orbit:
  La Sun = 140.207573 +/- -0.0000 deg
  a      =   7.169680 +/- 57.7258 AU
  e      =   0.871486 +/- 0.0442
  i      = 111.698771 +/- 1.0191 deg
  peri   = 143.643482 +/- 1.4851 deg
  node   = 140.207085 +/- 0.0001 deg
  Pi     = 283.850566 +/- 1.4850 deg
  q      =   0.921404 +/- 0.0052 AU
  f      =  36.352699 +/- 1.4851 deg
  M      =   1.305954 +/- nan deg
  Q      =  13.417955 +/- 115.4520 AU
  n      =   0.051340 +/- 0.0124 deg/day
  T      =  19.197747 +/- 399999775.6147 years
  Last perihelion JD = 2459414.083224 (2021-07-18 13:59:50.583327) +/- 0.9123 days
  Tj     =   0.300225 +/- 0.2725
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.379203e-03, +1.446665e-04, +3.565367e-02, -3.360481e-08, +7.610858e-04, +4.597236e-04
q   , +1.446665e-04, +2.069126e-05, +4.457324e-03, -4.123723e-09, +1.004854e-04, +5.645384e-05
Tp  , +3.565367e-02, +4.457324e-03, +1.015300e+00, -9.459972e-07, +2.236502e-02, +1.294804e-02
node, -3.360481e-08, -4.123723e-09, -9.459972e-07, +9.558606e-13, -2.077755e-08, -1.307444e-08
peri, +7.610858e-04, +1.004854e-04, +2.236502e-02, -2.077755e-08, +4.973661e-04, +2.844102e-04
i   , +4.597236e-04, +5.645384e-05, +1.294804e-02, -1.307444e-08, +2.844102e-04, +1.788417e-04

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: UK0032
  Avg. res. = 3.300e-06 s
  Stddev    = 1.82e-03 s

Begin point on the trajectory:
  Lon =     2.622560 +/- 0.0021 deg
  Lat =    53.001870 +/- 0.0001 deg
  Ht  = 111364.46 +/- 98.25 m
End point on the trajectory:
  Lon =     2.477919 +/- 0.0013 deg
  Lat =    52.926408 +/- 0.0003 deg
  Ht  = 97172.05 +/- 49.90 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
    UK002F,   False,    -1.306160,    51.883100,   80.00,   0.033087,   0.000000,   109283.75,    97172.05,          0.013540,     16.34,     70.99,              28.78, 0.2318,    True,    True, {"ff_name": "FF_UK002F_20210813_002826_664_0355584.fits"}
    UK002K,   False,    -0.382860,    53.537770,   34.00,   0.000000,   0.000000,   109117.79,    97190.80,          0.010487,     28.26,     31.83,              47.69, 0.5470,    True,    True, {"ff_name": "FF_UK002K_20210813_002836_338_0379136.fits"}
    UK0032,   False,    -0.023645,    52.984073,    6.00,   0.000000,  88.492599,   111364.46,    97419.12,          0.009717,     18.25,     29.15,              33.63, 0.3068,    True,    True, {"ff_name": "FF_UK0032_20210813_002832_573_0385024.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,     UK002F,       0,  0.051912, 2459439.519863605965,  66.25345,  31.02939,               63.58991,  18.97705,        63.57527,       18.97072,     66.25345,     +31.02939,      66.27057,      +31.03349,  3436533.91, -1871942.11,  5157232.54,      52.990846,       +2.601532,  109283.75,  314907.29,       0.00,             2824.41,  -236.16,      0.00,           60865.72,     81.58,    -18.72,          54.82,  +3.41,  +0.92
  1,     UK002F,       0,  0.092080, 2459439.519864070695,  66.32211,  30.80895,               63.69252,  18.77057,        63.67485,       18.76293,     66.32211,     +30.80895,      66.34290,      +30.81389,  3435716.44, -1872963.58,  5155066.61,      52.980941,       +2.582504,  107416.33,  312700.21,    2530.40,             5354.81,   -68.97,  62995.43,           60865.72,     97.82,    -22.45,          66.20,  +1.93,  -0.55
  2,     UK002F,       0,  0.132248, 2459439.519864535891,  66.40101,  30.59910,               63.78033,  18.56632,        63.77077,       18.56219,     66.40101,     +30.59910,      66.41249,      +30.60177,  3434937.53, -1873936.86,  5153002.85,      52.971495,       +2.564364,  105637.41,  310601.45,    4941.43,             7765.83,   -21.16,  60023.56,           60865.72,     52.62,    -12.09,          35.85,  +1.77,  -0.69
  3,     UK002F,       0,  0.172420, 2459439.519865000620,  66.48921,  30.38903,               63.86133,  18.35655,        63.86751,       18.35921,     66.48921,     +30.38903,      66.48252,      +30.38731,  3434160.68, -1874907.56,  5150944.55,      52.962067,       +2.546269,  103863.58,  308512.86,    7346.08,            10170.49,    20.05,  59859.04,           60865.72,    -33.76,      7.78,          23.16,  +1.52,  -0.93
  4,     UK002F,       0,  0.212596, 2459439.519865465816,  66.56737,  30.16668,               63.95713,  18.14273,        63.96816,       18.14748,     66.56737,     +30.16668,      66.55522,      +30.16360,  3433361.66, -1875905.98,  5148827.49,      52.952360,       +2.527661,  102039.52,  306369.83,    9819.39,            12643.80,   129.67,  61561.81,           60876.22,    -59.97,     13.83,          41.44,  +1.88,  -0.55
  5,     UK002F,       0,  0.252780, 2459439.519865931012,  66.65041,  29.93362,               64.05621,  17.91777,        64.07355,       17.92523,     66.65041,     +29.93362,      66.63112,      +29.92878,  3432535.07, -1876938.84,  5146637.39,      52.942311,       +2.508414,  100152.98,  304158.61,   12378.02,            15202.42,   324.14,  63672.70,           61278.85,    -93.64,     21.62,          65.17,  +1.63,  -0.79
  6,     UK002F,       0,  0.292940, 2459439.519866395742,  66.71641,  29.72449,               64.15061,  17.72045,        64.16699,       17.72749,     66.71641,     +29.72449,      66.69842,      +29.71993,  3431809.49, -1877845.48,  5144714.94,      52.933482,       +2.491497,   98497.34,  302221.00,   14623.96,            17448.37,   207.34,  55924.92,           60849.18,    -87.99,     20.31,          61.63,  +1.88,  -0.52
  7,     UK002F,       0,  0.333064, 2459439.519866860006,  66.74978,  29.55053,               64.24393,  17.56814,        64.24234,       17.56746,     66.74978,     +29.55053,      66.75279,      +29.55097,  3431228.59, -1878571.34,  5143175.83,      52.926408,       +2.477919,   97172.05,  300670.92,   16422.07,            19246.48,  -355.17,  44813.82,           59335.64,      8.47,     -1.95,           5.97,  +4.78,  +2.39
  0,     UK002K,       0,  0.050678, 2459439.519864052068,  30.22501,  12.36233,              105.83593,  26.52698,       105.83332,       26.52419,     30.22501,     +12.36233,      30.22877,      +12.36143,  3436461.27, -1872032.88,  5157040.07,      52.989966,       +2.599695,  109117.79,  236542.46,       0.00,             3049.27,    61.32,      0.00,           58129.73,     11.22,      9.95,          13.08,  +2.14,  +0.27
  1,     UK002K,       0,  0.090962, 2459439.519864518195,  30.09377,  11.92506,              106.23734,  26.24706,       106.22376,       26.23258,     30.09377,     +11.92506,      30.11284,      +11.92041,  3435663.26, -1873030.03,  5154925.71,      52.980297,       +2.581116,  107294.87,  234923.74,    2470.14,             5519.41,   161.42,  61318.26,           58129.73,     58.00,     51.51,          68.11,  +1.53,  -0.32
  2,     UK002K,       0,  0.131238, 2459439.519864984322,  30.01260,  11.52005,              106.57190,  25.96405,       106.57553,       25.96790,     30.01260,     +11.52005,      30.00811,      +11.52128,  3434950.37, -1873920.82,  5153036.86,      52.971651,       +2.564498,  105666.72,  233489.35,    4676.84,             7726.11,    -1.45,  54789.25,           58129.73,    -15.36,    -13.63,          18.14,  +1.29,  -0.55
  3,     UK002K,       0,  0.171514, 2459439.519865450449,  29.87878,  11.08649,              106.97013,  25.68710,       106.95985,       25.67621,     29.87878,     +11.08649,      29.89357,      +11.08298,  3434177.55, -1874886.48,  5150989.25,      52.962271,       +2.546496,  103902.09,  231949.01,    7069.01,            10118.27,    21.15,  59394.40,           58129.73,     43.29,     38.44,          51.48,  +1.19,  -0.64
  4,     UK002K,       0,  0.211830, 2459439.519865917042,  29.75442,  10.60552,              107.38870,  25.36525,       107.37906,       25.35507,     29.75442,     +10.60552,      29.76847,      +10.60224,  3433341.64, -1875931.00,  5148774.45,      52.952117,       +2.527036,  101993.83,  230300.18,    9656.49,            12705.76,   236.72,  64180.14,           59356.05,     40.27,     35.76,          48.24,  +1.17,  -0.64
  5,     UK002K,       0,  0.252086, 2459439.519866383169,  29.65867,  10.21882,              107.72008,  25.10342,       107.71389,       25.09692,     29.65867,     +10.21882,      29.66814,      +10.21672,  3432679.71, -1876758.11,  5147020.63,      52.944070,       +2.511589,  100483.05,  229004.94,   11705.43,            14754.70,   -82.74,  50897.73,           58498.81,     25.66,     22.78,          30.91,  +1.17,  -0.63
  6,     UK002K,       0,  0.292398, 2459439.519866849761,  29.54653,   9.74423,              108.12031,  24.77827,       108.12161,       24.77963,     29.54653,      +9.74423,      29.54593,       +9.74467,  3431879.45, -1877758.06,  5144900.31,      52.934333,       +2.492948,   98656.95,  227455.97,   14182.55,            17231.82,    22.69,  61448.59,           58508.87,     -5.35,     -4.75,           6.49,  +1.23,  -0.55
  7,     UK002K,       0,  0.332642, 2459439.519867315423,  29.44060,   9.36214,              108.45514,  24.52469,       108.45173,       24.52113,     29.44060,      +9.36214,      29.44658,       +9.36099,  3431236.81, -1878561.07,  5143197.60,      52.926508,       +2.477944,   97190.80,  226222.24,   16171.76,            19221.03,  -355.77,  49428.95,           57757.23,     13.94,     12.37,          16.99,  +1.51,  -0.26
  0,     UK0032,       0,  0.000000, 2459439.519863544963,  40.05994,  25.28741,               88.31050,  31.05967,        88.30484,       31.05347,     40.05994,     +25.28741,      40.06848,      +25.28600,  3437444.53, -1870804.26,  5159645.27,      53.001870,       +2.622560,  111364.46,  211001.96,       0.00,                5.69,    -0.70,      0.00,           57703.23,     24.57,     15.39,          28.34,  +3.02,  +1.40
  1,     UK0032,       0,  0.040196, 2459439.519864010159,  39.98119,  24.92811,               88.65107,  30.83861,        88.64188,       30.82857,     39.98119,     +24.92811,      39.99519,      +24.92584,  3436680.26, -1871759.25,  5157620.28,      52.992619,       +2.604762,  109618.10,  209046.95,    2365.73,             2371.42,     0.17,  58854.90,           57703.23,     39.49,     24.75,          45.98,  +2.11,  +0.51
  2,     UK0032,       0,  0.080416, 2459439.519864475820,  39.91271,  24.54241,               89.00257,  30.59098,        88.99955,       30.58769,     39.91271,     +24.54241,      39.91756,      +24.54166,  3435880.64, -1872758.41,  5155501.66,      52.982931,       +2.586146,  107791.39,  207011.28,    4840.86,             4846.55,   109.02,  61539.68,           57703.23,     12.84,      8.04,          15.09,  +1.66,  +0.08
  3,     UK0032,       0,  0.120600, 2459439.519864941016,  39.84413,  24.21640,               89.30700,  30.38760,        89.30223,       30.38243,     39.84413,     +24.21640,      39.85175,      +24.21523,  3435212.98, -1873592.68,  5153732.66,      52.974837,       +2.570573,  106266.44,  205317.45,    6907.53,             6913.22,  -188.46,  51430.34,           57703.23,     20.07,     12.58,          23.80,  +1.14,  -0.42
  4,     UK0032,       0,  0.160820, 2459439.519865406211,  39.78567,  23.83368,               89.64554,  30.13497,        89.65261,       30.14261,     39.78567,     +23.83368,      39.77580,      +23.83540,  3434450.11, -1874545.91,  5151711.41,      52.965580,       +2.552802,  104524.40,  203392.05,    9268.90,             9274.59,  -193.36,  58711.28,           57405.81,    -29.44,    -18.42,          35.22,  +0.96,  -0.58
  5,     UK0032,       0,  0.201068, 2459439.519865872338,  39.70361,  23.39279,               90.04547,  29.85201,        90.05618,       29.86353,     39.70361,     +23.39279,      39.68856,      +23.39538,  3433584.42, -1875627.63,  5149417.70,      52.955067,       +2.532655,  102548.01,  201219.83,   11948.58,            11954.27,   118.39,  66579.04,           58632.80,    -44.06,    -27.57,          53.27,  +1.10,  -0.42
  6,     UK0032,       0,  0.241276, 2459439.519866337534,  39.60633,  22.99931,               90.42007,  29.61326,        90.41806,       29.61110,     39.60633,     +22.99931,      39.61028,      +22.99883,  3432819.70, -1876583.18,  5147391.54,      52.945772,       +2.514837,  100802.54,  199310.25,   14315.68,            14321.37,   119.93,  58871.54,           59096.35,      8.19,      5.13,          10.00,  +1.13,  -0.37
  7,     UK0032,       0,  0.281516, 2459439.519866803195,  39.54103,  22.58380,               90.78411,  29.33787,        90.79288,       29.34722,     39.54103,     +22.58380,      39.52930,      +22.58591,  3432038.78, -1877558.98,  5145322.45,      52.936272,       +2.496643,   99020.49,  197370.78,   16732.95,            16738.64,   169.75,  60071.21,           59370.78,    -35.28,    -22.08,          43.50,  +1.16,  -0.32
  8,     UK0032,       0,  0.321720, 2459439.519867268391,  39.46449,  22.20620,               91.12733,  29.09733,        91.13441,       29.10486,     39.46449,     +22.20620,      39.45545,      +22.20790,  3431336.89, -1878436.01,  5143462.77,      52.927727,       +2.480271,   97419.12,  195635.80,   18905.55,            18911.24,   -22.98,  54039.57,           59143.49,    -28.20,    -17.65,          35.07,  +1.31,  -0.15
  9,     UK0032,       1,  0.361912, 2459439.519867733587,  39.40332,  21.86338,               91.43110,  28.87343,        91.44205,       28.88503,     39.40332,     +21.86338,      39.38885,      +21.86600,  3430712.39, -1879216.36,  5141808.12,      52.920119,       +2.465685,   95994.56,  194098.52,   20838.64,            20844.33,  -454.52,  48096.28,           58425.63,    -43.20,    -27.04,          54.16,  +5.34,  +3.90

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.