Orbital Analysis for matched events on 20210813_012025.942_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 63.29° Bg 39.99° Vg 57.91km/s
mass 0.09705g, abs. mag -1.5
Path Details
------------
start 2.98° 53.17° 107.38km
end   2.86° 53.12° 91.76km

Orbit Details
-------------
Semimajor axis 11.03A.U., eccentricity 0.91, inclination 110.37°, Period 36.64Y, LA Sun 140.24°, 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: 2459439.555855812971
Time: 2021-08-13 01:20:25.964449 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002K and UK0032
 Convergence angle = 16.88348 deg
 R.A. =  47.08605  Dec = +59.22044 deg

Best intersection: Stations UK002K and UK0032 with Qconv = 16.88 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3759898.78 +/- 171.16 m
 Y =  -1021063.58 +/- 212.14 m
 Z =   5169585.64 +/- 86.13 m
 Vx =    20261.54 +/- 955.51 m/s
 Vy =    21781.66 +/- 1171.08 m/s
 Vz =    50912.71 +/- 1726.67 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.757569e+04, +1.951016e+04, +8.603099e+03, +9.270671e+04, +1.067741e+05, +7.557869e+04
+1.951016e+04, +2.257865e+04, +9.783576e+03, +1.032261e+05, +1.220706e+05, +8.655796e+04
+8.603099e+03, +9.783576e+03, +4.550182e+03, +4.506489e+04, +5.265209e+04, +3.750175e+04
+9.270671e+04, +1.032261e+05, +4.506489e+04, +5.870334e+05, +6.905950e+05, +4.780277e+05
+1.067741e+05, +1.220706e+05, +5.265209e+04, +6.905950e+05, +8.280990e+05, +5.723394e+05
+7.557869e+04, +8.655796e+04, +3.750175e+04, +4.780277e+05, +5.723394e+05, +3.983190e+05

Timing offsets (from input data):
    UK000Z: 0.000000 s
    UK002K: 0.000000 s
    UK0032: 0.000362 s

Reference point on the trajectory:
  Time: 2021-08-13 01:20:25.964449 UTC
  Lon     = ++2.993486 +/- 0.0037 deg
  Lat     = +53.178070 +/- 0.0004 deg
  Lat geo = +52.996367 +/- 0.0004 deg
  Ht      =  108814.61 +/- 134.23 m

  JD dynamic   = 2459439.556656810921 
  LST apparent = 344.8067878888 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  47.07069 +/- 0.2413 deg
  Dec       = +59.70212 +/- 0.8510 deg
  Azimuth   =  53.57436 +/- 1.4112 deg
  Elevation = +56.29264 +/- 0.3528 deg
  Vavg      =  55.43840 +/- 0.9322 km/s
  Vinit     =  58.96673 +/- 1.4852 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  47.32322 +/- 0.2413 deg
  Dec       = +59.49136 +/- 0.8510 deg
  Azimuth   =  53.86768 +/- 1.4112 deg
  Elevation = +56.10791 +/- 0.3528 deg
  Vavg      =  55.56581 +/- 0.9322 km/s
  Vinit     =  59.09414 +/- 1.4852 km/s
Radiant (geocentric, J2000):
  R.A.   =  47.23699 +/- 0.2126 deg
  Dec    = +59.52854 +/- 0.8538 deg
  Vg     =  57.91310 +/- 1.5120 km/s
  Vinf   =  58.96673 +/- 1.4852 km/s
  Zc     =  33.81553 +/- 0.3493 deg
  Zg     =  34.12953 +/- 0.3371 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  63.29379 +/- 0.3112 deg
  Bg     = +39.99244 +/- 0.8271 deg
  Vh     =  40.87396 +/- 0.9228 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  85.32523 +/- 2.8620 deg
  Bh     = +65.59031 +/- 1.7010 deg
  Vh_x   =  -1.37665 +/- 0.9721 km/s
  Vh_y   = -16.83532 +/- 1.4141 km/s
  Vh_z   = -37.22039 +/- 0.3255 km/s
Orbit:
  La Sun = 140.242133 +/- -0.0000 deg
  a      =  11.030582 +/- 307.4672 AU
  e      =   0.913570 +/- 0.0816
  i      = 110.373624 +/- 2.1254 deg
  peri   = 151.193499 +/- 1.5185 deg
  node   = 140.242089 +/- 0.0001 deg
  Pi     = 291.435588 +/- 1.5183 deg
  q      =   0.953375 +/- 0.0035 AU
  f      =  28.802848 +/- 1.5185 deg
  M      =   0.551266 +/- nan deg
  Q      =  21.107790 +/- 614.9340 AU
  n      =   0.026903 +/- 0.0298 deg/day
  T      =  36.635178 +/- 399998481.2183 years
  Last perihelion JD = 2459419.066065 (2021-07-23 13:35:07.990243) +/- 1.2427 days
  Tj     =   0.059555 +/- 0.4967
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +3.428875e-03, +1.694525e-04, +6.834372e-02, -1.175951e-07, +1.272251e-03, +1.743598e-03
q   , +1.694525e-04, +9.325954e-06, +3.537885e-03, -5.870534e-09, +6.712630e-05, +8.708896e-05
Tp  , +6.834372e-02, +3.537885e-03, +1.393404e+00, -2.351001e-06, +2.613373e-02, +3.489619e-02
node, -1.175951e-07, -5.870534e-09, -2.351001e-06, +4.039053e-12, -4.385647e-08, -5.987017e-08
peri, +1.272251e-03, +6.712630e-05, +2.613373e-02, -4.385647e-08, +4.918894e-04, +6.508922e-04
i   , +1.743598e-03, +8.708896e-05, +3.489619e-02, -5.987017e-08, +6.508922e-04, +8.876625e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.216811
 a2 = 22.932634

Mean time residuals from time vs. length:
  Station with reference time: UK002K
  Avg. res. = 1.931e-06 s
  Stddev    = 1.39e-03 s

Begin point on the trajectory:
  Lon =     2.982154 +/- 0.0035 deg
  Lat =    53.173045 +/- 0.0002 deg
  Ht  = 107379.24 +/- 154.12 m
End point on the trajectory:
  Lon =     2.857200 +/- 0.0027 deg
  Lat =    53.118120 +/- 0.0003 deg
  Ht  = 91759.99 +/- 73.25 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
    UK000Z,    True,    -1.740490,    53.069201,  230.00,   0.000000,   0.000000,   106761.98,    93402.96,          0.038884,       nan,       nan,              44.33, 0.0000,    True,    True, {"ff_name": "FF_UK000Z_20210813_012023_433_0451328.fits"}
    UK002K,   False,    -0.382860,    53.537770,   34.00,   0.147614,  23.889897,   106535.11,    91759.99,          0.006877,      6.95,     28.53,              44.73, 1.0000,    True,    True, {"ff_name": "FF_UK002K_20210813_012021_446_0456704.fits"}
    UK0032,   False,    -0.023645,    52.984073,    6.00,   0.080712,  26.123622,   107379.24,    92449.48,          0.013503,      3.37,     52.79,              34.71, 1.0000,    True,    True, {"ff_name": "FF_UK0032_20210813_012017_663_0462592.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,     UK000Z,       1,  0.030627, 2459439.555856167339,  62.59686,  15.88957,               86.13216,  17.10006,        86.06203,       17.06500,     62.59686,     +15.88957,      62.67421,      +15.90394,  3759050.90, -1021975.08,  5167455.09,      53.170882,       +2.977244,  106761.98,  335941.83,       0.00,             2467.58,   665.94,      0.00,           50712.33,    442.31,    -33.16,         272.34,  +4.29,  +1.66
  1,     UK000Z,       1,  0.070823, 2459439.555856632534,  62.67710,  15.64902,               86.22569,  16.86378,        86.18349,       16.84272,     62.67710,     +15.64902,      62.72383,      +15.65768,  3758340.91, -1022738.33,  5165671.07,      53.164859,       +2.963502,  105043.41,  334479.86,    2066.24,             4533.83,   361.95,  51404.21,           50712.33,    265.16,    -20.06,         163.98,  +2.31,  -0.31
  2,     UK000Z,       1,  0.110987, 2459439.555857097730,  62.72517,  15.42843,               86.33120,  16.66229,        86.29241,       16.64294,     62.72517,     +15.42843,      62.76830,      +15.43639,  3757708.02, -1023418.70,  5164080.76,      53.159486,       +2.951232,  103511.59,  333180.91,    3908.13,             6375.71,  -164.50,  45859.17,           50712.33,    242.96,    -18.40,         150.84,  +2.90,  +0.29
  3,     UK000Z,       1,  0.151199, 2459439.555857562926,  62.79294,  15.15540,               86.45484,  16.40780,        86.42758,       16.39420,     62.79294,     +15.15540,      62.82355,      +15.16100,  3756927.59, -1024257.69,  5162119.71,      53.152855,       +2.936135,  101622.89,  331588.82,    6179.40,             8646.99,  -264.40,  56482.47,           50712.33,    170.08,    -12.93,         106.11,  +2.00,  -0.60
  4,     UK000Z,       1,  0.191419, 2459439.555858028587,  62.85497,  14.86309,               86.59500,  16.14145,        86.57098,       16.12949,     62.85497,     +14.86309,      62.88217,      +14.86802,  3756105.54, -1025141.41,  5160054.08,      53.145864,       +2.920239,   99633.72,  329921.07,    8571.80,            11039.38,  -243.64,  59482.74,           52883.42,    149.23,    -11.35,          93.57,  +1.44,  -1.15
  5,     UK000Z,       1,  0.231639, 2459439.555858493783,  62.91669,  14.56677,               86.73746,  15.87198,        86.71586,       15.86122,     62.91669,     +14.56677,      62.94139,      +14.57120,  3755281.16, -1026027.64,  5157982.59,      53.138847,       +2.904293,   97639.17,  328257.69,   10970.99,            13438.57,  -216.10,  59651.58,           54470.90,    133.64,    -10.17,          84.22,  +1.47,  -1.11
  6,     UK000Z,       1,  0.271867, 2459439.555858959444,  62.98462,  14.26814,               86.87598,  15.59679,        86.86199,       15.58983,     62.98462,     +14.26814,      63.00112,      +14.27102,  3754455.83, -1026914.89,  5155908.73,      53.131815,       +2.888324,   95642.60,  326601.67,   13372.91,            15840.49,  -186.29,  59707.70,           55599.12,     86.24,     -6.58,          54.62,  +1.18,  -1.39
  7,     UK000Z,       1,  0.312119, 2459439.555859425571,  63.05236,  13.92772,               87.04092,  15.28868,        87.02722,       15.28187,     63.05236,     +13.92772,      63.06870,      +13.93053,  3753529.90, -1027910.29,  5153582.07,      53.123918,       +2.870424,   93402.96,  324756.26,   16067.64,            18535.22,   134.91,  66946.45,           57015.90,     84.01,     -6.41,          53.51,  +1.37,  -1.19
  0,     UK002K,       1,  0.000000, 2459439.555855812971,  49.90310,  14.36294,               98.73539,  24.25262,        98.74231,       24.25710,     49.90310,     +14.36294,      49.89512,      +14.36267,  3759890.46, -1021072.53,  5169564.73,      53.177999,       +2.993420,  108794.46,  254629.75,       0.00,               24.22,    28.54,      0.00,           58014.40,    -33.40,     -8.13,          27.85,  +4.56,  +2.53
  1,     UK002K,       0,  0.040340, 2459439.555856280029,  49.91185,  13.92523,               99.01829,  23.89914,        99.02011,       23.90031,     49.91185,     +13.92523,      49.90993,      +13.92516,  3758957.18, -1022075.83,  5167219.59,      53.170088,       +2.975412,  106535.11,  252719.49,    2716.12,             2740.33,   365.94,  67330.60,           58014.40,     -8.71,     -2.12,           7.32,  +2.12,  +0.11
  2,     UK002K,       0,  0.080584, 2459439.555856745690,  49.92643,  13.61611,               99.21003,  23.64425,        99.21584,       23.64799,     49.92643,     +13.61611,      49.92009,      +13.61588,  3758305.47, -1022776.44,  5165581.99,      53.164558,       +2.962784,  104957.60,  251391.39,    4612.77,             4636.99,  -110.46,  47128.97,           58014.40,    -27.71,     -6.75,          23.40,  +2.00,  -0.00
  3,     UK002K,       0,  0.120912, 2459439.555857212283,  49.92512,  13.19481,               99.48803,  23.30888,        99.48060,       23.30409,     49.92512,     +13.19481,      49.93418,      +13.19510,  3757430.07, -1023717.52,  5163382.31,      53.157125,       +2.945874,  102838.89,  249622.56,    7160.44,             7184.65,    59.19,  63173.49,           58014.40,     35.29,      8.61,          30.02,  +1.39,  -0.60
  4,     UK002K,       0,  0.161224, 2459439.555857678875,  49.95377,  12.80276,               99.72018,  22.97886,        99.72646,       22.98290,     49.95377,     +12.80276,      49.94722,      +12.80252,  3756624.25, -1024583.79,  5161357.47,      53.150276,       +2.930290,  100888.85,  248005.61,    9505.58,             9529.80,    27.27,  58174.92,           58200.16,    -29.64,     -7.22,          25.37,  +1.39,  -0.58
  5,     UK002K,       0,  0.201516, 2459439.555858145468,  49.96223,  12.42585,               99.95839,  22.67238,        99.96138,       22.67430,     49.96223,     +12.42585,      49.95964,      +12.42573,  3755860.52, -1025404.81,  5159438.40,      53.143779,       +2.915507,   99040.89,  246483.46,   11728.24,            11752.46,  -125.96,  55163.71,           57819.55,    -14.04,     -3.42,          12.10,  +1.13,  -0.83
  6,     UK002K,       0,  0.241832, 2459439.555858612061,  49.97296,  12.02323,              100.21022,  22.34362,       100.21113,       22.34420,     49.97296,     +12.02323,      49.97292,      +12.02319,  3755054.91, -1026270.87,  5157414.07,      53.136920,       +2.899919,   97091.82,  244890.10,   14072.80,            14097.02,  -158.70,  58154.60,           57719.53,     -4.27,     -1.04,           3.71,  +1.14,  -0.80
  7,     UK002K,       0,  0.282160, 2459439.555859078653,  49.99256,  11.60250,              100.46497,  21.99472,       100.47100,       21.99859,     49.99256,     +11.60250,      49.98680,      +11.60226,  3754223.54, -1027164.61,  5155325.02,      53.129835,       +2.883833,   95080.68,  243258.97,   16492.33,            16516.54,  -117.18,  59996.23,           57867.71,    -28.07,     -6.84,          24.50,  +0.89,  -1.04
  8,     UK002K,       0,  0.322460, 2459439.555859545246,  49.99571,  11.21009,              100.71422,  21.67777,       100.71200,       21.67635,     49.99571,     +11.21009,      49.99961,      +11.21018,  3753458.93, -1027986.59,  5153403.73,      53.123313,       +2.869021,   93231.28,  241769.75,   18717.55,            18741.77,  -268.32,  55216.43,           57760.11,     10.28,      2.51,           9.03,  +1.23,  -0.69
  9,     UK002K,       0,  0.362712, 2459439.555860010907,  50.02239,  10.89535,              100.89286,  21.40918,       100.90523,       21.41709,     50.02239,     +10.89535,      50.00969,      +10.89487,  3752850.59, -1028640.57,  5151875.11,      53.118120,       +2.857200,   91759.99,  240591.01,   20487.98,            20512.20,  -871.41,  43983.75,           56955.00,    -56.99,    -13.88,          50.28,  +4.35,  +2.44
  0,     UK0032,       0,  0.023240, 2459439.555856070016,  60.12761,  25.29623,               82.83389,  26.82128,        82.83930,       26.82407,     60.12761,     +25.29623,      60.12165,      +25.29514,  3759305.88, -1021700.97,  5168095.81,      53.173045,       +2.982154,  107379.24,  230708.26,       0.00,             1725.51,   359.48,      0.00,           57000.25,    -22.43,      1.44,          20.10,  +3.29,  +1.47
  1,     UK0032,       0,  0.063456, 2459439.555856535677,  60.16198,  25.00517,               83.02277,  26.58208,        83.00305,       26.57190,     60.16198,     +25.00517,      60.18428,      +25.00914,  3758614.56, -1022444.15,  5166358.68,      53.167181,       +2.968770,  105705.77,  229065.00,    2011.93,             3737.44,     0.00,  50028.10,           57000.25,     81.24,     -5.16,          73.30,  +2.05,  +0.25
  2,     UK0032,       0,  0.103720, 2459439.555857001338,  60.24550,  24.67691,               83.20052,  26.28517,        83.19122,       26.28037,     60.24550,     +24.67691,      60.25631,      +24.67879,  3757828.63, -1023289.05,  5164383.80,      53.160510,       +2.953573,  103803.48,  227205.52,    4299.22,             6024.73,   -86.95,  56807.26,           57000.25,     38.06,     -2.43,          34.62,  +1.44,  -0.34
  3,     UK0032,       0,  0.144012, 2459439.555857467931,  60.31890,  24.29488,               83.42400,  25.95328,        83.40667,       25.94435,     60.31890,     +24.29488,      60.33882,      +24.29836,  3756939.63, -1024244.75,  5162149.95,      53.152957,       +2.936400,  101652.03,  225113.12,    6886.44,             8611.95,   124.39,  64211.93,           57000.25,     70.42,     -4.48,          64.65,  +1.40,  -0.36
  4,     UK0032,       0,  0.184296, 2459439.555857934058,  60.43131,  23.95577,               83.58479,  25.62993,        83.60156,       25.63855,     60.43131,     +23.95577,      60.41338,      +23.95240,  3756145.04, -1025098.95,  5160153.33,      53.146200,       +2.921029,   99729.30,  223250.73,    9198.92,            10924.43,    61.46,  57404.43,           57796.25,    -67.69,      4.36,          62.67,  +1.17,  -0.57
  5,     UK0032,       0,  0.224548, 2459439.555858399719,  60.47058,  23.61250,               83.80335,  25.34672,        83.79063,       25.34017,     60.47058,     +23.61250,      60.48568,      +23.61506,  3755382.76, -1025918.42,  5158237.88,      53.139712,       +2.906271,   97884.97,  221471.73,   11417.38,            13142.89,   -93.62,  55114.14,           57640.52,     51.05,     -3.25,          47.64,  +1.22,  -0.51
  6,     UK0032,       0,  0.264832, 2459439.555858866312,  60.57446,  23.25961,               83.97796,  25.01710,        83.99016,       25.02337,     60.57446,     +23.25961,      60.56199,      +23.25716,  3754587.36, -1026773.50,  5156239.22,      53.132936,       +2.890876,   95960.75,  219624.49,   13732.22,            15457.72,  -154.20,  57462.92,           57565.86,    -48.62,      3.13,          45.76,  +1.03,  -0.68
  7,     UK0032,       0,  0.305120, 2459439.555859332439,  60.65170,  22.88987,               84.18374,  24.69016,        84.19509,       24.69599,     60.65170,     +22.88987,      60.64035,      +22.88759,  3753779.91, -1027641.53,  5154210.28,      53.126051,       +2.875246,   94007.63,  217758.69,   16082.12,            17807.63,  -179.95,  58327.62,           57598.27,    -44.93,      2.89,          42.64,  +1.01,  -0.68
  8,     UK0032,       0,  0.345348, 2459439.555859798100,  60.70147,  22.58828,               84.36074,  24.43103,        84.36030,       24.43080,     60.70147,     +22.58828,      60.70340,      +22.58837,  3753135.68, -1028334.08,  5152591.48,      53.120554,       +2.862738,   92449.48,  216274.83,   17956.99,            19682.50,  -677.19,  46606.21,           56881.42,      1.74,     -0.11,           1.67,  +2.14,  +0.46

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.