Orbital Analysis for matched events on 20210813_212222.150_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 61.75° Bg 39.33° Vg 61.69km/s
mass 0.01297g, abs. mag 0.6
Path Details
------------
start -2.28° 51.48° 117.73km
end   -2.51° 51.21° 98.53km

Orbit Details
-------------
Semimajor axis -5.68A.U., eccentricity 1.17, inclination 114.09°, Period 1000000000.00Y, LA Sun 141.04°, 

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: 2459440.390534149949
Time: 2021-08-13 21:22:22.150556 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK001Z and UK002H
 Convergence angle = 22.49474 deg
 R.A. =  45.19949  Dec = +58.63838 deg

Best intersection: Stations UK001Z and UK002H with Qconv = 22.49 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =    762643.17 +/- 126.32 m
 Y =  -3981488.99 +/- 29.38 m
 Z =   5059006.14 +/- 317.31 m
 Vx =    22681.57 +/- 409.82 m/s
 Vy =    22961.72 +/- 658.78 m/s
 Vz =    53730.03 +/- 839.73 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+3.291188e+03, -7.311745e+02, +1.086107e+04, +1.160122e+02, +1.998074e+03, +8.807976e+03
-7.311745e+02, +1.624386e+02, -2.412909e+03, -2.577342e+01, -4.438945e+02, -1.956791e+03
+1.086107e+04, -2.412909e+03, +3.584205e+04, +3.828457e+02, +6.593736e+03, +2.906673e+04
+1.160122e+02, -2.577342e+01, +3.828457e+02, +4.089354e+00, +7.043079e+01, +3.104753e+02
+1.998074e+03, -4.438945e+02, +6.593736e+03, +7.043079e+01, +1.213027e+03, +5.347304e+03
+8.807976e+03, -1.956791e+03, +2.906673e+04, +3.104753e+02, +5.347304e+03, +2.357216e+04

Timing offsets (from input data):
    UK001Z: 0.000000 s
    UK002H: 0.000655 s

Reference point on the trajectory:
  Time: 2021-08-13 21:22:22.150556 UTC
  Lon     = +-2.276591 +/- 0.0017 deg
  Lat     = +51.478435 +/- 0.0014 deg
  Lat geo = +51.294179 +/- 0.0014 deg
  Ht      =  117717.65 +/- 277.72 m

  JD dynamic   = 2459440.391334890854 
  LST apparent = 280.8435035636 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  45.35167 +/- 0.5405 deg
  Dec       = +59.00702 +/- 0.2216 deg
  Azimuth   =  29.10770 +/- 0.1423 deg
  Elevation = +29.27407 +/- 0.3363 deg
  Vavg      =  60.78101 +/- 0.2613 km/s
  Vinit     =  62.67863 +/- 0.8332 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  45.05660 +/- 0.5405 deg
  Dec       = +58.81618 +/- 0.2216 deg
  Azimuth   =  29.37765 +/- 0.1423 deg
  Elevation = +29.20965 +/- 0.3363 deg
  Vavg      =  60.90701 +/- 0.2613 km/s
  Vinit     =  62.80463 +/- 0.8332 km/s
Radiant (geocentric, J2000):
  R.A.   =  45.53950 +/- 0.5508 deg
  Dec    = +58.48925 +/- 0.2378 deg
  Vg     =  61.68989 +/- 0.8468 km/s
  Vinf   =  62.67863 +/- 0.8332 km/s
  Zc     =  60.88696 +/- 0.3365 deg
  Zg     =  61.42237 +/- 0.3551 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  61.75190 +/- 0.2530 deg
  Bg     = +39.33288 +/- 0.3191 deg
  Vh     =  43.67595 +/- 0.8815 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  77.10043 +/- 0.9395 deg
  Bh     = +63.54048 +/- 0.0396 deg
  Vh_x   =  -4.34442 +/- 0.3854 km/s
  Vh_y   = -18.96936 +/- 0.3028 km/s
  Vh_z   = -39.10087 +/- 0.7979 km/s
Orbit:
  La Sun = 141.043681 +/- nan deg
  a      =  -5.678893 +/- 384.9368 AU
  e      =   1.172062 +/- 0.0839
  i      = 114.089686 +/- 0.1495 deg
  peri   = 159.102565 +/- 1.5162 deg
  node   = 141.041670 +/- 0.0000 deg
  Pi     = 300.144235 +/- 1.5162 deg
  q      =   0.977121 +/- 0.0039 AU
  f      =  20.893252 +/- 1.5162 deg
  M      =        nan +/- nan deg
  Q      = -12.334906 +/- 769.8754 AU
  n      =   0.072830 +/- 0.0420 deg/day
  T      = 1000000000.000000 +/- 339924352.7686 years
  Last perihelion JD = NaN 
  Tj     =  -1.437734 +/- 0.4596
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.061405e-04, +1.236032e-06, +2.016864e-03, -4.713620e-10, +2.839543e-05, +5.931076e-06
q   , +1.236032e-06, +7.411330e-09, +1.209325e-05, -2.826318e-12, +1.702609e-07, +3.556313e-08
Tp  , +2.016864e-03, +1.209325e-05, +1.973287e-02, -4.611775e-09, +2.778190e-04, +5.802926e-05
node, -4.713620e-10, -2.826318e-12, -4.611775e-09, +1.077819e-15, -6.492917e-11, -1.356204e-11
peri, +2.839543e-05, +1.702609e-07, +2.778190e-04, -6.492917e-11, +3.911414e-06, +8.169938e-07
i   , +5.931076e-06, +3.556313e-08, +5.802926e-05, -1.356204e-11, +8.169938e-07, +1.706490e-07

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 26.166509
 a2 = 5.792196

Mean time residuals from time vs. length:
  Station with reference time: UK001Z
  Avg. res. = 6.126e-06 s
  Stddev    = 2.48e-03 s

Begin point on the trajectory:
  Lon =    -2.276498 +/- 0.0016 deg
  Lat =    51.478539 +/- 0.0013 deg
  Ht  = 117725.19 +/- 273.55 m
End point on the trajectory:
  Lon =    -2.514492 +/- 0.0004 deg
  Lat =    51.212314 +/- 0.0011 deg
  Ht  = 98533.72 +/- 60.11 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,   6.381962,   9.392296,   117725.19,   105910.59,          0.011665,     13.58,     22.58,              26.53, 1.0000,    True,   False, {"ff_name": "FF_UK001Z_20210813_212212_385_0104704.fits"}
    UK002H,   False,    -2.412630,    53.386080,   20.00,  36.990073,   5.217580,   111552.66,    98533.72,          0.011327,     40.37,     30.68,             113.81, 1.0000,    True,    True, {"ff_name": "FF_UK002H_20210813_212221_281_0091648.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,  0.000000, 2459440.390534149949, 346.48881,  68.79006,               34.86784,  54.58102,        34.88245,       54.57916,    346.48881,     +68.79006,     346.49214,      +68.78147,   762648.75, -3981483.35,  5059019.35,      51.478539,       -2.276498,  117725.19,  143705.47,       0.00,               15.41,   421.61,      0.00,           60051.83,    -18.63,     11.24,          31.23,  +4.19,  +3.40
  1,     UK001Z,       0,  0.039684, 2459440.390534609091, 345.45563,  68.73464,               35.00859,  54.95053,        35.01689,       54.94948,    345.45563,     +68.73464,     345.45789,      +68.72982,   761890.09, -3982251.38,  5057222.18,      51.464435,       -2.289235,  116700.26,  141827.29,    2096.49,             2081.08,    -0.06,  52829.60,           60051.83,    -10.34,      6.24,          17.56,  +3.43,  +2.67
  2,     UK001Z,       0,  0.079296, 2459440.390535067767, 344.20661,  68.65625,               35.18777,  55.39954,        35.18526,       55.39986,    344.20661,     +68.65625,     344.20623,      +68.65769,   760992.42, -3983160.13,  5055095.71,      51.447740,       -2.304271,  115488.18,  139613.89,    4577.12,             4561.71,    -2.26,  62623.20,           60051.83,      3.05,     -1.84,           5.27,  +2.76,  +2.04
  3,     UK001Z,       0,  0.118892, 2459440.390535525978, 342.90276,  68.56257,               35.38307,  55.87151,        35.36681,       55.87359,    342.90276,     +68.56257,     342.89821,      +68.57174,   760077.33, -3984086.53,  5052927.95,      51.430712,       -2.319589,  114253.30,  137367.17,    7105.91,             7090.49,    44.71,  63864.71,           60051.83,     19.21,    -11.59,          33.69,  +1.87,  +1.18
  4,     UK001Z,       0,  0.158488, 2459440.390535984188, 341.60037,  68.47933,               35.54632,  56.34696,        35.55223,       56.34621,    341.60037,     +68.47933,     341.60302,      +68.47605,   759192.84, -3984981.94,  5050832.70,      51.414246,       -2.334396,  113060.42,  135205.10,    9550.12,             9534.71,     7.10,  61728.75,           60853.81,     -6.79,      4.09,          12.09,  +1.58,  +0.93
  5,     UK001Z,       0,  0.198104, 2459440.390536442865, 340.36606,  68.38969,               35.70753,  56.80081,        35.73312,       56.79756,    340.36606,     +68.38969,     340.37609,      +68.37570,   758373.56, -3985811.34,  5048891.93,      51.398986,       -2.348118,  111956.10,  133211.00,   11814.12,            11798.71,  -211.98,  57148.72,           60553.87,    -28.66,     17.25,          51.79,  +1.21,  +0.59
  6,     UK001Z,       0,  0.237632, 2459440.390536900144, 338.89106,  68.22791,               35.98439,  57.34918,        35.96317,       57.35189,    338.89106,     +68.22791,     338.88381,      +68.23926,   757398.27, -3986798.68,  5046581.56,      51.380812,       -2.364416,  110642.25,  130849.55,   14509.27,            14493.86,     5.61,  68183.29,           61262.23,     23.01,    -13.87,          42.35,  +0.97,  +0.39
  7,     UK001Z,       0,  0.277196, 2459440.390537358355, 337.49421,  68.11781,               36.15032,  57.87257,        36.18313,       57.86842,    337.49421,     +68.11781,     337.50886,      +68.10060,   756519.80, -3987688.00,  5044500.58,      51.364434,       -2.379108,  109459.56,  128733.55,   16936.84,            16921.43,   -46.64,  61358.03,           61565.59,    -34.54,     20.76,          64.57,  +0.88,  +0.33
  8,     UK001Z,       0,  0.316760, 2459440.390537816100, 336.16597,  67.95011,               36.41130,  58.37850,        36.40667,       58.37909,    336.16597,     +67.95011,     336.16529,      +67.95250,   755678.27, -3988539.92,  5042507.09,      51.348737,       -2.393183,  108327.22,  126717.02,   19262.34,            19246.93,  -200.96,  58778.11,           61521.59,      4.74,     -2.85,           9.00,  +0.88,  +0.37
  9,     UK001Z,       0,  0.356300, 2459440.390538273845, 334.72392,  67.80505,               36.60733,  58.93126,        36.65364,       58.92541,    334.72392,     +67.80505,     334.74641,      +67.78177,   754805.78, -3989423.19,  5040440.26,      51.332455,       -2.407766,  107153.89,  124637.98,   21673.40,            21657.98,  -268.21,  60977.72,           61469.57,    -45.88,     27.55,          88.57,  +0.64,  +0.16
 10,     UK001Z,       0,  0.395796, 2459440.390538731124, 333.20909,  67.58426,               36.92613,  59.52513,        36.93428,       59.52410,    333.20909,     +67.58426,     333.21462,      +67.58026,   753880.72, -3990359.68,  5038248.89,      51.315184,       -2.423211,  105910.59,  122447.39,   24229.73,            24214.32,  -187.43,  64723.83,           61588.72,     -7.81,      4.70,          15.35,  +0.70,  +0.26
  0,     UK002H,       0,  0.208679, 2459440.390535098035, 281.70586, -11.11169,              178.91461,  25.49659,       178.92005,       25.49934,    281.70586,     -11.11169,     281.70116,      -11.10900,   758074.15, -3986114.45,  5048182.64,      51.393408,       -2.352586,  111552.66,  249956.32,       0.00,            12626.12,   -47.36,      0.00,           61444.31,     14.86,    -19.58,          20.28,  +3.92,  +1.93
  1,     UK002H,       0,  0.249075, 2459440.390535565559, 281.41766, -11.56969,              179.23204,  25.04139,       179.21221,       25.03138,    281.41766,     -11.56969,     281.43660,      -11.57955,   757124.61, -3987075.72,  5045933.30,      51.375711,       -2.368460,  110273.75,  251135.22,    2623.97,            15250.09,    44.64,  64956.20,           61444.31,    -54.55,     71.80,          74.06,  +3.26,  +1.26
  2,     UK002H,       0,  0.289399, 2459440.390536032151, 281.21059, -11.94871,              179.45836,  24.66379,       179.44472,       24.65691,    281.21059,     -11.94871,     281.22398,      -11.95552,   756359.06, -3987850.72,  5044119.80,      51.361436,       -2.381286,  109243.21,  252101.59,    4739.50,            17365.62,  -367.29,  52463.19,           61444.31,    -37.73,     49.67,          51.03,  +2.31,  +0.30
  3,     UK002H,       0,  0.329831, 2459440.390536500141, 280.93990, -12.45187,              179.75124,  24.16175,       179.74931,       24.16078,    280.93990,     -12.45187,     280.94255,      -12.45284,   755336.73, -3988885.68,  5041698.03,      51.342365,       -2.398353,  107867.85,  253414.05,    7564.61,            20190.73,   -76.39,  69873.20,           61444.31,     -5.37,      7.07,           7.22,  +2.35,  +0.33
  4,     UK002H,       0,  0.370183, 2459440.390536967199, 280.70381, -12.86046,              180.00389,  23.75346,       179.99924,       23.75112,    280.70381,     -12.86046,     280.70919,      -12.86280,   754485.42, -3989747.50,  5039681.37,      51.326475,       -2.412587,  106723.24,  254525.79,    9917.14,            22543.27,  -253.07,  58300.28,           61360.69,    -13.05,     17.18,          17.48,  +1.69,  -0.34
  5,     UK002H,       0,  0.410555, 2459440.390537434723, 280.47148, -13.29544,              180.25009,  23.31817,       180.25866,       23.32248,    280.47148,     -13.29544,     280.46458,      -13.29111,   753587.47, -3990656.55,  5037554.22,      51.309707,       -2.427586,  105516.61,  255716.75,   12398.56,            25024.69,  -302.11,  61463.90,           61351.54,     24.23,    -31.92,          32.32,  +1.46,  -0.58
  6,     UK002H,       0,  0.450907, 2459440.390537901781, 280.22549, -13.70395,              180.50835,  22.90869,       180.50758,       22.90831,    280.22549,     -13.70395,     280.22757,      -13.70434,   752712.58, -3991542.24,  5035481.72,      51.293362,       -2.442200,  104341.67,  256894.94,   14816.23,            27442.36,  -413.65,  59914.51,           61194.40,     -2.19,      2.88,           2.91,  +1.35,  -0.70
  7,     UK002H,       0,  0.491243, 2459440.390538368374, 279.97908, -14.09866,              180.76472,  22.51236,       180.74872,       22.50434,    279.97908,     -14.09866,     279.99577,      -14.10680,   751852.19, -3992413.26,  5033443.55,      51.277280,       -2.456569,  103186.84,  258070.54,   17193.85,            29819.97,  -564.24,  58945.20,           60941.67,    -45.83,     60.31,          60.54,  +1.18,  -0.88
  8,     UK002H,       0,  0.531599, 2459440.390538835432, 279.75202, -14.51693,              180.99823,  22.09202,       180.99426,       22.09003,    279.75202,     -14.51693,     279.75749,      -14.51896,   750962.31, -3993314.13,  5031335.53,      51.260639,       -2.471419,  101993.12,  259303.84,   19652.95,            32279.08,  -634.59,  60935.29,           60823.27,    -11.45,     15.07,          15.06,  +1.29,  -0.78
  9,     UK002H,       0,  0.571947, 2459440.390539302491, 279.51604, -14.92262,              181.23892,  21.68361,       181.23476,       21.68153,    279.51604,     -14.92262,     279.52187,      -14.92476,   750077.25, -3994210.12,  5029238.93,      51.244080,       -2.486185,  100806.56,  260547.78,   22098.74,            34724.87,  -717.76,  60617.39,           60751.76,    -12.07,     15.88,          15.79,  +1.51,  -0.57
 10,     UK002H,       0,  0.612271, 2459440.390539769083, 279.28541, -15.30470,              181.47218,  21.29832,       181.46203,       21.29324,    279.28541,     -15.30470,     279.29716,      -15.30993,   749228.72, -3995069.13,  5027228.86,      51.228198,       -2.500344,   99669.62,  261756.37,   24443.58,            37069.71,  -900.37,  58149.97,           60594.61,    -29.67,     39.05,          38.65,  +1.83,  -0.26
 11,     UK002H,       0,  0.652591, 2459440.390540235676, 279.05488, -15.68218,              181.70334,  20.91709,       181.68593,       20.90839,    279.05488,     -15.68218,     279.07380,      -15.69118,   748380.51, -3995927.82,  5025219.53,      51.212314,       -2.514492,   98533.72,  262979.94,   26787.56,            39413.68, -1083.60,  58134.28,           60409.42,    -51.24,     67.39,          66.40,  +3.27,  +1.17

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.