Orbital Analysis for matched events on 20210813_012521.530_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 64.68° Bg 39.00° Vg 57.46km/s
mass 0.04466g, abs. mag -1.0
Path Details
------------
start 1.40° 53.01° 110.42km
end   1.27° 52.95° 95.01km

Orbit Details
-------------
Semimajor axis 6.60A.U., eccentricity 0.86, inclination 110.95°, Period 16.96Y, LA Sun 140.25°, last Perihelion 2021-07-20

Full details below
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Detailed report below graphs

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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: 2459439.559276972432
Time: 2021-08-13 01:25:21.570531 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000Z and UK0032
 Convergence angle = 28.56638 deg
 R.A. =  49.01059  Dec = +57.58301 deg

Best intersection: Stations UK000Z and UK0032 with Qconv = 28.57 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3769774.56 +/- 205.65 m
 Y =  -1048295.46 +/- 184.41 m
 Z =   5161082.31 +/- 226.39 m
 Vx =    19416.91 +/- 846.72 m/s
 Vy =    22881.11 +/- 738.00 m/s
 Vz =    50244.89 +/- 1385.27 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.145543e+04, +9.136200e+03, +1.262687e+04, +4.123218e+04, +2.891146e+04, +3.611970e+04
+9.136200e+03, +8.253690e+03, +1.082601e+04, +3.035966e+04, +2.369981e+04, +2.859129e+04
+1.262687e+04, +1.082601e+04, +1.551207e+04, +3.678344e+04, +2.574082e+04, +3.272390e+04
+4.123218e+04, +3.035966e+04, +3.678344e+04, +2.958484e+05, +2.353553e+05, +2.481389e+05
+2.891146e+04, +2.369981e+04, +2.574082e+04, +2.353553e+05, +2.027462e+05, +2.033265e+05
+3.611970e+04, +2.859129e+04, +3.272390e+04, +2.481389e+05, +2.033265e+05, +2.213654e+05

Timing offsets (from input data):
    UK000Z: 0.001722 s
    UK0032: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 01:25:21.570531 UTC
  Lon     = ++1.411497 +/- 0.0034 deg
  Lat     = +53.014742 +/- 0.0003 deg
  Lat geo = +52.832832 +/- 0.0003 deg
  Ht      =  112064.44 +/- 269.92 m

  JD dynamic   = 2459439.560078177601 
  LST apparent = 344.4598632772 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  49.68207 +/- 0.3677 deg
  Dec       = +59.15174 +/- 0.4946 deg
  Azimuth   =  53.47286 +/- 0.9005 deg
  Elevation = +54.59431 +/- 0.1027 deg
  Vavg      =  58.53409 +/- 0.9579 km/s
  Vinit     =  58.52444 +/- 1.3037 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  49.90843 +/- 0.3677 deg
  Dec       = +58.93429 +/- 0.4946 deg
  Azimuth   =  53.75791 +/- 0.9005 deg
  Elevation = +54.41143 +/- 0.1027 deg
  Vavg      =  58.66747 +/- 0.9579 km/s
  Vinit     =  58.65782 +/- 1.3037 km/s
Radiant (geocentric, J2000):
  R.A.   =  49.86779 +/- 0.3939 deg
  Dec    = +58.96253 +/- 0.4928 deg
  Vg     =  57.46325 +/- 1.3262 km/s
  Vinf   =  58.52444 +/- 1.3037 km/s
  Zc     =  35.51423 +/- 0.1025 deg
  Zg     =  35.84997 +/- 0.1030 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  64.68220 +/- 0.4412 deg
  Bg     = +39.00145 +/- 0.4078 deg
  Vh     =  40.20817 +/- 0.9501 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  88.25647 +/- 2.3094 deg
  Bh     = +64.08297 +/- 1.0331 deg
  Vh_x   =  -0.53469 +/- 0.8885 km/s
  Vh_y   = -17.56562 +/- 1.0148 km/s
  Vh_z   = -36.16435 +/- 0.4984 km/s
Orbit:
  La Sun = 140.245418 +/- 0.0000 deg
  a      =   6.600228 +/- 28.7649 AU
  e      =   0.858525 +/- 0.0843
  i      = 110.950282 +/- 1.4764 deg
  peri   = 146.119725 +/- 2.1558 deg
  node   = 140.245329 +/- 0.0001 deg
  Pi     = 286.365054 +/- 2.1557 deg
  q      =   0.933765 +/- 0.0065 AU
  f      =  33.876607 +/- 2.1559 deg
  M      =   1.397620 +/- nan deg
  Q      =  12.266691 +/- 57.5321 AU
  n      =   0.058125 +/- 0.0199 deg/day
  T      =  16.956609 +/- 498887590.2033 years
  Last perihelion JD = 2459415.515163 (2021-07-20 00:21:50.069378) +/- 1.1384 days
  Tj     =   0.375546 +/- 0.5045
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.038695e-03, +1.907304e-04, +5.174591e-02, -5.043774e-08, +1.080064e-03, +7.218289e-04
q   , +1.907304e-04, +1.956367e-05, +5.075829e-03, -4.820775e-09, +1.077161e-04, +6.903113e-05
Tp  , +5.174591e-02, +5.075829e-03, +1.345816e+00, -1.297155e-06, +2.832911e-02, +1.857107e-02
node, -5.043774e-08, -4.820775e-09, -1.297155e-06, +1.319443e-12, -2.715187e-08, -1.890388e-08
peri, +1.080064e-03, +1.077161e-04, +2.832911e-02, -2.715187e-08, +5.981291e-04, +3.887529e-04
i   , +7.218289e-04, +6.903113e-05, +1.857107e-02, -1.890388e-08, +3.887529e-04, +2.708485e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = -9.188409
 a2 = 5.835791

Mean time residuals from time vs. length:
  Station with reference time: UK0032
  Avg. res. = 3.934e-06 s
  Stddev    = 1.98e-03 s

Begin point on the trajectory:
  Lon =     1.397724 +/- 0.0028 deg
  Lat =    53.008588 +/- 0.0001 deg
  Ht  = 110418.00 +/- 210.65 m
End point on the trajectory:
  Lon =     1.267236 +/- 0.0024 deg
  Lat =    52.950722 +/- 0.0001 deg
  Ht  = 95007.32 +/- 171.75 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,   False,    -1.740490,    53.069201,  230.00,   6.942795,   6.544672,   108417.82,    95064.21,          0.018265,      9.26,     72.43,              36.93, 1.0000,    True,    True, {"ff_name": "FF_UK000Z_20210813_012520_602_0458752.fits"}
    UK0032,   False,    -0.023645,    52.984073,    6.00,   4.062579,   8.350061,   110418.00,    95007.32,          0.015933,     21.60,     31.47,              20.36, 1.0000,    True,    True, {"ff_name": "FF_UK0032_20210813_012514_873_0470016.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,       0,  0.076865, 2459439.559277847409,  54.23737,  20.16899,               90.83595,  26.17878,        90.82526,       26.17178,     54.23737,     +20.16899,      54.25032,      +20.16976,  3768290.02, -1050044.86,  5157240.78,      53.001105,       +1.380837,  108417.82,  237359.59,       0.00,             4474.56,   172.93,      0.00,           55867.51,     48.83,      6.28,          42.78,  +3.59,  +1.71
  1,     UK000Z,       0,  0.117077, 2459439.559278313071,  54.25485,  19.84236,               91.05434,  25.91712,        91.04018,       25.90787,     54.25485,     +19.84236,      54.27204,      +19.84337,  3767580.60, -1050880.85,  5155405.02,      52.994580,       +1.366083,  106675.54,  235694.40,    2138.27,             6612.82,   -42.19,  53174.80,           55867.51,     64.22,      8.27,          56.67,  +1.80,  -0.06
  2,     UK000Z,       0,  0.157329, 2459439.559278778732,  54.29556,  19.47159,               91.28418,  25.60713,        91.28371,       25.60683,     54.29556,     +19.47159,      54.29676,      +19.47162,  3766784.81, -1051818.62,  5153345.76,      52.987254,       +1.349549,  104721.42,  233836.99,    4536.85,             9011.41,     0.68,  59589.31,           55867.51,      2.09,      0.27,           1.86,  +1.60,  -0.24
  3,     UK000Z,       0,  0.197545, 2459439.559279244393,  54.30611,  19.13187,               91.51516,  25.33876,        91.50481,       25.33201,     54.30611,     +19.13187,      54.31912,      +19.13261,  3766069.75, -1052661.26,  5151495.40,      52.980666,       +1.334672,  102965.77,  232175.52,    6692.12,            11166.68,  -197.67,  53592.31,           55867.51,     46.37,      5.96,          41.53,  +1.15,  -0.68
  4,     UK000Z,       0,  0.237841, 2459439.559279710520,  54.35662,  18.70159,               91.77620,  24.97599,        91.78465,       24.98149,     54.35662,     +18.70159,      54.34766,      +18.70098,  3765174.31, -1053716.46,  5149178.29,      52.972408,       +1.316079,  100767.59,  230109.20,    9391.06,            13865.61,   142.96,  66977.74,           57989.89,    -37.59,     -4.81,          33.97,  +1.28,  -0.53
  5,     UK000Z,       0,  0.278081, 2459439.559280176181,  54.39907,  18.34891,               91.98798,  24.67757,        92.01304,       24.69384,     54.39907,     +18.34891,      54.37080,      +18.34711,  3764451.64, -1054568.06,  5147308.25,      52.965737,       +1.301037,   98993.78,  228449.30,   11569.26,            16043.81,   -33.87,  54130.16,           58044.35,   -110.68,    -14.13,         100.74,  +2.37,  +0.58
  6,     UK000Z,       0,  0.318309, 2459439.559280641843,  54.42784,  18.00946,               92.20053,  24.39723,        92.23145,       24.41729,     54.42784,     +18.00946,      54.39289,      +18.00724,  3763767.19, -1055374.62,  5145537.11,      52.959414,       +1.286779,   97313.99,  226884.82,   13632.24,            18106.80,  -325.20,  51282.38,           57339.61,   -135.78,    -17.31,         124.44,  +3.24,  +1.46
  7,     UK000Z,       0,  0.358597, 2459439.559281108435,  54.43097,  17.54486,               92.51916,  24.03471,        92.52713,       24.03988,     54.43097,     +17.54486,      54.42312,      +17.54429,  3762850.34, -1056455.04,  5143164.59,      52.950937,       +1.267731,   95064.21,  224805.37,   16395.72,            20870.27,    80.44,  68592.98,           57984.80,    -34.72,     -4.45,          32.12,  +3.29,  +1.53
  0,     UK0032,       1,  0.000000, 2459439.559276972432,  40.12004,  38.10275,               87.38512,  48.59660,        87.39497,       48.60940,     40.12004,     +38.10275,      40.10226,      +38.10602,  3769780.46, -1048288.51,  5161097.58,      53.014796,       +1.411786,  112078.93,  148397.83,       0.00,               17.78,   214.65,      0.00,           58123.91,    -30.72,    -20.99,          51.72,  +4.21,  +3.35
  1,     UK0032,       0,  0.040108, 2459439.559277436696,  39.99908,  37.82111,               87.80278,  48.48728,        87.79500,       48.47726,     39.99908,     +37.82111,      40.01314,      +37.81854,  3769104.35, -1049085.25,  5159348.00,      53.008588,       +1.397724,  110418.00,  146501.87,    2037.88,             2020.10,  -130.33,  50809.86,           58123.91,     23.77,     16.29,          40.58,  +2.33,  +1.50
  2,     UK0032,       0,  0.080264, 2459439.559277901426,  39.87063,  37.45238,               88.32443,  48.32484,        88.30798,       48.30389,     39.87063,     +37.45238,      39.89996,      +37.44700,  3768257.21, -1050083.52,  5157155.89,      53.000803,       +1.380143,  108337.24,  144133.90,    4591.22,             4573.44,    72.90,  63585.48,           58123.91,     49.03,     33.64,          85.10,  +1.69,  +0.90
  3,     UK0032,       0,  0.120440, 2459439.559278366622,  39.79809,  37.09548,               88.78634,  48.13502,        88.78906,       48.13843,     39.79809,     +37.09548,      39.79387,      +37.09635,  3767482.18, -1050996.83,  5155150.35,      52.993674,       +1.364040,  106433.86,  141972.61,    6927.24,             6909.46,    57.64,  58144.62,           58123.91,     -7.90,     -5.41,          13.91,  +1.27,  +0.51
  4,     UK0032,       0,  0.160576, 2459439.559278830886,  39.67374,  36.76484,               89.25676,  47.99232,        89.24583,       47.97872,     39.67374,     +36.76484,      39.69319,      +36.76136,  3766763.01, -1051844.32,  5153289.34,      52.987053,       +1.349082,  104667.88,  139971.72,    9094.91,             9077.13,  -123.62,  54008.13,           57485.03,     31.10,     21.33,          55.58,  +1.13,  +0.40
  5,     UK0032,       0,  0.200772, 2459439.559279296082,  39.58591,  36.36206,               89.77658,  47.77856,        89.78320,       47.78668,     39.58591,     +36.36206,      39.57554,      +36.36413,  3765936.90, -1052817.81,  5151151.64,      52.979441,       +1.331920,  102639.63,  137680.88,   11584.87,            11567.09,    13.89,  61945.52,           57940.50,    -18.36,    -12.57,          33.33,  +0.90,  +0.21
  6,     UK0032,       0,  0.240944, 2459439.559279761277,  39.47449,  35.97661,               90.29258,  47.58885,        90.30040,       47.59834,     39.47449,     +35.97661,      39.46241,      +35.97902,  3765161.33, -1053731.75,  5149144.70,      52.972288,       +1.315793,  100735.72,  135536.26,   13922.52,            13904.74,     0.49,  58190.96,           58129.93,    -21.20,    -14.51,          39.09,  +0.99,  +0.33
  7,     UK0032,       0,  0.281092, 2459439.559280226007,  39.32405,  35.59941,               90.82808,  47.42659,        90.81278,       47.40821,     39.32405,     +35.59941,      39.35052,      +35.59472,  3764411.11, -1054615.82,  5147203.37,      52.965363,       +1.300185,   98894.30,  133467.84,   16183.75,            16165.97,   -87.91,  56322.41,           58058.25,     40.51,     27.82,          75.94,  +0.75,  +0.12
  8,     UK0032,       0,  0.321264, 2459439.559280690737,  39.20191,  35.19807,               91.36437,  47.22948,        91.34518,       47.20669,     39.20191,     +35.19807,      39.23458,      +35.19225,  3763649.84, -1055512.91,  5145233.44,      52.958330,       +1.284345,   97026.01,  131375.74,   18478.30,            18460.52,  -144.41,  57118.04,           57962.09,     49.60,     34.09,          94.50,  +0.93,  +0.34
  9,     UK0032,       0,  0.361484, 2459439.559281156398,  39.10180,  34.74300,               91.93717,  46.98085,        91.93507,       46.97840,     39.10180,     +34.74300,      39.10668,      +34.74237,  3762827.16, -1056482.37,  5143104.60,      52.950722,       +1.267236,   95007.32,  129123.42,   20957.94,            20940.16,   -18.62,  61651.94,           58114.73,      5.27,      3.62,          10.22,  +1.00,  +0.44

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.