Orbital Analysis for matched events on 20210810_020306.945_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 60.94° Bg 38.92° Vg 56.81km/s
mass 0.01082g, abs. mag 0.4
Path Details
------------
start 1.95° 52.89° 108.21km
end   1.87° 52.86° 96.24km

Orbit Details
-------------
Semimajor axis 4.66A.U., eccentricity 0.80, inclination 110.83°, Period 10.07Y, LA Sun 137.39°, last Perihelion 2021-07-16

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: 2459436.585497054271
Time: 2021-08-10 02:03:06.945489 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002K and UK0032
 Convergence angle = 17.06380 deg
 R.A. =  45.29675  Dec = +54.12109 deg

Best intersection: Stations UK002K and UK0032 with Qconv = 17.06 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3878366.92 +/- 232.81 m
 Y =   -579073.95 +/- 231.27 m
 Z =   5149784.88 +/- 157.39 m
 Vx =    21822.89 +/- 1149.83 m/s
 Vy =    21517.93 +/- 1268.65 m/s
 Vz =    49107.95 +/- 1812.75 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+4.792764e+04, +4.758502e+04, +3.019740e+04, +1.897007e+05, +1.901706e+05, +7.358854e+04
+4.758502e+04, +4.858464e+04, +2.964827e+04, +2.001887e+05, +2.105228e+05, +8.198252e+04
+3.019740e+04, +2.964827e+04, +2.249902e+04, +1.172742e+05, +1.161465e+05, +3.917177e+04
+1.897007e+05, +2.001887e+05, +1.172742e+05, +1.237992e+06, +1.362253e+06, +5.828184e+05
+1.901706e+05, +2.105228e+05, +1.161465e+05, +1.362253e+06, +1.588501e+06, +6.931309e+05
+7.358854e+04, +8.198252e+04, +3.917177e+04, +5.828184e+05, +6.931309e+05, +3.301984e+05

Timing offsets (from input data):
    UK002K: -0.001187 s
    UK0032: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-10 02:03:06.945489 UTC
  Lon     = ++1.951570 +/- 0.0038 deg
  Lat     = +52.894385 +/- 0.0007 deg
  Lat geo = +52.712152 +/- 0.0007 deg
  Ht      =  108194.77 +/- 240.31 m

  JD dynamic   = 2459436.586297795177 
  LST apparent = 351.5079749217 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  44.59685 +/- 0.4111 deg
  Dec       = +58.03248 +/- 1.1042 deg
  Azimuth   =  58.61846 +/- 2.0738 deg
  Elevation = +60.27375 +/- 0.4293 deg
  Vavg      =  56.99043 +/- 1.4887 km/s
  Vinit     =  57.88653 +/- 1.4204 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  44.91553 +/- 0.4111 deg
  Dec       = +57.84050 +/- 1.1042 deg
  Azimuth   =  58.91318 +/- 2.0738 deg
  Elevation = +60.06403 +/- 0.4293 deg
  Vavg      =  57.11206 +/- 1.4887 km/s
  Vinit     =  58.00816 +/- 1.4204 km/s
Radiant (geocentric, J2000):
  R.A.   =  44.70907 +/- 0.3988 deg
  Dec    = +57.88157 +/- 1.1104 deg
  Vg     =  56.81278 +/- 1.4460 km/s
  Vinf   =  57.88653 +/- 1.4204 km/s
  Zc     =  29.82152 +/- 0.4244 deg
  Zg     =  30.10717 +/- 0.4161 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  60.94239 +/- 0.4794 deg
  Bg     = +38.92473 +/- 1.0667 deg
  Vh     =  39.49716 +/- 0.7722 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  83.95657 +/- 2.9854 deg
  Bh     = +64.65870 +/- 1.9728 deg
  Vh_x   =  -1.77981 +/- 1.1656 km/s
  Vh_y   = -16.81121 +/- 1.4229 km/s
  Vh_z   = -35.69652 +/- 0.1541 km/s
Orbit:
  La Sun = 137.391164 +/- -0.0000 deg
  a      =   4.664223 +/- 11.8948 AU
  e      =   0.798581 +/- 0.0655
  i      = 110.825279 +/- 2.4523 deg
  peri   = 146.611970 +/- 1.6886 deg
  node   = 137.391269 +/- 0.0002 deg
  Pi     = 284.003239 +/- 1.6884 deg
  q      =   0.939463 +/- 0.0048 AU
  f      =  33.384368 +/- 1.6887 deg
  M      =   2.369322 +/- 0.9931 deg
  Q      =   8.388984 +/- 23.7871 AU
  n      =   0.097844 +/- 0.0386 deg/day
  T      =  10.073250 +/- 87.9232 years
  Last perihelion JD = 2459412.371044 (2021-07-16 20:54:18.208251) +/- 1.4987 days
  Tj     =   0.710632 +/- 0.4179
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +3.944634e-03, +2.223458e-04, +8.621069e-02, -1.771645e-07, +1.612775e-03, +2.503756e-03
q   , +2.223458e-04, +2.083199e-05, +6.116277e-03, -1.139698e-08, +1.250908e-04, +1.616075e-04
Tp  , +8.621069e-02, +6.116277e-03, +2.079304e+00, -4.092008e-06, +4.049694e-02, +5.796185e-02
node, -1.771645e-07, -1.139698e-08, -4.092008e-06, +8.610334e-12, -7.833906e-08, -1.218717e-07
peri, +1.612775e-03, +1.250908e-04, +4.049694e-02, -7.833906e-08, +8.012851e-04, +1.110097e-03
i   , +2.503756e-03, +1.616075e-04, +5.796185e-02, -1.218717e-07, +1.110097e-03, +1.725633e-03

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 14.246942
 a2 = 8.848533

Mean time residuals from time vs. length:
  Station with reference time: UK0032
  Avg. res. = 4.453e-06 s
  Stddev    = 2.11e-03 s

Begin point on the trajectory:
  Lon =     1.951660 +/- 0.0042 deg
  Lat =    52.894418 +/- 0.0006 deg
  Ht  = 108207.41 +/- 270.11 m
End point on the trajectory:
  Lon =     1.865318 +/- 0.0036 deg
  Lat =    52.862889 +/- 0.0004 deg
  Ht  = 96243.44 +/- 202.45 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
    UK002K,   False,    -0.382860,    53.537770,   34.00,  21.997403,   8.902278,   106829.11,    96849.13,          0.010073,     14.86,     31.55,              43.47, 1.0000,    True,    True, {"ff_name": "FF_UK002K_20210810_020304_266_0509696.fits"}
    UK0032,   False,    -0.023645,    52.984073,    6.00,   6.980957,   9.284596,   108207.41,    96243.44,          0.023251,     11.84,     67.34,              28.40, 1.0000,    True,    True, {"ff_name": "FF_UK0032_20210810_020301_519_0515840.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,     UK002K,       0,  0.029887, 2459436.585497417022,  42.39980,  11.95753,              113.93893,  30.97654,       113.94196,       30.97838,     42.39980,     +11.95753,      42.39669,      +11.95762,  3877774.05,  -579658.54,  5148450.73,      52.890796,       +1.941710,  106829.11,  202951.52,       0.00,             1572.64,   132.08,      0.00,           57436.17,    -10.19,     -4.79,          11.44,  +3.87,  +2.33
  1,     UK002K,       0,  0.070195, 2459436.585497883614,  42.38658,  11.53405,              114.22471,  30.63121,       114.22875,       30.63366,     42.38658,     +11.53405,      42.38254,      +11.53417,  3876993.63,  -580428.05,  5146694.57,      52.886068,       +1.928732,  105031.61,  201513.00,    2070.09,             3642.74,  -131.11,  51356.89,           57436.17,    -13.53,     -6.37,          15.31,  +2.57,  +1.05
  2,     UK002K,       0,  0.110567, 2459436.585498350672,  42.37683,  11.02727,              114.55832,  30.21387,       114.56882,       30.22023,     42.37683,     +11.02727,      42.36601,      +11.02758,  3876074.49,  -581334.35,  5144626.24,      52.880494,       +1.913472,  102914.77,  199834.67,    4508.16,             6080.81,   -30.04,  60390.15,           57436.17,    -34.97,    -16.45,          39.89,  +2.10,  +0.60
  3,     UK002K,       0,  0.150923, 2459436.585498817731,  42.33128,  10.52023,              114.92323,  29.81481,       114.90689,       29.80493,     42.33128,     +10.52023,      42.34948,      +10.51974,  3875168.26,  -582227.91,  5142586.95,      52.874993,       +1.898417,  100827.87,  198195.33,    6912.00,             8484.64,    37.73,  59565.72,           57436.17,     54.06,     25.47,          62.20,  +1.95,  +0.46
  4,     UK002K,       0,  0.191219, 2459436.585499284323,  42.32228,  10.11424,              115.18738,  29.47984,       115.17548,       29.47266,     42.32228,     +10.11424,      42.33588,      +10.11388,  3874454.43,  -582931.77,  5140980.61,      52.870657,       +1.886519,   99184.16,  196913.30,    8805.49,            10378.13,  -401.38,  46989.54,           55660.94,     39.17,     18.45,          45.36,  +3.12,  +1.65
  5,     UK002K,       0,  0.231651, 2459436.585499752313,  42.31693,   9.52795,              115.55859,  28.99113,       115.55929,       28.99155,     42.31693,      +9.52795,      42.31715,       +9.52797,  3873440.26,  -583931.77,  5138698.44,      52.864489,       +1.869680,   96849.13,  195112.85,   11495.62,            13068.27,   -51.71,  66534.73,           56710.47,     -2.29,     -1.08,           2.68,  +5.53,  +4.08
  0,     UK0032,       0,  0.000000, 2459436.585497054271,  51.79715,  27.73606,               93.55840,  38.28671,        93.50804,       38.25871,     51.79715,     +27.73606,      51.85143,      +27.74234,  3878372.41,  -579068.54,  5149797.23,      52.894418,       +1.951660,  108207.41,  172458.33,       0.00,               14.56,   304.03,      0.00,           56177.72,    143.61,     25.28,         174.41,  +3.49,  +2.31
  1,     UK0032,       0,  0.040264, 2459436.585497520398,  51.89101,  27.39710,               93.77268,  37.98109,        93.76369,       37.97611,     51.89101,     +27.39710,      51.90085,      +27.39823,  3877605.66,  -579824.58,  5148071.80,      52.889776,       +1.938910,  106441.25,  170704.02,    2033.86,             2019.31,   -21.96,  50513.23,           56177.72,     25.42,      4.44,          31.18,  +2.90,  +1.74
  2,     UK0032,       0,  0.080552, 2459436.585497986525,  51.94959,  26.98471,               94.07652,  37.64172,        94.06717,       37.63656,     51.94959,     +26.98471,      51.95997,      +26.98588,  3876707.71,  -580709.97,  5146051.17,      52.884335,       +1.924001,  104373.10,  168659.21,    4415.71,             4401.15,    27.75,  59120.41,           56177.72,     26.18,      4.58,          32.50,  +2.08,  +0.94
  3,     UK0032,       0,  0.120844, 2459436.585498453118,  52.01728,  26.57199,               94.36988,  37.29565,        94.36892,       37.29512,     52.01728,     +26.57199,      52.01881,      +26.57212,  3875828.01,  -581577.39,  5144071.57,      52.878999,       +1.909387,  102347.14,  166664.55,    6749.18,             6734.63,    28.86,  57914.07,           56177.72,      2.66,      0.47,           3.35,  +1.94,  +0.83
  4,     UK0032,       0,  0.161108, 2459436.585498918779,  52.06613,  26.19471,               94.64620,  36.98623,        94.64151,       36.98365,     52.06613,     +26.19471,      52.07184,      +26.19530,  3875044.43,  -582350.01,  5142308.30,      52.874241,       +1.896347,  100542.73,  164894.49,    8827.66,             8813.10,  -223.41,  51621.15,           55538.55,     12.91,      2.26,          16.39,  +1.83,  +0.74
  5,     UK0032,       0,  0.201420, 2459436.585499385372,  52.13328,  25.75450,               94.95695,  36.61810,        94.95734,       36.61832,     52.13328,     +25.75450,      52.13370,      +25.75445,  3874149.01,  -583232.92,  5140293.33,      52.868800,       +1.881463,   98480.94,  162882.10,   11202.83,            11188.27,  -181.76,  58919.70,           55839.31,     -1.08,     -0.19,           1.38,  +2.92,  +1.86
  6,     UK0032,       0,  0.241744, 2459436.585499852430,  52.16229,  25.25885,               95.34187,  36.23025,        95.30550,       36.21030,     52.16229,     +25.25885,      52.20221,      +25.26336,  3873177.17,  -584191.18,  5138106.41,      52.862889,       +1.865318,   96243.44,  160710.12,   13780.69,            13766.13,    61.88,  63928.66,           56814.37,     98.02,     17.23,         127.73,  +5.17,  +4.14

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.