Orbital Analysis for matched events on 20210813_015142.523_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 67.08° Bg 41.63° Vg 57.08km/s
mass 0.10809g, abs. mag -1.4
Path Details
------------
start 2.89° 53.29° 109.31km
end   2.76° 53.23° 89.63km

Orbit Details
-------------
Semimajor axis 23.57A.U., eccentricity 0.96, inclination 106.79°, Period 114.42Y, LA Sun 140.26°, 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: 2459439.577575502917
Time: 2021-08-13 01:51:42.523452 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002K and UK0032
 Convergence angle = 18.40580 deg
 R.A. =  51.55494  Dec = +62.03396 deg

Best intersection: Stations UK002K and UK0032 with Qconv = 18.41 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3852948.77 +/- 76.43 m
 Y =   -504025.49 +/- 152.90 m
 Z =   5177847.12 +/- 63.21 m
 Vx =    16916.73 +/- 413.15 m/s
 Vy =    21217.59 +/- 718.10 m/s
 Vz =    51426.83 +/- 897.82 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+6.441056e+03, +1.250585e+04, +4.426259e+03, +2.348876e+04, +3.596659e+04, +2.087351e+04
+1.250585e+04, +2.680040e+04, +9.023834e+03, +4.531855e+04, +7.614596e+04, +4.472940e+04
+4.426259e+03, +9.023834e+03, +4.367068e+03, +1.774654e+04, +2.877512e+04, +1.950226e+04
+2.348876e+04, +4.531855e+04, +1.774654e+04, +1.055229e+05, +1.670694e+05, +9.131144e+04
+3.596659e+04, +7.614596e+04, +2.877512e+04, +1.670694e+05, +2.918849e+05, +1.571801e+05
+2.087351e+04, +4.472940e+04, +1.950226e+04, +9.131144e+04, +1.571801e+05, +1.066864e+05

Timing offsets (from input data):
    UK002K: 0.000000 s
    UK0032: -0.000990 s

Reference point on the trajectory:
  Time: 2021-08-13 01:51:42.523452 UTC
  Lon     = ++2.893438 +/- 0.0024 deg
  Lat     = +53.294649 +/- 0.0002 deg
  Lat geo = +53.113175 +/- 0.0002 deg
  Ht      =  109268.31 +/- 81.46 m

  JD dynamic   = 2459439.578376243822 
  LST apparent = 352.5471434679 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  51.43473 +/- 0.3240 deg
  Dec       = +62.18109 +/- 0.5223 deg
  Azimuth   =  49.99727 +/- 0.9285 deg
  Elevation = +58.56067 +/- 0.2445 deg
  Vavg      =  57.42389 +/- 0.5792 km/s
  Vinit     =  58.14706 +/- 0.7335 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  51.74114 +/- 0.3240 deg
  Dec       = +61.96974 +/- 0.5223 deg
  Azimuth   =  50.33892 +/- 0.9285 deg
  Elevation = +58.37810 +/- 0.2445 deg
  Vavg      =  57.53768 +/- 0.5792 km/s
  Vinit     =  58.26085 +/- 0.7335 km/s
Radiant (geocentric, J2000):
  R.A.   =  51.60989 +/- 0.3070 deg
  Dec    = +62.04852 +/- 0.5260 deg
  Vg     =  57.07837 +/- 0.7471 km/s
  Vinf   =  58.14706 +/- 0.7335 km/s
  Zc     =  31.55626 +/- 0.2424 deg
  Zg     =  31.85656 +/- 0.2377 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  67.08017 +/- 0.1317 deg
  Bg     = +41.63129 +/- 0.5367 deg
  Vh     =  41.39414 +/- 0.4150 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  96.71277 +/- 1.6753 deg
  Bh     = +66.35685 +/- 0.9168 deg
  Vh_x   =   1.94049 +/- 0.4097 km/s
  Vh_y   = -16.48686 +/- 0.8159 km/s
  Vh_z   = -37.91956 +/- 0.1511 km/s
Orbit:
  La Sun = 140.262988 +/- -0.0000 deg
  a      =  23.568974 +/- 34.5493 AU
  e      =   0.960715 +/- 0.0359
  i      = 106.785021 +/- 1.1796 deg
  peri   = 145.495688 +/- 0.4758 deg
  node   = 140.263366 +/- 0.0001 deg
  Pi     = 285.759055 +/- 0.4757 deg
  q      =   0.925897 +/- 0.0012 AU
  f      =  34.500813 +/- 0.4758 deg
  M      =   0.203952 +/- nan deg
  Q      =  46.212051 +/- 69.0983 AU
  n      =   0.008614 +/- 0.0097 deg/day
  T      = 114.422561 +/- 339934556.1593 years
  Last perihelion JD = 2459415.900892 (2021-07-20 09:37:17.029146) +/- 0.4320 days
  Tj     =  -0.120311 +/- 0.2274
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +7.623730e-04, +1.508409e-05, +1.163588e-02, -2.488219e-08, +1.836862e-04, +3.911267e-04
q   , +1.508409e-05, +1.862368e-06, +4.195575e-04, -3.165018e-10, +9.240234e-06, +4.968322e-06
Tp  , +1.163588e-02, +4.195575e-04, +2.006193e-01, -3.561251e-07, +3.483793e-03, +5.597491e-03
node, -2.488219e-08, -3.165018e-10, -3.561251e-07, +1.026591e-12, -5.329094e-09, -1.614281e-08
peri, +1.836862e-04, +9.240234e-06, +3.483793e-03, -5.329094e-09, +6.437581e-05, +8.374955e-05
i   , +3.911267e-04, +4.968322e-06, +5.597491e-03, -1.614281e-08, +8.374955e-05, +2.538483e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 4.490220
 a2 = 10.301612

Mean time residuals from time vs. length:
  Station with reference time: UK002K
  Avg. res. = 4.583e-06 s
  Stddev    = 2.14e-03 s

Begin point on the trajectory:
  Lon =     2.893711 +/- 0.0024 deg
  Lat =    53.294786 +/- 0.0002 deg
  Ht  = 109307.78 +/- 74.95 m
End point on the trajectory:
  Lon =     2.755891 +/- 0.0028 deg
  Lat =    53.226154 +/- 0.0002 deg
  Ht  = 89630.70 +/- 73.95 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,   0.000002,  47.685583,   109307.78,    89630.70,          0.012380,      2.31,     51.76,              45.10, 1.0000,    True,    True, {"ff_name": "FF_UK002K_20210813_015136_820_0503552.fits"}
    UK0032,   False,    -0.023645,    52.984073,    6.00,   0.000001,  47.786870,   106333.21,    90489.69,          0.012290,     16.70,     43.76,              35.39, 1.0000,    True,    True, {"ff_name": "FF_UK0032_20210813_015133_028_0509440.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,  0.000000, 2459439.577575502917,  59.31254,  16.83269,               95.75450,  25.28081,        95.75863,       25.28324,     59.31254,     +16.83269,      59.30790,      +16.83229,  3852962.23,  -504008.61,  5177888.04,      53.294786,       +2.893711,  109307.78,  246870.01,       0.00,               46.26,   -16.99,      0.00,           59931.05,    -19.20,      0.87,          16.06,  +3.97,  +2.01
  1,     UK002K,       0,  0.040312, 2459439.577575969510,  59.34119,  16.44634,               95.99392,  24.95983,        95.99235,       24.95890,     59.34119,     +16.44634,      59.34312,      +16.44649,  3852286.88,  -504855.66,  5175834.96,      53.287907,       +2.879865,  107327.28,  245243.91,    2321.36,             2275.10,  -132.17,  57584.90,           59931.05,      7.24,     -0.33,           6.10,  +2.42,  +0.47
  2,     UK002K,       0,  0.080652, 2459439.577576436568,  59.35246,  16.02082,               96.27298,  24.61777,        96.24725,       24.60267,     59.35246,     +16.02082,      59.38166,      +16.02328,  3851556.28,  -505772.01,  5173613.94,      53.280459,       +2.864895,  105185.01,  243498.39,    4832.62,             4786.36,    33.44,  62252.31,           59931.05,    118.24,     -5.26,         100.26,  +1.63,  -0.30
  3,     UK002K,       0,  0.120988, 2459439.577576903161,  59.40909,  15.61461,               96.49963,  24.26366,        96.49159,       24.25895,     59.40909,     +15.61461,      59.41862,      +15.61539,  3850861.80,  -506643.05,  5171502.73,      53.273374,       +2.850653,  103148.89,  241851.26,    7219.71,             7173.45,    75.11,  59180.13,           59931.05,     36.77,     -1.65,          31.40,  +1.32,  -0.60
  4,     UK002K,       0,  0.161296, 2459439.577577369753,  59.44476,  15.23565,               96.72410,  23.94301,        96.71757,       23.93919,     59.44476,     +15.23565,      59.45275,      +15.23628,  3850224.60,  -507442.26,  5169565.62,      53.266867,       +2.837568,  101280.88,  240350.12,    9409.95,             9363.69,   -78.45,  54337.58,           58815.25,     29.70,     -1.33,          25.51,  +1.05,  -0.85
  5,     UK002K,       0,  0.201616, 2459439.577577836346,  59.47571,  14.83919,               96.96294,  23.61090,        96.95244,       23.60476,     59.47571,     +14.83919,      59.48832,      +14.84020,  3849567.28,  -508266.68,  5167567.39,      53.260149,       +2.824071,   99354.11,  238813.19,   11669.30,            11623.04,  -163.58,  56035.55,           58099.35,     47.55,     -2.13,          41.11,  +0.87,  -1.02
  6,     UK002K,       0,  0.241980, 2459439.577578303404,  59.52646,  14.39310,               97.21680,  23.22731,        97.21597,       23.22682,     59.52646,     +14.39310,      59.52840,      +14.39318,  3848835.53,  -509184.47,  5165342.87,      53.252664,       +2.809061,   97209.39,  237117.05,   14184.51,            14138.25,     4.58,  62313.20,           58295.56,      3.72,     -0.17,           3.24,  +1.00,  -0.87
  7,     UK002K,       0,  0.282300, 2459439.577578770462,  59.54119,  13.99017,               97.47073,  22.89872,        97.45130,       22.88738,     59.54119,     +13.99017,      59.56413,      +13.99203,  3848187.53,  -509997.22,  5163372.94,      53.246031,       +2.795745,   95310.33,  235626.16,   16411.86,            16365.60,  -112.56,  55241.77,           58122.85,     87.07,     -3.88,          76.29,  +0.73,  -1.13
  8,     UK002K,       0,  0.322660, 2459439.577579237521,  59.59476,  13.54787,               97.71669,  22.51550,        97.71002,       22.51162,     59.59476,     +13.54787,      59.60356,      +13.54851,  3847480.56,  -510883.93,  5161223.75,      53.238787,       +2.781229,   93238.68,  234013.98,   18841.90,            18795.64,   -29.33,  60209.21,           58181.46,     29.70,     -1.33,          26.21,  +0.88,  -0.97
  9,     UK002K,       0,  0.363004, 2459439.577579704579,  59.62865,  13.11891,               97.96889,  22.15402,        97.95877,       22.14812,     59.62865,     +13.11891,      59.64150,      +13.11988,  3846806.37,  -511729.52,  5159174.24,      53.231873,       +2.767375,   91263.34,  232489.42,   21159.24,            21112.98,   -57.89,  57439.31,           58170.80,     44.92,     -2.01,          39.89,  +0.67,  -1.16
 10,     UK002K,       0,  0.403296, 2459439.577580170706,  59.67358,  12.76163,               98.16389,  21.84276,        98.16595,       21.84396,     59.67358,     +12.76163,      59.67296,      +12.76143,  3846249.12,  -512428.45,  5157480.17,      53.226154,       +2.755891,   89630.70,  231237.51,   23074.68,            23028.42,  -485.31,  47538.98,           57682.24,     -9.08,      0.41,           8.11,  +1.57,  -0.25
  0,     UK0032,       1,  0.015912, 2459439.577575698961,  70.28389,  28.20663,               78.92008,  27.61694,        78.88905,       27.60274,     70.28389,     +28.20663,      70.31792,      +28.21453,  3852589.02,  -504476.71,  5176753.46,      53.290985,       +2.886082,  108213.28,  226820.58,       0.00,             1236.58,   248.08,      0.00,           56032.60,    114.54,    -43.55,         111.43,  +4.33,  +2.55
  1,     UK0032,       0,  0.056184, 2459439.577576164622,  70.40704,  27.89428,               79.06483,  27.31218,        79.05934,       27.30968,     70.40704,     +27.89428,      70.41328,      +27.89568,  3851947.87,  -505280.86,  5174804.37,      53.284452,       +2.872927,  106333.21,  225035.52,    2203.78,             3440.37,   110.17,  54722.46,           56032.60,     20.13,     -7.67,          19.75,  +2.23,  +0.47
  2,     UK0032,       0,  0.096452, 2459439.577576630749,  70.49064,  27.56292,               79.25173,  27.01617,        79.23362,       27.00790,     70.49064,     +27.56292,      70.51082,      +27.56752,  3851298.59,  -506095.21,  5172830.58,      53.277831,       +2.859603,  104429.49,  223235.66,    4435.50,             5672.09,     0.42,  55421.71,           56032.60,     66.02,    -25.13,          65.27,  +1.11,  -0.63
  3,     UK0032,       0,  0.136748, 2459439.577577097341,  70.61592,  27.21757,               79.41669,  26.68454,        79.41867,       26.68544,     70.61592,     +27.21757,      70.61434,      +27.21707,  3850616.82,  -506950.32,  5170757.98,      53.270873,       +2.845617,  102430.68,  221354.75,    6778.94,             8015.52,     0.77,  58155.53,           56032.60,     -7.15,      2.73,           7.13,  +0.97,  -0.76
  4,     UK0032,       0,  0.177040, 2459439.577577563468,  70.72939,  26.86884,               79.59133,  26.35681,        79.60302,       26.36213,     70.72939,     +26.86884,      70.71739,      +26.86587,  3849945.12,  -507792.79,  5168716.01,      53.264011,       +2.831831,  100461.63,  219510.29,    9087.74,            10324.32,   -33.29,  57301.74,           56478.53,    -42.04,     16.04,          42.28,  +0.81,  -0.90
  5,     UK0032,       0,  0.217320, 2459439.577578030061,  70.82638,  26.52995,               79.76945,  26.04566,        79.77972,       26.05033,     70.82638,     +26.52995,      70.81610,      +26.52734,  3849308.13,  -508591.73,  5166779.56,      53.257499,       +2.818745,   98594.51,  217768.89,   11277.24,            12513.82,  -185.96,  54356.99,           56302.84,    -36.74,     14.02,          37.25,  +0.74,  -0.95
  6,     UK0032,       0,  0.257620, 2459439.577578496188,  70.94805,  26.17501,               79.93946,  25.70732,        79.96609,       25.71942,     70.94805,     +26.17501,      70.92016,      +26.16825,  3848643.61,  -509425.18,  5164759.44,      53.250700,       +2.805098,   96646.92,  215961.47,   13561.35,            14797.93,  -245.18,  56677.52,           56280.25,    -94.59,     36.15,          96.72,  +0.59,  -1.08
  7,     UK0032,       0,  0.297940, 2459439.577578962781,  71.03217,  25.76624,               80.17526,  25.35020,        80.17315,       25.34924,     71.03217,     +25.76624,      71.03572,      +25.76678,  3847913.97,  -510340.33,  5162541.33,      53.243228,       +2.790125,   94508.69,  213988.50,   16069.31,            17305.89,   -81.71,  62201.44,           56764.75,      7.46,     -2.85,           7.70,  +0.48,  -1.17
  8,     UK0032,       0,  0.338248, 2459439.577579429373,  71.14560,  25.39362,               80.36099,  25.00225,        80.36497,       25.00406,     71.14560,     +25.39362,      71.14269,      +25.39261,  3847245.77,  -511178.41,  5160509.99,      53.236380,       +2.776394,   92550.72,  212190.81,   18366.09,            19602.68,  -128.71,  56980.89,           57005.20,    -13.97,      5.33,          14.54,  +0.50,  -1.13
  9,     UK0032,       0,  0.378576, 2459439.577579896431,  71.25176,  24.99090,               80.57224,  24.63532,        80.56927,       24.63397,     71.25176,     +24.99090,      71.25657,      +24.99165,  3846542.31,  -512060.72,  5158371.48,      53.229164,       +2.761944,   90489.69,  210309.41,   20784.05,            22020.63,   -55.71,  59957.31,           57288.79,     10.34,     -3.94,          10.85,  +0.40,  -1.21
 10,     UK0032,       1,  0.418808, 2459439.577580362093,  71.32027,  24.69787,               80.73141,  24.37310,        80.71631,       24.36624,     71.32027,     +24.69787,      71.33841,      +24.70168,  3846040.73,  -512689.82,  5156846.67,      53.224015,       +2.751590,   89020.21,  208971.82,   22508.12,            23744.70,  -671.02,  42853.08,           56788.29,     52.36,    -19.94,          55.31,  +3.99,  +2.39

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.