Orbital Analysis for matched events on 20210813_232233.722_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 64.64° Bg 38.13° Vg 63.19km/s
mass 0.02304g, abs. mag -0.2
Path Details
------------
start 1.13° 54.16° 111.98km
end   0.94° 54.04° 96.09km

Orbit Details
-------------
Semimajor axis -3.46A.U., eccentricity 1.28, inclination 115.88°, Period 1000000000.00Y, LA Sun 141.12°, 

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: 2459440.474001421593
Time: 2021-08-13 23:22:33.722826 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000Z and UK002K
 Convergence angle = 62.40246 deg
 R.A. =  48.87236  Dec = +57.80003 deg

Best intersection: Stations UK000Z and UK002K with Qconv = 62.40 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2664012.37 +/- 297.94 m
 Y =  -2722072.51 +/- 263.59 m
 Z =   5237602.80 +/- 532.72 m
 Vx =    21487.88 +/- 963.21 m/s
 Vy =    25788.57 +/- 832.24 m/s
 Vz =    54673.57 +/- 1651.87 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+6.455229e+04, +5.601441e+04, +1.114161e+05, +1.248601e+05, +5.230878e+04, +9.854673e+04
+5.601441e+04, +4.869732e+04, +9.691495e+04, +1.109773e+05, +4.871759e+04, +9.195026e+04
+1.114161e+05, +9.691495e+04, +1.970682e+05, +2.204911e+05, +8.872533e+04, +1.802579e+05
+1.248601e+05, +1.109773e+05, +2.204911e+05, +3.179181e+05, +2.011341e+05, +3.783907e+05
+5.230878e+04, +4.871759e+04, +8.872533e+04, +2.011341e+05, +1.878500e+05, +3.292927e+05
+9.854673e+04, +9.195026e+04, +1.802579e+05, +3.783907e+05, +3.292927e+05, +6.128936e+05

Timing offsets (from input data):
    UK000Z: -0.002704 s
    UK002K: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 23:22:33.722826 UTC
  Lon     = ++1.131815 +/- 0.0060 deg
  Lat     = +54.155254 +/- 0.0026 deg
  Lat geo = +53.975541 +/- 0.0026 deg
  Ht      =  111873.02 +/- 443.82 m

  JD dynamic   = 2459440.474802162498 
  LST apparent = 314.3823950683 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  50.19783 +/- 0.5478 deg
  Dec       = +58.45163 +/- 0.2243 deg
  Azimuth   =  43.84143 +/- 0.4504 deg
  Elevation = +41.28105 +/- 0.1337 deg
  Vavg      =  64.03650 +/- 1.3307 km/s
  Vinit     =  64.15589 +/- 1.7859 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  50.15018 +/- 0.5478 deg
  Dec       = +58.24180 +/- 0.2243 deg
  Azimuth   =  44.07855 +/- 0.4504 deg
  Elevation = +41.16771 +/- 0.1337 deg
  Vavg      =  64.18151 +/- 1.3307 km/s
  Vinit     =  64.30090 +/- 1.7859 km/s
Radiant (geocentric, J2000):
  R.A.   =  50.35368 +/- 0.5835 deg
  Dec    = +58.12522 +/- 0.2098 deg
  Vg     =  63.18926 +/- 1.8165 km/s
  Vinf   =  64.15589 +/- 1.7859 km/s
  Zc     =  48.84869 +/- 0.1342 deg
  Zg     =  49.24371 +/- 0.1517 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  64.63937 +/- 0.4394 deg
  Bg     = +38.12724 +/- 0.1337 deg
  Vh     =  44.81102 +/- 1.5283 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  81.95776 +/- 2.4840 deg
  Bh     = +60.53226 +/- 0.8671 deg
  Vh_x   =  -3.08403 +/- 0.9234 km/s
  Vh_y   = -21.82724 +/- 1.2112 km/s
  Vh_z   = -39.01394 +/- 1.0622 km/s
Orbit:
  La Sun = 141.123845 +/- 0.0000 deg
  a      =  -3.456761 +/- 10.3002 AU
  e      =   1.276446 +/- 0.1360
  i      = 115.880812 +/- 1.3838 deg
  peri   = 154.005149 +/- 3.2718 deg
  node   = 141.122560 +/- 0.0001 deg
  Pi     = 295.127709 +/- 3.2717 deg
  q      =   0.955606 +/- 0.0100 AU
  f      =  25.990748 +/- 3.2718 deg
  M      =        nan +/- nan deg
  Q      =  -7.869127 +/- 20.6060 AU
  n      =   0.153356 +/- 0.0456 deg/day
  T      = 1000000000.000000 +/- 442216626.0660 years
  Last perihelion JD = NaN 
  Tj     =  -2.069954 +/- 0.7978
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +4.720281e-03, +4.338982e-04, +1.259228e-01, -7.782798e-08, +2.561050e-03, +1.042104e-03
q   , +4.338982e-04, +5.406729e-05, +1.356801e-02, -8.089908e-09, +2.907730e-04, +1.084517e-04
Tp  , +1.259228e-01, +1.356801e-02, +3.640579e+00, -2.199572e-06, +7.611746e-02, +2.947251e-02
node, -7.782798e-08, -8.089908e-09, -2.199572e-06, +1.396125e-12, -4.576731e-08, -1.868709e-08
peri, +2.561050e-03, +2.907730e-04, +7.611746e-02, -4.576731e-08, +1.605836e-03, +6.133546e-04
i   , +1.042104e-03, +1.084517e-04, +2.947251e-02, -1.868709e-08, +6.133546e-04, +2.501318e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 57.231922
 a2 = 6.740123

Mean time residuals from time vs. length:
  Station with reference time: UK002K
  Avg. res. = 3.025e-06 s
  Stddev    = 1.74e-03 s

Begin point on the trajectory:
  Lon =     1.133122 +/- 0.0052 deg
  Lat =    54.156053 +/- 0.0020 deg
  Ht  = 111983.18 +/- 372.50 m
End point on the trajectory:
  Lon =     0.942805 +/- 0.0028 deg
  Lat =    54.040196 +/- 0.0010 deg
  Ht  = 96093.57 +/- 212.83 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,  20.297427,  10.733142,   109627.13,    96677.41,          0.018725,     14.35,     75.56,              18.51, 1.0000,    True,    True, {"ff_name": "FF_UK000Z_20210813_232228_836_0278272.fits"}
    UK002K,   False,    -0.382860,    53.537770,   34.00, 145.875603,   2.698750,   111983.18,    96093.57,          0.015066,     39.22,     14.45,               9.07, 1.0000,    True,    True, {"ff_name": "FF_UK002K_20210813_232225_676_0283392.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,  0.038480, 2459440.474001897499,  52.42369,  39.59968,               56.56139,  24.95312,        56.56274,       24.95404,     52.42369,     +39.59968,      52.42188,      +39.59959,  2662871.98, -2723441.14,  5234701.22,      54.138951,       +1.104984,  109627.13,  249918.54,       0.00,             3404.82,   -41.20,      0.00,           62445.09,     -6.57,     -1.24,           5.52,  +3.03,  +1.04
  1,     UK000Z,       0,  0.078648, 2459440.474002362229,  52.43252,  39.39197,               56.70456,  24.79089,        56.70005,       24.78780,     52.43252,     +39.39197,      52.43949,      +39.39229,  2661938.08, -2724561.96,  5232325.01,      54.125588,       +1.082985,  107788.63,  247273.74,    2788.33,             6193.15,   170.12,  69416.73,           62445.09,     21.77,      4.13,          18.48,  +1.72,  -0.25
  2,     UK000Z,       0,  0.118808, 2459440.474002826959,  52.47082,  39.19731,               56.81890,  24.62360,        56.82932,       24.63070,     52.47082,     +39.19731,      52.45608,      +39.19656,  2661073.74, -2725599.29,  5230125.79,      54.113209,       +1.062614,  106087.65,  244828.25,    5368.97,             8773.79,   174.26,  64259.05,           62445.09,    -49.71,     -9.39,          42.62,  +2.42,  +0.48
  3,     UK000Z,       0,  0.158936, 2459440.474003291223,  52.46466,  39.03222,               56.94063,  24.50105,        56.93739,       24.49884,     52.46466,     +39.03222,      52.47006,      +39.03244,  2660360.83, -2726454.89,  5228311.87,      54.102992,       +1.045784,  104685.10,  242811.91,    7497.49,            10902.31,  -271.67,  53043.12,           62445.09,     15.31,      2.90,          13.24,  +1.36,  -0.57
  4,     UK000Z,       0,  0.199128, 2459440.474003756419,  52.52461,  38.80962,               57.05992,  24.30124,        57.08509,       24.31833,     52.52461,     +38.80962,      52.48882,      +38.80781,  2659406.20, -2727600.58,  5225882.91,      54.089300,       +1.023306,  102807.61,  240117.98,   10347.71,            13752.53,    -0.00,  70915.24,           63261.49,   -117.82,    -22.14,         102.98,  +1.49,  -0.41
  5,     UK000Z,       0,  0.239248, 2459440.474004221149,  52.47980,  38.63759,               57.21122,  24.19267,        57.19592,       24.18224,     52.47980,     +38.63759,      52.50307,      +38.63866,  2658699.46, -2728448.78,  5224084.68,      54.079156,       +1.006622,  101418.08,  238123.77,   12457.82,            15862.64,  -463.83,  52594.83,           61972.34,     71.15,     13.53,          62.73,  +1.38,  -0.50
  6,     UK000Z,       0,  0.279412, 2459440.474004685879,  52.52181,  38.44072,               57.32311,  24.02119,        57.32547,       24.02279,     52.52181,     +38.44072,      52.51956,      +38.44055,  2657887.54, -2729423.20,  5222018.84,      54.067493,       +0.987482,   99822.23,  235836.69,   14881.95,            18286.77,  -616.45,  60355.90,           61338.55,    -10.85,     -2.05,           9.66,  +1.27,  -0.59
  7,     UK000Z,       0,  0.319592, 2459440.474005151074,  52.51337,  38.20863,               57.49250,  23.84816,        57.47604,       23.83696,     52.51337,     +38.20863,      52.53855,      +38.20977,  2656962.06, -2730533.90,  5219664.08,      54.054189,       +0.965689,   98003.82,  233234.47,   17645.11,            21049.93,  -431.08,  68769.55,           61694.13,     75.02,     14.27,          67.53,  +1.33,  -0.51
  8,     UK000Z,       0,  0.359724, 2459440.474005615339,  52.50230,  38.03625,               57.62120,  23.72198,        57.58736,       23.69891,     52.50230,     +38.03625,      52.55277,      +38.03857,  2656286.81, -2731344.30,  5217945.96,      54.044475,       +0.949745,   96677.41,  231335.90,   19661.21,            23066.03,  -989.68,  50236.70,           61096.68,    153.20,     29.28,         139.07,  +2.07,  +0.25
  0,     UK002K,       0,  0.000000, 2459440.474001421593,  37.92974,  52.42076,               54.79033,  41.95703,        54.79429,       41.93276,     37.92974,     +52.42076,      37.95851,      +52.40373,  2664068.29, -2722005.40,  5237745.09,      54.156053,       +1.133122,  111983.18,  165768.85,       0.00,              166.97,  -810.34,      0.00,           75664.67,     24.45,     66.40,          88.04,  +4.34,  +3.24
  1,     UK002K,       0,  0.040092, 2459440.474001885392,  37.68963,  52.27697,               55.06368,  41.98683,        55.06811,       41.95906,     37.68963,     +52.27697,      37.72266,      +52.25755,  2662837.62, -2723482.39,  5234613.78,      54.138460,       +1.104185,  109559.47,  162135.85,    3674.39,             3507.43,   -42.02,  91649.04,           75664.67,     27.30,     74.26,         100.66,  +2.09,  +1.04
  2,     UK002K,       0,  0.080184, 2459440.474002349656,  37.53064,  52.14227,               55.28726,  41.98289,        55.28766,       41.98025,     37.53064,     +52.14227,      37.53410,      +52.14044,  2661886.90, -2724623.38,  5232194.79,      54.124855,       +1.081793,  107687.90,  159329.23,    6512.91,             6345.95,   224.37,  70800.18,           75664.67,      2.57,      6.93,           9.57,  +2.12,  +1.11
  3,     UK002K,       0,  0.120268, 2459440.474002813455,  37.36877,  52.01748,               55.50190,  41.98652,        55.49984,       42.00048,     37.36877,     +52.01748,      37.35272,      +52.02715,  2660998.63, -2725689.44,  5229934.67,      54.112133,       +1.060864,  105939.87,  156707.71,    9165.02,             8998.05,   304.84,  66163.65,           75664.67,    -13.40,    -36.01,          50.57,  +2.62,  +1.64
  4,     UK002K,       0,  0.160312, 2459440.474003277253,  37.20046,  51.94239,               55.66678,  42.02358,        55.66779,       42.01681,     37.20046,     +51.94239,      37.20914,      +51.93770,  2660313.60, -2726511.57,  5228191.69,      54.102315,       +1.044685,  104592.19,  154685.29,   11210.30,            11043.33,  -218.93,  51075.80,           69640.33,      6.37,     17.25,          24.52,  +1.99,  +1.04
  5,     UK002K,       0,  0.200380, 2459440.474003740586,  36.99907,  51.83205,               55.88635,  42.05577,        55.88907,       42.03720,     36.99907,     +51.83205,      37.02185,      +51.81920,  2659441.30, -2727558.46,  5225972.21,      54.089804,       +1.024132,  102876.62,  152112.97,   13814.71,            13647.74,  -185.12,  64999.85,           67255.21,     17.12,     46.56,          67.26,  +1.94,  +1.03
  6,     UK002K,       0,  0.240460, 2459440.474004204851,  36.87170,  51.71301,               56.07820,  42.04646,        56.07706,       42.05465,     36.87170,     +51.71301,      36.86302,      +51.71864,  2658721.09, -2728422.81,  5224139.73,      54.079466,       +1.007133,  101460.60,  149988.93,   15965.01,            15798.05,  -606.19,  53650.23,           64945.27,     -7.49,    -20.21,          29.64,  +1.97,  +1.09
  7,     UK002K,       0,  0.280532, 2459440.474004668649,  36.66349,  51.59827,               56.30655,  42.07982,        56.30721,       42.07508,     36.66349,     +51.59827,      36.67026,      +51.59501,  2657868.86, -2729445.61,  5221971.32,      54.067225,       +0.987051,   99785.53,  147477.99,   18509.49,            18342.53,  -632.56,  63497.70,           63862.09,      4.25,     11.52,          17.17,  +1.82,  +0.98
  8,     UK002K,       0,  0.320616, 2459440.474005132448,  36.43406,  51.45995,               56.57135,  42.10973,        56.57297,       42.09776,     36.43406,     +51.45995,      36.44951,      +51.45175,  2656921.42, -2730582.67,  5219560.67,      54.053605,       +0.964746,   97923.98,  144688.92,   21338.24,            21171.28,  -375.43,  70570.58,           63803.92,     10.48,     28.50,          43.28,  +1.62,  +0.82
  9,     UK002K,       0,  0.360712, 2459440.474005596712,  36.21512,  51.31002,               56.84374,  42.12773,        56.84471,       42.12035,     36.21512,     +51.31002,      36.22532,      +51.30498,  2655989.49, -2731701.12,  5217189.48,      54.040196,       +0.942805,   96093.57,  141947.13,   24120.68,            23953.71,  -165.39,  69394.41,           64079.43,      6.34,     17.23,          26.68,  +2.74,  +1.98

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.