Orbital Analysis for matched events on 20210810_012803.901_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 63.77° Bg 40.64° Vg 56.48km/s
mass 0.03045g, abs. mag -0.6
Path Details
------------
start -5.54° 51.62° 108.47km
end   -5.67° 51.54° 93.26km

Orbit Details
-------------
Semimajor axis 7.38A.U., eccentricity 0.88, inclination 107.68°, Period 20.07Y, LA Sun 137.37°, last Perihelion 2021-07-15

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: 2459436.561156264972
Time: 2021-08-10 01:28:03.917829 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0020 and UK0024
 Convergence angle = 6.28281 deg
 R.A. =  47.30666  Dec = +60.86369 deg

Best intersection: Stations UK0020 and UK0024 with Qconv = 6.28 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3664811.12 +/- 114.47 m
 Y =  -1690612.46 +/- 219.04 m
 Z =   5061661.46 +/- 192.40 m
 Vx =    19285.36 +/- 896.76 m/s
 Vy =    20798.30 +/- 1539.65 m/s
 Vz =    50083.30 +/- 1268.74 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+8.864375e+03, +1.632466e+04, -1.475113e+04, +3.730617e+04, +7.260203e+04, -8.091037e+04
+1.632466e+04, +3.153825e+04, -2.862675e+04, +7.157291e+04, +1.467088e+05, -1.601823e+05
-1.475113e+04, -2.862675e+04, +2.672788e+04, -6.612602e+04, -1.354748e+05, +1.480927e+05
+3.730617e+04, +7.157291e+04, -6.612602e+04, +2.317389e+05, +4.668102e+05, -4.929981e+05
+7.260203e+04, +1.467088e+05, -1.354748e+05, +4.668102e+05, +1.001406e+06, -1.036808e+06
-8.091037e+04, -1.601823e+05, +1.480927e+05, -4.929981e+05, -1.036808e+06, +1.086559e+06

Timing offsets (from input data):
    UK0020: -0.000164 s
    UK0024: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-10 01:28:03.917829 UTC
  Lon     = +-5.534128 +/- 0.0035 deg
  Lat     = +51.616864 +/- 0.0011 deg
  Lat geo = +51.432554 +/- 0.0011 deg
  Ht      =  108655.92 +/- 144.74 m

  JD dynamic   = 2459436.561957197264 
  LST apparent = 335.2356715997 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  47.16158 +/- 0.8085 deg
  Dec       = +60.47588 +/- 1.7227 deg
  Azimuth   =  48.09265 +/- 2.3397 deg
  Elevation = +50.98838 +/- 0.9698 deg
  Vavg      =  55.91760 +/- 0.3298 km/s
  Vinit     =  57.55720 +/- 0.4729 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  47.34422 +/- 0.8085 deg
  Dec       = +60.23398 +/- 1.7227 deg
  Azimuth   =  48.40165 +/- 2.3397 deg
  Elevation = +50.81896 +/- 0.9698 deg
  Vavg      =  56.05607 +/- 0.3298 km/s
  Vinit     =  57.69566 +/- 0.4729 km/s
Radiant (geocentric, J2000):
  R.A.   =  47.46077 +/- 0.7989 deg
  Dec    = +60.26027 +/- 1.7429 deg
  Vg     =  56.47735 +/- 0.4820 km/s
  Vinf   =  57.55720 +/- 0.4729 km/s
  Zc     =  39.13492 +/- 0.9642 deg
  Zg     =  39.52062 +/- 0.9808 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  63.77067 +/- 0.3630 deg
  Bg     = +40.63727 +/- 1.7660 deg
  Vh     =  40.37414 +/- 1.2552 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  92.59761 +/- 2.0457 deg
  Bh     = +65.65135 +/- 1.6870 deg
  Vh_x   =   0.75441 +/- 0.5725 km/s
  Vh_y   = -16.62867 +/- 0.5850 km/s
  Vh_z   = -36.78300 +/- 1.6328 km/s
Orbit:
  La Sun = 137.367811 +/- -0.0000 deg
  a      =   7.384110 +/- 38.1085 AU
  e      =   0.875314 +/- 0.1033
  i      = 107.677482 +/- 1.8973 deg
  peri   = 143.449069 +/- 3.6172 deg
  node   = 137.367737 +/- 0.0001 deg
  Pi     = 280.816806 +/- 3.6173 deg
  q      =   0.920697 +/- 0.0119 AU
  f      =  36.547195 +/- 3.6172 deg
  M      =   1.254545 +/- nan deg
  Q      =  13.847522 +/- 76.2145 AU
  n      =   0.049120 +/- 0.0567 deg/day
  T      =  20.065401 +/- 344827521.6923 years
  Last perihelion JD = 2459411.021469 (2021-07-15 12:30:54.888873) +/- 2.7719 days
  Tj     =   0.354984 +/- 0.5710
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +7.058281e-03, +8.406712e-04, +2.096066e-01, +1.584533e-07, +4.466590e-03, -2.302811e-03
q   , +8.406712e-04, +1.049355e-04, +2.568498e-02, +1.927833e-08, +5.512627e-04, -2.798256e-04
Tp  , +2.096066e-01, +2.568498e-02, +6.341485e+00, +4.784230e-06, +1.356700e-01, -6.945486e-02
node, +1.584533e-07, +1.927833e-08, +4.784230e-06, +3.638572e-12, +1.021798e-07, -5.280127e-08
peri, +4.466590e-03, +5.512627e-04, +1.356700e-01, +1.021798e-07, +2.905998e-03, -1.483238e-03
i   , -2.302811e-03, -2.798256e-04, -6.945486e-02, -5.280127e-08, -1.483238e-03, +7.663118e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 8.373486
 a2 = 11.491926

Mean time residuals from time vs. length:
  Station with reference time: UK0024
  Avg. res. = 4.102e-07 s
  Stddev    = 6.40e-04 s

Begin point on the trajectory:
  Lon =    -5.535743 +/- 0.0031 deg
  Lat =    51.615962 +/- 0.0013 deg
  Ht  = 108467.20 +/- 175.24 m
End point on the trajectory:
  Lon =    -5.667516 +/- 0.0045 deg
  Lat =    51.542959 +/- 0.0012 deg
  Ht  = 93264.18 +/- 150.62 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
    UK0020,   False,    -3.515726,    50.691998,   17.00,   2.812359,  17.220673,   108467.20,    97925.39,          0.009653,      2.89,     34.47,              72.09, 1.0000,    True,   False, {"ff_name": "FF_UK0020_20210810_012803_387_0455936.fits"}
    UK0024,   False,    -2.949770,    50.877440,   82.00,   4.242090,  13.412812,   107265.95,    93264.18,          0.008332,      6.31,     32.25,              80.71, 1.0000,    True,    True, {"ff_name": "FF_UK0024_20210810_012759_901_0460032.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,     UK0020,       0,  0.011176, 2459436.561156456359, 241.12306,  46.25776,              306.82779,  30.81202,       306.81378,       30.82211,    241.12306,     +46.25776,     241.14560,      +46.25580,  3664729.74, -1690700.22,  5061450.12,      51.615962,       -5.535743,  108467.20,  206920.79,       0.00,              242.88,   151.34,      0.00,           56184.40,    -56.53,      4.74,          56.55,  +2.78,  +1.20
  1,     UK0020,       0,  0.051468, 2459436.561156922486, 241.03534,  45.68379,              306.38820,  30.37616,       306.38321,       30.37975,    241.03534,     +45.68379,     241.04347,      +45.68310,  3664003.35, -1691483.60,  5059563.72,      51.607903,       -5.550330,  106782.86,  206293.41,    2167.91,             2410.78,     0.16,  53804.95,           56184.40,    -20.12,      1.69,          20.19,  +1.39,  -0.18
  2,     UK0020,       0,  0.091784, 2459436.561157389544, 240.93389,  45.07871,              305.93516,  29.90955,       305.93287,       29.91119,    240.93389,     +45.07871,     240.93785,      +45.07839,  3663241.02, -1692305.73,  5057583.98,      51.599439,       -5.565634,  105015.48,  205657.24,    4443.08,             4685.95,   -45.15,  56433.41,           56184.40,     -9.21,      0.77,           9.27,  +1.24,  -0.33
  3,     UK0020,       0,  0.132116, 2459436.561157856137, 240.81300,  44.45178,              305.48053,  29.41525,       305.46969,       29.42299,    240.81300,     +44.45178,     240.83048,      +44.45031,  3662454.13, -1693154.36,  5055540.45,      51.590696,       -5.581429,  103191.46,  205024.81,    6791.57,             7034.44,   -18.06,  58228.89,           56184.40,    -43.52,      3.65,          43.93,  +1.06,  -0.50
  4,     UK0020,       0,  0.172432, 2459436.561158322729, 240.73033,  43.82053,              305.00643,  28.93500,       305.01016,       28.93234,    240.73033,     +43.82053,     240.72521,      +43.82103,  3661670.62, -1693999.33,  5053505.71,      51.581983,       -5.597158,  101375.61,  204420.12,    9129.95,             9372.83,    -0.15,  58001.46,           56760.64,     14.97,     -1.26,          15.16,  +0.81,  -0.74
  5,     UK0020,       0,  0.212732, 2459436.561158789322, 240.62484,  43.24393,              304.59547,  28.47850,       304.59226,       28.48078,    240.62484,     +43.24393,     240.63063,      +43.24350,  3660955.87, -1694770.16,  5051649.52,      51.574028,       -5.611525,   99719.38,  203891.19,   11263.13,            11506.01,  -186.52,  52932.51,           56378.60,    -12.86,      1.08,          13.05,  +0.76,  -0.79
  6,     UK0020,       0,  0.253060, 2459436.561159255914, 240.51009,  42.61622,              304.15345,  27.97909,       304.14134,       27.98766,    240.51009,     +42.61622,     240.52959,      +42.61462,  3660181.53, -1695605.24,  5049638.61,      51.565404,       -5.627078,   97925.39,  203341.27,   13574.13,            13817.01,  -196.69,  57305.07,           56341.43,    -48.44,      4.07,          49.31,  +0.72,  -0.82
  0,     UK0024,       1,  0.000000, 2459436.561156264972, 247.53378,  36.89805,              295.52925,  27.59784,       295.51309,       27.60802,    247.53378,     +36.89805,     247.55534,      +36.89499,  3664812.09, -1690611.41,  5061663.98,      51.616875,       -5.534039,  108658.17,  227547.81,       0.00,                2.90,   554.64,      0.00,           53565.39,    -68.48,     13.38,          63.25,  +4.39,  +2.60
  1,     UK0024,       0,  0.040360, 2459436.561156732496, 247.46276,  36.45301,              295.21799,  27.24434,       295.22094,       27.24248,    247.46276,     +36.45301,     247.45892,      +36.45356,  3664211.70, -1691258.91,  5060104.79,      51.610215,       -5.546126,  107265.95,  227290.11,    1791.87,             1788.97,    17.70,  44397.25,           53565.39,     12.52,     -2.45,          11.58,  +1.86,  +0.08
  2,     UK0024,       0,  0.080820, 2459436.561157200485, 247.34129,  35.89667,              294.85342,  26.78213,       294.85547,       26.78085,    247.34129,     +35.89667,     247.33884,      +35.89705,  3663456.20, -1692073.68,  5058142.78,      51.601829,       -5.561294,  105514.31,  226983.16,    4046.67,             4043.77,   -56.26,  55729.00,           53565.39,      8.69,     -1.70,           8.04,  +1.67,  -0.11
  3,     UK0024,       0,  0.121320, 2459436.561157669406, 247.19732,  35.29949,              294.47548,  26.27618,       294.46519,       26.28262,    247.19732,     +35.29949,     247.21136,      +35.29757,  3662644.56, -1692948.99,  5056034.99,      51.592812,       -5.577579,  103632.85,  226677.35,    6469.00,             6466.10,    35.00,  59810.64,           53565.39,    -43.73,      8.55,          40.54,  +1.25,  -0.53
  4,     UK0024,       0,  0.161788, 2459436.561158137862, 247.08953,  34.72678,              294.09781,  25.80645,       294.09661,       25.80719,    247.08953,     +34.72678,     247.09172,      +34.72656,  3661873.69, -1693780.33,  5054033.08,      51.584242,       -5.593058,  101846.22,  226411.10,    8769.66,             8766.76,     6.43,  56851.28,           54920.10,     -5.09,      1.00,           4.73,  +1.24,  -0.53
  5,     UK0024,       0,  0.202244, 2459436.561158605851, 246.96316,  34.17863,              293.75533,  25.34181,       293.74452,       25.34856,    246.96316,     +34.17863,     246.97809,      +34.17664,  3661133.18, -1694578.94,  5052109.99,      51.576002,       -5.607936,  100130.22,  226177.56,   10979.73,            10976.83,  -112.03,  54628.98,           55265.25,    -46.00,      8.99,          42.74,  +1.09,  -0.68
  6,     UK0024,       0,  0.242688, 2459436.561159073841, 246.86916,  33.62835,              293.39366,  24.89275,       293.39651,       24.89097,    246.86916,     +33.62835,     246.86639,      +33.62888,  3660397.16, -1695372.70,  5050198.58,      51.567807,       -5.622728,   98424.92,  225966.77,   13176.37,            13173.47,  -243.23,  54313.31,           55286.52,     12.14,     -2.38,          11.29,  +0.94,  -0.83
  7,     UK0024,       0,  0.283176, 2459436.561159542762, 246.73907,  33.03560,              293.02709,  24.39059,       293.02198,       24.39376,    246.73907,     +33.03560,     246.74680,      +33.03467,  3659600.17, -1696232.21,  5048128.84,      51.558925,       -5.638733,   96578.70,  225761.72,   15554.98,            15552.08,  -195.00,  58748.35,           55584.10,    -21.77,      4.26,          20.27,  +0.91,  -0.86
  8,     UK0024,       0,  0.323632, 2459436.561160010751, 246.64408,  32.46441,              292.65752,  23.92269,       292.66639,       23.91719,    246.64408,     +32.46441,     246.63391,      +32.46603,  3658839.00, -1697053.10,  5046152.09,      51.550436,       -5.654030,   94815.72,  225589.66,   17826.72,            17823.82,  -251.79,  56153.33,           55760.89,     37.85,     -7.42,          35.27,  +0.87,  -0.90
  9,     UK0024,       0,  0.364040, 2459436.561160478741, 246.55068,  31.96223,              292.34215,  23.50429,       292.35501,       23.49633,    246.55068,     +31.96223,     246.53558,      +31.96457,  3658169.01, -1697775.65,  5044412.15,      51.542959,       -5.667516,   93264.18,  225458.33,   19826.31,            19823.41,  -577.98,  49484.97,           55509.03,     54.94,    -10.77,          51.22,  +2.13,  +0.36

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.