Orbital Analysis for matched events on 20210816_235415.380_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 71.22° Bg 33.59° Vg 55.44km/s
mass 0.00388g, abs. mag 1.1
Path Details
------------
start -0.84° 51.23° 109.03km
end   -0.93° 51.17° 102.69km

Orbit Details
-------------
Semimajor axis 2.12A.U., eccentricity 0.61, inclination 115.61°, Period 3.09Y, LA Sun 144.03°, last Perihelion 2021-07-07

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: 2459443.496011352167
Time: 2021-08-16 23:54:15.380827 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0001 and UK002B
 Convergence angle = 28.83108 deg
 R.A. =  61.90459  Dec = +55.39707 deg

Best intersection: Stations UK0001 and UK002B with Qconv = 28.83 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3264248.41 +/- 153.10 m
 Y =  -2432011.59 +/- 106.80 m
 Z =   5034653.32 +/- 321.79 m
 Vx =    15168.35 +/- 1397.08 m/s
 Vy =    28072.77 +/- 2374.38 m/s
 Vz =    46669.14 +/- 2760.14 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.514855e+04, +1.445632e+04, +4.849306e+04, +1.264500e+05, +5.036775e+04, +2.331251e+05
+1.445632e+04, +1.220621e+04, +3.081669e+04, +5.372960e+04, +2.219307e+04, +8.602090e+04
+4.849306e+04, +3.081669e+04, +9.915072e+04, +2.478962e+05, +9.352084e+04, +4.719271e+05
+1.264500e+05, +5.372960e+04, +2.478962e+05, +1.604085e+06, +5.845939e+05, +3.108211e+06
+5.036775e+04, +2.219307e+04, +9.352084e+04, +5.845939e+05, +2.269970e+05, +1.086078e+06
+2.331251e+05, +8.602090e+04, +4.719271e+05, +3.108211e+06, +1.086078e+06, +6.263773e+06

Timing offsets (from input data):
    UK0001: 0.000000 s
    UK000S: 0.000000 s
    UK002B: 0.002114 s

Reference point on the trajectory:
  Time: 2021-08-16 23:54:15.380827 UTC
  Lon     = +-0.840568 +/- 0.0024 deg
  Lat     = +51.228568 +/- 0.0014 deg
  Lat geo = +51.043710 +/- 0.0014 deg
  Ht      =  109163.88 +/- 293.19 m

  JD dynamic   = 2459443.496812093072 
  LST apparent = 323.3122354827 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  61.61665 +/- 1.7824 deg
  Dec       = +55.63882 +/- 0.6964 deg
  Azimuth   =  43.89322 +/- 0.3510 deg
  Elevation = +36.33817 +/- 1.1785 deg
  Vavg      =  54.87760 +/- 2.5146 km/s
  Vinit     =  56.53466 +/- 2.8812 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  61.54037 +/- 1.7824 deg
  Dec       = +55.39378 +/- 0.6964 deg
  Azimuth   =  44.16113 +/- 0.3510 deg
  Elevation = +36.21465 +/- 1.1785 deg
  Vavg      =  55.04391 +/- 2.5146 km/s
  Vinit     =  56.70098 +/- 2.8812 km/s
Radiant (geocentric, J2000):
  R.A.   =  61.95878 +/- 1.8525 deg
  Dec    = +55.21662 +/- 0.7452 deg
  Vg     =  55.43501 +/- 2.9367 km/s
  Vinf   =  56.53466 +/- 2.8812 km/s
  Zc     =  53.79515 +/- 1.1787 deg
  Zg     =  54.36603 +/- 1.2491 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  71.21901 +/- 1.0412 deg
  Bg     = +33.59232 +/- 0.9463 deg
  Vh     =  36.52527 +/- 2.7764 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  96.17970 +/- 4.4820 deg
  Bh     = +57.11100 +/- 0.2956 deg
  Vh_x   =   2.13504 +/- 1.4157 km/s
  Vh_y   = -19.71846 +/- 1.5501 km/s
  Vh_z   = -30.67115 +/- 2.4075 km/s
Orbit:
  La Sun = 144.027473 +/- -0.0000 deg
  a      =   2.120878 +/- 48.8440 AU
  e      =   0.607965 +/- 0.1767
  i      = 115.613070 +/- 1.4742 deg
  peri   = 121.807156 +/- 15.2729 deg
  node   = 144.026413 +/- 0.0001 deg
  Pi     = 265.833569 +/- 15.2728 deg
  q      =   0.831458 +/- 0.0621 AU
  f      =  58.188886 +/- 15.2730 deg
  M      =  12.928978 +/- nan deg
  Q      =   3.410298 +/- 97.7062 AU
  n      =   0.319103 +/- 0.1957 deg/day
  T      =   3.088689 +/- 339934631.9418 years
  Last perihelion JD = 2459402.980148 (2021-07-07 11:31:24.766254) +/- 9.1050 days
  Tj     =   2.015613 +/- 1.2930
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.053065e-02, +8.601438e-03, +1.355863e+00, -2.506825e-07, +3.686477e-02, +3.315073e-03
q   , +8.601438e-03, +4.003714e-03, +6.111782e-01, -1.161669e-07, +1.699109e-02, +1.539830e-03
Tp  , +1.355863e+00, +6.111782e-01, +9.422662e+01, -1.773313e-05, +2.601778e+00, +2.348824e-01
node, -2.506825e-07, -1.161669e-07, -1.773313e-05, +3.694853e-12, -4.919836e-07, -4.895066e-08
peri, +3.686477e-02, +1.699109e-02, +2.601778e+00, -4.919836e-07, +7.218222e-02, +6.519900e-03
i   , +3.315073e-03, +1.539830e-03, +2.348824e-01, -4.895066e-08, +6.519900e-03, +6.485631e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.014469
 a2 = 53.070970

Mean time residuals from time vs. length:
  Station with reference time: UK0001
  Avg. res. = 6.504e-06 s
  Stddev    = 2.55e-03 s

Begin point on the trajectory:
  Lon =    -0.842399 +/- 0.0019 deg
  Lat =    51.227373 +/- 0.0010 deg
  Ht  = 109025.90 +/- 269.51 m
End point on the trajectory:
  Lon =    -0.927394 +/- 0.0021 deg
  Lat =    51.172350 +/- 0.0011 deg
  Ht  = 102686.13 +/- 329.28 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
    UK0001,   False,    -1.778230,    50.857470,   24.00,   0.000000,   0.000000,   109025.90,   102686.13,          0.030723,     66.50,     19.92,              19.99, 1.0000,    True,    True, {"ff_name": "FF_UK0001_20210816_235408_192_0347904.fits"}
    UK000S,    True,    -1.778230,    50.857470,   24.00,  69.661108,   0.000000,   107446.83,   103226.81,          0.119639,       nan,       nan,              19.99, 0.0000,    True,    True, {"ff_name": "FF_UK000S_20210816_235416_290_0343296.fits"}
    UK002B,   False,    -1.367130,    50.815550,   22.00,   0.000000,   0.000000,   108518.43,   103268.45,          0.026899,     39.26,     40.46,              24.64, 1.0000,    True,    True, {"ff_name": "FF_UK002B_20210816_235412_218_0351744.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,     UK0001,       0,  0.000000, 2459443.496011352167,  24.11009,  55.79194,               57.49096,  54.04315,        57.54829,       54.02040,     24.11009,     +55.79194,      24.12910,      +55.75273,  3264185.93, -2432127.22,  5034461.09,      51.227373,       -0.842399,  109025.90,  134106.81,       0.00,              232.87,    -0.16,      0.00,           55659.17,    -27.49,     91.06,         146.30,  +6.07,  +5.43
  1,     UK0001,       0,  0.039836, 2459443.496011813171,  23.50828,  55.67444,               57.86647,  54.32659,        57.88700,       54.31839,     23.50828,     +55.67444,      23.51546,      +55.66048,  3263567.60, -2433271.59,  5032558.65,      51.215546,       -0.860681,  107660.62,  131950.14,    2304.61,             2537.47,    52.33,  57852.33,           55659.17,     -9.63,     32.02,          52.26,  +5.01,  +4.41
  2,     UK0001,       0,  0.079680, 2459443.496012274176,  22.95272,  55.56050,               58.22345,  54.58802,        58.20600,       54.59503,     22.95272,     +55.56050,      22.94693,      +55.57230,  3263010.09, -2434303.41,  5030843.31,      51.204876,       -0.877179,  106430.05,  130009.55,    4382.55,             4615.42,  -122.30,  52151.94,           55659.17,      8.01,    -26.74,          44.28,  +2.58,  +2.01
  3,     UK0001,       0,  0.119508, 2459443.496012735181,  22.32179,  55.41971,               58.64947,  54.88314,        58.57883,       54.91173,     22.32179,     +55.41971,      22.29676,      +55.46723,  3262388.77, -2435453.32,  5028931.66,      51.192976,       -0.895546,  105059.14,  127852.85,    6698.31,             6931.18,   -58.20,  58144.02,           55659.17,     31.64,   -106.24,         178.84,  +1.64,  +1.11
  4,     UK0001,       0,  0.159288, 2459443.496013195720,  21.62529,  55.31855,               59.03198,  55.22796,        58.98283,       55.24788,     21.62529,     +55.31855,      21.60781,      +55.35134,  3261748.82, -2436637.70,  5026962.72,      51.180712,       -0.914456,  103647.69,  125637.85,    9083.47,             9316.34,    78.02,  59958.96,           56649.42,     21.59,    -72.23,         123.76,  +1.92,  +1.42
  5,     UK0001,       0,  0.199112, 2459443.496013656724,  21.12426,  55.26893,               59.26893,  55.48427,        59.26896,       55.48426,     21.12426,     +55.26893,      21.12510,      +55.26891,  3261312.72, -2437444.81,  5025620.94,      51.172350,       -0.927394,  102686.13,  124130.31,   10708.90,            10941.76,  -548.00,  40815.11,           54670.66,     -0.01,      0.03,           0.06,  +6.30,  +5.83
  0,     UK000S,       1,  0.052679, 2459443.496011961717,  23.46265,  55.55678,               58.07174,  54.31342,        57.94075,       54.36645,     23.46265,     +55.55678,      23.41708,      +55.64608,  3263470.76, -2433450.82,  5032260.68,      51.213693,       -0.863571,  107446.83,  131611.87,       0.00,             2898.42,  -312.77,      0.00,           60167.14,     60.45,   -204.83,         334.70,  +4.03,  +3.43
  1,     UK000S,       1,  0.092367, 2459443.496012421325,  22.83383,  55.41950,               58.49114,  54.60727,        58.30749,       54.68216,     22.83383,     +55.41950,      22.76806,      +55.54398,  3262837.59, -2434622.66,  5030312.58,      51.201573,       -0.882286,  106049.39,  129409.97,    2359.92,             5258.34,  -196.60,  59461.69,           60167.14,     82.70,   -281.75,         468.02,  +2.22,  +1.66
  2,     UK000S,       1,  0.132031, 2459443.496012880467,  22.12390,  55.31976,               58.87588,  54.95868,        58.71399,       55.02478,     22.12390,     +55.31976,      22.06484,      +55.42861,  3262171.15, -2435856.07,  5028262.12,      51.188807,       -0.901972,  104579.12,  127099.06,    4843.83,             7742.26,    44.92,  62623.93,           60167.14,     71.48,   -242.57,         410.39,  +1.41,  +0.89
  3,     UK000S,       1,  0.171711, 2459443.496013339609,  21.47124,  55.18507,               59.30231,  55.27018,        59.10740,       55.35023,     21.47124,     +55.18507,      21.39833,      +55.31527,  3261557.95, -2436990.96,  5026375.44,      51.177053,       -0.920098,  103226.81,  124978.36,    7129.34,            10027.77,    87.14,  57598.57,           60167.14,     84.13,   -286.29,         492.47,  +2.65,  +2.17
  0,     UK002B,       0,  0.018451, 2459443.496011541225,  11.29161,  66.55913,               38.44095,  61.36248,        38.52043,       61.36875,     11.29161,     +66.55913,      11.29119,      +66.52053,  3263956.13, -2432552.53,  5033754.04,      51.222979,       -0.849200,  108518.43,  123304.50,       0.00,             1089.38,  -186.77,      0.00,           57771.55,    -59.62,     57.85,         138.96,  +4.61,  +4.16
  1,     UK002B,       0,  0.058027, 2459443.496011999436,   9.96384,  66.52233,               38.32892,  61.88966,        38.33246,       61.88993,      9.96384,     +66.52233,       9.96414,      +66.52064,  3263271.31, -2433819.96,  5031647.01,      51.209876,       -0.869428,  107006.57,  121007.15,    2552.44,             3641.82,   128.25,  64494.59,           57771.55,     -2.56,      2.49,           6.09,  +4.19,  +3.78
  2,     UK002B,       0,  0.097643, 2459443.496012457646,   8.79182,  66.54743,               38.08498,  62.34287,        38.16025,       62.34882,      8.79182,     +66.54743,       8.79531,      +66.51201,  3262689.38, -2434896.96,  5029856.58,      51.198735,       -0.886640,  105722.37,  119062.87,    4721.35,             5810.73,    57.49,  54748.36,           57771.55,    -52.86,     51.27,         127.58,  +1.76,  +1.38
  3,     UK002B,       0,  0.137251, 2459443.496012916323,   7.57897,  66.50998,               37.94062,  62.82280,        37.97561,       62.82555,      7.57897,     +66.50998,       7.58176,      +66.49379,  3262103.97, -2435980.40,  5028055.43,      51.187520,       -0.903953,  104430.95,  117115.15,    6903.25,             7992.63,     0.16,  55087.36,           57771.55,    -23.78,     23.09,          58.38,  +1.64,  +1.30
  4,     UK002B,       0,  0.176887, 2459443.496013374999,   6.44975,  66.49337,               37.74367,  63.26441,        37.79757,       63.26867,      6.44975,     +66.49337,       6.45495,      +66.46881,  3261576.84, -2436955.99,  5026433.57,      51.177415,       -0.919557,  103268.45,  115368.35,    8867.97,             9957.35,  -275.93,  49569.03,           55760.43,    -35.58,     34.52,          88.63,  +2.51,  +2.20

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.