Orbital Analysis for matched events on 20210813_224412.935_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 63.65° Bg 38.73° Vg 60.10km/s
mass 0.04280g, abs. mag -1.1
Path Details
------------
start -0.54° 52.69° 110.28km
end   -0.72° 52.56° 96.08km

Orbit Details
-------------
Semimajor axis -32.32A.U., eccentricity 1.03, inclination 113.51°, Period 1000000000.00Y, LA Sun 141.10°, 

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: 2459440.447371935938
Time: 2021-08-13 22:44:12.935265 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000S and UK000Z
 Convergence angle = 10.38208 deg
 R.A. =  47.73864  Dec = +58.59596 deg

Best intersection: Stations UK000S and UK000Z with Qconv = 10.38 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2152015.21 +/- 891.12 m
 Y =  -3301740.79 +/- 303.95 m
 Z =   5137391.99 +/- 438.20 m
 Vx =    21012.00 +/- 9580.63 m/s
 Vy =    23613.33 +/- 9816.71 m/s
 Vz =    52301.43 +/- 16776.74 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+7.833494e+05, -1.994248e+05, +3.944897e+05, +1.953363e+06, -1.095776e+06, -1.251422e+05
-1.994248e+05, +5.077075e+04, -1.004508e+05, -4.980413e+05, +2.793668e+05, +3.174219e+04
+3.944897e+05, -1.004508e+05, +1.990336e+05, +9.965651e+05, -5.587166e+05, -6.103686e+04
+1.953363e+06, -4.980413e+05, +9.965651e+05, +5.316870e+06, -2.971304e+06, -2.432791e+05
-1.095776e+06, +2.793668e+05, -5.587166e+05, -2.971304e+06, +1.660760e+06, +1.382143e+05
-1.251422e+05, +3.174219e+04, -6.103686e+04, -2.432791e+05, +1.382143e+05, +3.059841e+04

Timing offsets (from input data):
    UK000S: -0.001646 s
    UK000Z: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 22:44:12.935265 UTC
  Lon     = +-0.542133 +/- 0.0059 deg
  Lat     = +52.688922 +/- 0.0020 deg
  Lat geo = +52.506386 +/- 0.0020 deg
  Ht      =  110289.26 +/- 534.09 m

  JD dynamic   = 2459440.448172676843 
  LST apparent = 303.0955849071 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  48.33615 +/- 5.1242 deg
  Dec       = +58.85327 +/- 0.5685 deg
  Azimuth   =  38.52113 +/- 2.7712 deg
  Elevation = +36.74735 +/- 1.7092 deg
  Vavg      =  60.17438 +/- 2.6637 km/s
  Vinit     =  61.11083 +/- 19.0156 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  48.20040 +/- 5.1242 deg
  Dec       = +58.63123 +/- 0.5685 deg
  Azimuth   =  38.78327 +/- 2.7712 deg
  Elevation = +36.64689 +/- 1.7092 deg
  Vavg      =  60.31830 +/- 2.6637 km/s
  Vinit     =  61.25476 +/- 19.0156 km/s
Radiant (geocentric, J2000):
  R.A.   =  48.58812 +/- 5.1463 deg
  Dec    = +58.44295 +/- 0.5374 deg
  Vg     =  60.09507 +/- 1.7446 km/s
  Vinf   =  61.11083 +/- 1.7176 km/s
  Zc     =  53.39555 +/- 1.7150 deg
  Zg     =  53.87850 +/- 1.7516 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  63.65473 +/- 3.5344 deg
  Bg     = +38.73341 +/- 0.5569 deg
  Vh     =  42.17619 +/- 1.5991 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  82.21775 +/- 8.9714 deg
  Bh     = +63.06696 +/- 0.9086 deg
  Vh_x   =  -2.58680 +/- 2.9571 km/s
  Vh_y   = -18.92771 +/- 1.0041 km/s
  Vh_z   = -37.60161 +/- 1.5294 km/s
Orbit:
  La Sun = 141.098269 +/- -0.0000 deg
  a      = -32.321397 +/- 36.7466 AU
  e      =   1.029651 +/- 0.1618
  i      = 113.505878 +/- 0.7938 deg
  peri   = 153.323238 +/- 8.0497 deg
  node   = 141.096858 +/- 0.0001 deg
  Pi     = 294.420096 +/- 8.0496 deg
  q      =   0.958370 +/- 0.0217 AU
  f      =  26.672679 +/- 8.0497 deg
  M      =        nan +/- nan deg
  Q      = -65.601164 +/- 73.4889 AU
  n      =   0.005364 +/- 0.1148 deg/day
  T      = 1000000000.000000 +/- 304543438.6998 years
  Last perihelion JD = NaN 
  Tj     =  -0.648690 +/- 0.8719
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.308551e-04, -5.579019e-05, -4.031998e-03, +6.849254e-10, -1.561584e-04, -9.174932e-06
q   , -5.579019e-05, +8.137266e-04, +1.348104e-01, -1.537133e-08, +3.662847e-03, +2.009228e-04
Tp  , -4.031998e-03, +1.348104e-01, +2.245370e+01, -2.555042e-06, +6.090052e-01, +3.339256e-02
node, +6.849254e-10, -1.537133e-08, -2.555042e-06, +2.909645e-13, -6.934566e-08, -3.802916e-09
peri, -1.561584e-04, +3.662847e-03, +6.090052e-01, -6.934566e-08, +1.652739e-02, +9.063433e-04
i   , -9.174932e-06, +2.009228e-04, +3.339256e-02, -3.802916e-09, +9.063433e-04, +4.970446e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.121280
 a2 = 21.706646

Mean time residuals from time vs. length:
  Station with reference time: UK000Z
  Avg. res. = 8.004e-06 s
  Stddev    = 2.83e-03 s

Begin point on the trajectory:
  Lon =    -0.542189 +/- 0.0076 deg
  Lat =    52.688879 +/- 0.0024 deg
  Ht  = 110284.65 +/- 708.62 m
End point on the trajectory:
  Lon =    -0.716291 +/- 0.0075 deg
  Lat =    52.556737 +/- 0.0038 deg
  Ht  = 96080.32 +/- 712.02 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
    UK000S,   False,    -1.778230,    50.857470,   24.00,   0.000000,   0.000000,   108034.42,    99281.47,          0.019057,     79.46,      2.65,              18.53, 1.0000,    True,    True, {"ff_name": "FF_UK000S_20210813_224407_842_0232448.fits"}
    UK000Z,   False,    -1.740490,    53.069201,  230.00,   0.130170,  21.533674,   110284.65,    96080.32,          0.005389,     12.90,      1.76,              53.71, 1.0000,    True,    True, {"ff_name": "FF_UK000Z_20210813_224411_976_0221184.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,     UK000S,       1,  0.020728, 2459440.447372648865,  79.99856,  59.36509,               22.09882,  25.32600,        22.14762,       25.27284,     79.99856,     +59.36509,      79.97062,      +59.29749,  2151490.87, -3302330.05,  5136086.82,      52.680475,       -0.553454,  109376.96,  247119.38,       0.00,             1525.00,   200.45,      0.00,           61900.30,     11.14,    297.76,         248.71,  +5.12,  +3.16
  1,     UK000S,       0,  0.060856, 2459440.447373113129,  80.26223,  59.28925,               22.00608,  25.19635,        22.02139,       25.17978,     80.26223,     +59.28925,      80.25339,      +59.26815,  2150719.00, -3303197.48,  5134165.55,      52.668035,       -0.569905,  108034.42,  244959.44,    2244.88,             3769.88,    -6.93,  55942.94,           61900.30,      3.19,     92.28,          77.75,  +2.53,  +0.58
  2,     UK000S,       0,  0.100968, 2459440.447373577394,  80.57817,  59.25739,               21.86412,  25.09359,        21.88078,       25.07557,     80.57817,     +59.25739,      80.56851,      +59.23446,  2149871.95, -3304149.39,  5132057.15,      52.654374,       -0.587939,  106561.68,  242591.41,    4708.41,             6233.41,     5.32,  61416.26,           61900.30,      3.46,     99.43,          84.59,  +2.33,  +0.41
  3,     UK000S,       0,  0.141116, 2459440.447374042124,  80.92293,  59.18838,               21.72595,  24.95144,        21.72115,       24.95660,     80.92293,     +59.18838,      80.92639,      +59.19496,  2148926.38, -3305212.02,  5129703.52,      52.639114,       -0.608048,  104918.34,  239950.80,    7458.48,             8983.48,   301.92,  68498.37,           61900.30,     -0.93,    -28.26,          24.30,  +2.06,  +0.16
  4,     UK000S,       0,  0.181224, 2459440.447374506388,  81.17686,  59.13605,               21.62438,  24.84563,        21.60277,       24.86882,     81.17686,     +59.13605,      81.19111,      +59.16562,  2148241.67, -3305981.51,  5127999.18,      52.628057,       -0.622654,  103728.79,  238039.20,    9449.89,            10974.89,  -157.71,  49651.09,           60095.61,     -4.00,   -126.12,         109.34,  +2.10,  +0.22
  5,     UK000S,       0,  0.221324, 2459440.447374970652,  81.51003,  59.13436,               21.45724,  24.76690,        21.46095,       24.76291,     81.51003,     +59.13436,      81.50851,      +59.12928,  2147431.45, -3306892.04,  5125982.43,      52.614965,       -0.639903,  102321.69,  235779.74,   11806.33,            13331.33,  -251.81,  58764.10,           59389.82,      0.73,     21.50,          18.82,  +1.52,  -0.34
  6,     UK000S,       0,  0.261460, 2459440.447375434916,  81.89364,  59.09756,               21.28162,  24.64577,        21.29132,       24.63533,     81.89364,     +59.09756,      81.88835,      +59.08429,  2146477.68, -3307963.89,  5123608.38,      52.599544,       -0.660175,  100666.01,  233123.29,   14580.25,            16105.25,    69.36,  69113.02,           60179.83,      1.92,     55.55,          49.18,  +1.57,  -0.27
  7,     UK000S,       0,  0.301596, 2459440.447375899646,  82.20285,  59.02732,               21.15936,  24.51220,        21.14621,       24.52628,     82.20285,     +59.02732,      82.21275,      +59.04525,  2145679.78, -3308860.57,  5121622.31,      52.586634,       -0.677158,   99281.47,  230902.55,   16900.84,            18425.84,   -62.79,  57818.24,           60312.13,     -2.45,    -74.44,          66.54,  +1.63,  -0.19
  0,     UK000Z,       0,  0.000000, 2459440.447371935938, 341.51451,  25.61305,              117.20078,  49.72264,       117.20468,       49.73002,    341.51451,     +25.61305,     341.50715,      +25.61750,  2152012.57, -3301743.77,  5137385.40,      52.688879,       -0.542189,  110284.65,  143368.26,       0.00,                7.70,   -50.18,      0.00,           59720.04,      2.64,    -19.34,          28.08,  +3.69,  +2.91
  1,     UK000Z,       0,  0.039972, 2459440.447372398805, 340.87049,  24.79601,              118.66737,  49.40286,       118.66593,       49.40028,    340.87049,     +24.79601,     340.87289,      +24.79445,  2150988.88, -3302894.19,  5134837.32,      52.672385,       -0.563954,  108503.78,  141735.49,    2977.27,             2984.97,   484.36,  74483.80,           59720.04,     -0.92,      6.73,           9.88,  +2.59,  +1.83
  2,     UK000Z,       0,  0.079952, 2459440.447372861207, 340.42237,  24.22200,              119.68549,  49.16895,       119.67983,       49.15916,    340.42237,     +24.22200,     340.43192,      +24.21609,  2150284.69, -3303685.56,  5133084.50,      52.661031,       -0.578976,  107279.22,  140636.04,    5025.33,             5033.03,    89.21,  51227.10,           59720.04,     -3.48,     25.46,          37.69,  +1.28,  +0.54
  3,     UK000Z,       0,  0.119948, 2459440.447373324540, 339.93960,  23.57115,              120.80315,  48.88375,       120.80035,       48.87909,    339.93960,     +23.57115,     339.94437,      +23.56834,  2149510.64, -3304555.44,  5131157.80,      52.648544,       -0.595468,  105933.65,  139453.03,    7276.55,             7284.25,  -103.76,  56286.16,           59720.04,     -1.65,     12.08,          18.04,  +1.35,  +0.63
  4,     UK000Z,       0,  0.159948, 2459440.447373787407, 339.39149,  22.82175,              122.07037,  48.54272,       122.07105,       48.54381,    339.39149,     +22.82175,     339.39084,      +22.82241,  2148637.38, -3305536.81,  5128984.14,      52.634448,       -0.614051,  104416.19,  138151.28,    9816.33,             9824.03,    -8.41,  63494.56,           59848.77,      0.39,     -2.82,           4.25,  +1.26,  +0.56
  5,     UK000Z,       0,  0.199940, 2459440.447374250274, 338.82821,  22.05912,              123.35427,  48.18905,       123.35274,       48.18669,    338.82821,     +22.05912,     338.83109,      +22.05770,  2147760.90, -3306521.80,  5126802.47,      52.620290,       -0.632697,  102893.78,  136879.90,   12365.46,            12373.16,    96.78,  63741.12,           60441.67,     -0.83,      6.07,           9.24,  +1.81,  +1.13
  6,     UK000Z,       0,  0.239940, 2459440.447374713141, 338.32234,  21.35773,              124.50987,  47.84936,       124.50910,       47.84821,    338.32234,     +21.35773,     338.32422,      +21.35704,  2146973.41, -3307406.78,  5124842.32,      52.607561,       -0.649465,  101526.48,  135767.82,   14655.77,            14663.47,   -57.34,  57257.67,           60312.14,     -0.41,      2.96,           4.54,  +0.70,  +0.04
  7,     UK000Z,       0,  0.279948, 2459440.447375176009, 337.78603,  20.60401,              125.73109,  47.47207,       125.73141,       47.47252,    337.78603,     +20.60401,     337.78649,      +20.60428,  2146143.21, -3308339.76,  5122775.85,      52.594134,       -0.667130,  100085.56,  134628.20,   17070.31,            17078.01,   -87.73,  60351.32,           60261.44,      0.16,     -1.16,           1.80,  +0.77,  +0.12
  8,     UK000Z,       0,  0.319964, 2459440.447375639342, 337.23766,  19.81497,              126.98044,  47.06136,       126.98504,       47.06775,    337.23766,     +19.81497,     337.23241,      +19.81886,  2145293.38, -3309294.80,  5120660.54,      52.580380,       -0.685206,   98611.18,  133497.14,   19541.92,            19549.62,   -61.53,  61765.55,           60338.13,      2.25,    -16.43,          25.62,  +0.70,  +0.07
  9,     UK000Z,       0,  0.359972, 2459440.447376102209, 336.75027,  19.11716,              128.07643,  46.69147,       128.08120,       46.69790,    336.75027,     +19.11716,     336.74512,      +19.12110,  2144551.50, -3310128.53,  5118813.89,      52.568366,       -0.701005,   97324.52,  132538.91,   21699.61,            21707.31,  -348.76,  53931.42,           60027.57,      2.27,    -16.54,          25.97,  +1.17,  +0.56
 10,     UK000Z,       0,  0.399980, 2459440.447376565542, 336.26780,  18.43646,              129.14328,  46.32688,       129.14196,       46.32515,    336.26780,     +18.43646,     336.27094,      +18.43540,  2143833.85, -3310935.03,  5117027.58,      52.556737,       -0.716291,   96080.32,  131638.98,   23786.79,            23794.49,  -706.50,  52169.29,           59500.88,     -0.61,      4.45,           7.04,  +4.00,  +3.40

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.