Orbital Analysis for matched events on 20210813_234327.780_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 47.96° Bg 34.22° Vg 60.89km/s
mass 0.02300g, abs. mag -1.0
Path Details
------------
start 1.29° 51.18° 108.12km
end   1.12° 51.12° 93.99km

Orbit Details
-------------
Semimajor axis 6.64A.U., eccentricity 0.85, inclination 121.35°, Period 17.09Y, LA Sun 141.14°, last Perihelion 2004-07-17

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: 2459440.488515976816
Time: 2021-08-13 23:43:27.780397 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000F and UK002B
 Convergence angle = 42.95180 deg
 R.A. =  31.73936  Dec = +48.83376 deg

Best intersection: Stations UK000F and UK002B with Qconv = 42.95 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3110718.18 +/- 106.83 m
 Y =  -2631075.62 +/- 68.02 m
 Z =   5030352.89 +/- 67.78 m
 Vx =    34113.84 +/- 940.64 m/s
 Vy =    20811.35 +/- 710.91 m/s
 Vz =    47260.36 +/- 1228.33 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+6.984286e+03, +3.101676e+03, +1.727959e+03, +1.520774e+04, +7.519637e+03, -6.931890e+03
+3.101676e+03, +2.906305e+03, +1.592687e+03, +1.767365e+04, +1.592573e+04, +5.225073e+03
+1.727959e+03, +1.592687e+03, +3.725451e+03, +1.785322e+04, +1.328910e+04, +2.087239e+04
+1.520774e+04, +1.767365e+04, +1.785322e+04, +2.389104e+05, +1.855041e+05, +1.511677e+05
+7.519637e+03, +1.592573e+04, +1.328910e+04, +1.855041e+05, +1.831780e+05, +1.130551e+05
-6.931890e+03, +5.225073e+03, +2.087239e+04, +1.511677e+05, +1.130551e+05, +2.771190e+05

Timing offsets (from input data):
    UK000F: 0.000000 s
    UK002B: 0.000216 s
    UK002N: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 23:43:27.780397 UTC
  Lon     = ++1.285008 +/- 0.0016 deg
  Lat     = +51.180121 +/- 0.0004 deg
  Lat geo = +50.995164 +/- 0.0004 deg
  Ht      =  108054.24 +/- 69.67 m

  JD dynamic   = 2459440.489316717722 
  LST apparent = 319.7751344565 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  31.38552 +/- 0.2628 deg
  Dec       = +49.78394 +/- 0.5277 deg
  Azimuth   =  62.42377 +/- 0.5856 deg
  Elevation = +46.27280 +/- 0.3730 deg
  Vavg      =  58.95020 +/- 0.9821 km/s
  Vinit     =  61.89029 +/- 1.1166 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  31.51897 +/- 0.2628 deg
  Dec       = +49.58515 +/- 0.5277 deg
  Azimuth   =  62.60684 +/- 0.5856 deg
  Elevation = +46.09699 +/- 0.3730 deg
  Vavg      =  59.13267 +/- 0.9821 km/s
  Vinit     =  62.07277 +/- 1.1166 km/s
Radiant (geocentric, J2000):
  R.A.   =  31.53538 +/- 0.2552 deg
  Dec    = +49.49009 +/- 0.5270 deg
  Vg     =  60.88727 +/- 1.1338 km/s
  Vinf   =  61.89029 +/- 1.1166 km/s
  Zc     =  43.81307 +/- 0.3715 deg
  Zg     =  44.18952 +/- 0.3657 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  47.96451 +/- 0.2336 deg
  Bg     = +34.22399 +/- 0.5174 deg
  Vh     =  40.22065 +/- 0.9016 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  42.67257 +/- 0.4524 deg
  Bh     = +58.36754 +/- 1.2367 deg
  Vh_x   = -15.50947 +/- 0.9023 km/s
  Vh_y   = -14.29799 +/- 0.8157 km/s
  Vh_z   = -34.24507 +/- 0.4159 km/s
Orbit:
  La Sun = 141.137785 +/- -0.0000 deg
  a      =   6.635629 +/- 15.2273 AU
  e      =   0.848324 +/- 0.0848
  i      = 121.352984 +/- 1.2273 deg
  peri   = 189.652944 +/- 0.6591 deg
  node   = 141.136199 +/- 0.0001 deg
  Pi     = 330.789143 +/- 0.6591 deg
  q      =   1.006465 +/- 0.0008 AU
  f      = 350.342833 +/- 0.6591 deg
  M      = 359.578568 +/- nan deg
  Q      =  12.264792 +/- 30.4546 AU
  n      =   0.057661 +/- 0.0257 deg/day
  T      =  17.093215 +/- 249443806.0080 years
  Last perihelion JD = 2453204.392579 (2004-07-17 21:25:18.846761) +/- 42048.6407 days
  Tj     =   0.162134 +/- 0.4726
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +3.398935e-03, +2.303298e-05, -1.789138e+03, -4.064228e-08, -4.662229e-04, +4.562987e-04
q   , +2.303298e-05, +6.739506e-07, +1.930937e+00, +3.746185e-11, -9.745037e-06, -4.094249e-07
Tp  , -1.789138e+03, +1.930937e+00, +1.694738e+09, +2.765944e-02, +6.516527e+01, -3.099691e+02
node, -4.064228e-08, +3.746185e-11, +2.765944e-02, +1.334177e-12, +1.666967e-09, -1.504061e-08
peri, -4.662229e-04, -9.745037e-06, +6.516527e+01, +1.666967e-09, +1.478075e-04, -1.884260e-05
i   , +4.562987e-04, -4.094249e-07, -3.099691e+02, -1.504061e-08, -1.884260e-05, +1.695742e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 29.424731
 a2 = 10.662068

Mean time residuals from time vs. length:
  Station with reference time: UK000F
  Avg. res. = 3.188e-06 s
  Stddev    = 1.79e-03 s

Begin point on the trajectory:
  Lon =     1.285781 +/- 0.0014 deg
  Lat =    51.180374 +/- 0.0003 deg
  Ht  = 108119.04 +/- 42.60 m
End point on the trajectory:
  Lon =     1.115601 +/- 0.0048 deg
  Lat =    51.124778 +/- 0.0006 deg
  Ht  = 93988.70 +/- 194.53 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
    UK000F,   False,    -1.306160,    51.883100,   80.00,   0.000000,   0.000000,   108119.04,    99415.46,          0.021779,     82.32,     13.49,              42.68, 1.0000,    True,    True, {"ff_name": "FF_UK000F_20210813_234319_140_0306176.fits"}
    UK002B,   False,    -1.367130,    50.815550,   22.00,  27.847202,  10.776909,   107464.92,    93988.70,          0.014367,     33.47,     39.75,              19.25, 1.0000,    True,    True, {"ff_name": "FF_UK002B_20210813_234325_023_0326144.fits"}
    UK002N,    True,    -0.727590,    51.263100,   57.00,   0.000000,   0.000000,   110391.30,    95300.44,          0.300017,       nan,       nan,              24.23, 0.0000,    True,    True, {"ff_name": "FF_UK002N_20210813_234327_666_0327168.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,     UK000F,       0,  0.000000, 2459440.488515976816,  13.09786,   9.06738,              112.46258,  27.74949,       112.47666,       27.76568,     13.09786,      +9.06738,      13.07808,       +9.07340,  3110767.62, -2631045.46,  5030421.38,      51.180374,       +1.285781,  108119.04,  225338.66,       0.00,               89.70,     0.19,      0.00,           63344.44,    -13.06,    -79.29,          73.56,  +4.36,  +2.60
  1,     UK000F,       0,  0.080684, 2459440.488516910467,  12.82055,   8.18331,              113.28849,  27.18403,       113.30409,       27.20181,     12.82055,      +8.18331,      12.79911,       +8.18994,  3107900.91, -2632794.31,  5026449.92,      51.165648,       +1.240620,  104361.53,  221574.06,    5200.87,             5111.17,    28.11,  64459.77,           63344.44,    -14.17,    -86.04,          81.18,  +0.53,  -1.20
  2,     UK000F,       0,  0.121000, 2459440.488517377060,  12.67191,   7.77258,              113.68776,  26.93118,       113.69090,       26.93474,     12.67191,      +7.77258,      12.66805,       +7.77391,  3106583.84, -2633597.80,  5024625.29,      51.158871,       +1.219850,  102635.84,  219863.56,    7590.34,             7500.64,   -77.60,  59268.41,           63344.44,     -2.81,    -17.15,          16.30,  +0.14,  -1.57
  3,     UK000F,       0,  0.161372, 2459440.488517844584,  12.53406,   7.29544,              114.11784,  26.61668,       114.12892,       26.62921,     12.53406,      +7.29544,      12.51935,       +7.30012,  3105108.63, -2634497.76,  5022581.58,      51.151272,       +1.196600,  100703.44,  217964.15,   10266.70,            10177.00,   100.13,  66292.56,           63344.44,     -9.85,    -59.93,          57.47,  +0.63,  -1.06
  4,     UK000F,       0,  0.201596, 2459440.488518310245,  12.38458,   6.98981,              114.44810,  26.44904,       114.42436,       26.42224,     12.38458,      +6.98981,      12.41837,       +6.97975,  3104125.19, -2635097.71,  5021219.14,      51.146200,       +1.181042,   99415.46,  216703.98,   12050.89,            11961.19,  -605.16,  44356.27,           60639.57,     20.83,    127.70,         123.16,  +3.48,  +1.80
  0,     UK002B,       0,  0.008596, 2459440.488516073674,  37.56342,  29.77370,               76.72048,  28.42322,        76.72860,       28.42797,     37.56342,     +29.77370,      37.55377,      +29.77200,  3110268.68, -2631349.84,  5029730.16,      51.177814,       +1.277947,  107464.92,  219658.43,       0.00,              815.50,   194.01,      0.00,           59437.42,    -25.17,    -21.16,          30.88,  +3.11,  +1.40
  1,     UK002B,       0,  0.048720, 2459440.488516537938,  37.59801,  29.56935,               76.86073,  28.25762,        76.85888,       28.25653,     37.59801,     +29.56935,      37.60041,      +29.56974,  3109029.21, -2632105.98,  5028013.04,      51.171449,       +1.258400,  105840.21,  217544.11,    2248.67,             3064.17,   -40.61,  56043.06,           59437.42,      5.68,      4.78,           7.04,  +1.73,  +0.04
  2,     UK002B,       0,  0.088880, 2459440.488517002668,  37.67611,  29.35225,               76.98021,  28.05597,        77.00129,       28.06830,     37.67611,     +29.35225,      37.65139,      +29.34784,  3107697.33, -2632918.51,  5026167.88,      51.164601,       +1.237403,  104094.76,  215276.08,    4665.02,             5480.51,  -109.78,  60167.94,           59437.42,    -64.21,    -53.92,          80.34,  +1.72,  +0.06
  3,     UK002B,       0,  0.129020, 2459440.488517467398,  37.70394,  29.11482,               77.15043,  27.87060,        77.15026,       27.87051,     37.70394,     +29.11482,      37.70467,      +29.11485,  3106328.77, -2633753.40,  5024271.92,      51.157558,       +1.215827,  102301.68,  212949.45,    7147.89,             7963.39,  -111.18,  61855.41,           59437.42,      0.49,      0.41,           0.62,  +1.31,  -0.33
  4,     UK002B,       0,  0.169188, 2459440.488517932128,  37.76498,  28.86614,               77.30558,  27.65649,        77.30913,       27.65857,     37.76498,     +28.86614,      37.76146,      +28.86540,  3104896.44, -2634627.20,  5022287.62,      51.150178,       +1.193248,  100425.53,  210518.89,    9746.46,            10561.96,     1.38,  64692.47,           60755.20,    -10.61,     -8.92,          13.58,  +1.28,  -0.34
  5,     UK002B,       0,  0.209308, 2459440.488518396858,  37.79527,  28.66490,               77.44396,  27.49476,        77.43529,       27.48969,     37.79527,     +28.66490,      37.80645,      +28.66670,  3103776.91, -2635310.18,  5020736.65,      51.144403,       +1.175560,   98959.41,  208619.81,   11777.55,            12593.04,  -450.57,  50625.34,           59685.48,     25.66,     21.61,          33.17,  +1.35,  -0.25
  6,     UK002B,       0,  0.249472, 2459440.488518861588,  37.86795,  28.43301,               77.57618,  27.28484,        77.58415,       27.28949,     37.86795,     +28.43301,      37.85954,      +28.43135,  3102478.19, -2636102.47,  5018937.44,      51.137698,       +1.155062,   97259.01,  206421.76,   14133.72,            14949.22,  -580.16,  58663.84,           59193.84,    -23.37,    -19.66,          30.52,  +0.93,  -0.64
  7,     UK002B,       0,  0.289652, 2459440.488519326784,  37.93467,  28.16472,               77.74048,  27.05233,        77.75385,       27.06012,     37.93467,     +28.16472,      37.92006,      +28.16195,  3101025.80, -2636988.51,  5016925.34,      51.130191,       +1.132153,   95357.89,  203969.21,   16768.69,            17584.19,  -431.94,  65579.11,           59521.58,    -38.76,    -32.58,          51.20,  +1.60,  +0.05
  8,     UK002B,       0,  0.329756, 2459440.488519790582,  37.92932,  27.95843,               77.90628,  26.90828,        77.87800,       26.89175,     37.92932,     +27.95843,      37.96419,      +27.96425,  3099979.58, -2637626.76,  5015475.93,      51.124778,       +1.115601,   93988.70,  202202.62,   18666.78,            19482.27, -1015.90,  47329.05,           58862.61,     81.32,     68.62,         108.54,  +2.93,  +1.40
  0,     UK002N,       1, -0.074355, 2459440.488515116274,  21.41126,  26.37135,               92.30064,  36.53583,        92.50226,       36.81317,     21.41126,     +26.37135,      21.06550,      +26.45705,  3112500.48, -2629988.32,  5032822.04,      51.189259,       +1.313176,  110391.30,  181423.57,       0.00,             3233.50,  7745.86,     -0.00,           51532.82,   -248.25,   -985.75,        1155.73,  +5.06,  +3.77
  1,     UK002N,       1, -0.034199, 2459440.488515581004,  21.32618,  26.15982,               92.55210,  36.43737,        92.74661,       36.70409,     21.32618,     +26.15982,      20.99404,      +26.24234,  3111566.74, -2630557.95,  5031528.46,      51.184473,       +1.298415,  109166.82,  179875.87,    1694.01,             1539.49,  3566.58,  42185.84,           51532.82,   -236.35,   -941.16,        1112.75,  +2.28,  +1.01
  2,     UK002N,       1,  0.006009, 2459440.488516046200,  21.21201,  25.87980,               92.88554,  36.30755,        93.06903,       36.55817,     21.21201,     +25.87980,      20.90038,      +25.95748,  3110354.34, -2631297.58,  5029848.83,      51.178254,       +1.279296,  107577.21,  177873.24,    3893.59,              660.09,   198.70,  54705.00,           51532.82,   -219.12,   -876.01,        1047.14,  +1.21,  -0.04
  3,     UK002N,       1,  0.046241, 2459440.488516511861,  21.12314,  25.57537,               93.21878,  36.14378,        93.40939,       36.40249,     21.12314,     +25.57537,      20.80167,      +25.65548,  3109098.51, -2632063.71,  5028109.05,      51.171805,       +1.259493,  105931.04,  175804.37,    6171.94,             2938.44,   -12.92,  56630.30,           51532.82,   -224.21,   -895.65,        1083.27,  +0.89,  -0.34
  4,     UK002N,       1,  0.086481, 2459440.488516977523,  21.02596,  25.25964,               93.56731,  35.97644,        93.76221,       36.23938,     21.02596,     +25.25964,      20.69949,      +25.34102,  3107821.92, -2632842.50,  5026340.49,      51.165242,       +1.239360,  104258.01,  173707.00,    8487.98,             5254.48,  -187.34,  57555.63,           53354.27,   -225.64,   -901.37,        1103.35,  +0.68,  -0.52
  5,     UK002N,       1,  0.126753, 2459440.488517443649,  20.91023,  24.90233,               93.96506,  35.78987,        94.16107,       36.05263,     20.91023,     +24.90233,      20.58429,      +24.98366,  3106408.49, -2633704.77,  5024382.36,      51.157968,       +1.217083,  102406.11,  171392.62,   11052.27,             7818.77,  -115.50,  63674.12,           55350.93,   -222.80,   -890.87,        1105.15,  +0.51,  -0.66
  6,     UK002N,       1,  0.167021, 2459440.488517909776,  20.78870,  24.54512,               94.36604,  35.60617,        94.55947,       35.86393,     20.78870,     +24.54512,      20.46931,      +24.62495,  3105027.28, -2634547.38,  5022468.88,      51.150852,       +1.195304,  100596.88,  169137.95,   13558.08,            10324.58,  -101.88,  62228.53,           56801.23,   -215.80,   -864.45,        1086.56,  +0.44,  -0.70
  7,     UK002N,       1,  0.207317, 2459440.488518376369,  20.65734,  24.15672,               94.79986,  35.40501,        94.99031,       35.65721,     20.65734,     +24.15672,      20.34519,      +24.23487,  3103566.57, -2635438.50,  5020445.25,      51.143318,       +1.172275,   98684.01,  166762.08,   16208.14,            12974.64,    54.24,  65764.82,           58153.48,   -208.30,   -836.03,        1065.69,  +0.42,  -0.69
  8,     UK002N,       1,  0.247577, 2459440.488518842496,  20.54764,  23.81290,               95.17713,  35.22203,        95.36851,       35.47398,     20.54764,     +23.81290,      20.23606,      +23.89098,  3102311.94, -2636203.90,  5018707.11,      51.136840,       +1.152466,   97041.38,  164726.90,   18484.34,            15250.84,  -161.26,  56537.45,           58676.27,   -205.85,   -826.88,        1066.99,  +0.67,  -0.41
  9,     UK002N,       1,  0.287849, 2459440.488519308623,  20.39840,  23.44631,               95.60454,  35.04622,        95.77775,       35.27325,     20.39840,     +23.44631,      20.11818,      +23.51687,  3100981.89, -2637015.30,  5016864.51,      51.129964,       +1.131472,   95300.44,  162577.18,   20897.34,            17663.84,  -240.71,  59917.61,           59010.07,   -182.48,   -737.00,         963.29,  +1.52,  +0.46

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.