Orbital Analysis for matched events on 20210810_213828.176_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 62.34° Bg 37.48° Vg 58.37km/s
mass 0.02637g, abs. mag -1.1
Path Details
------------
start -3.24° 51.34° 106.94km
end   -3.35° 51.21° 98.64km

Orbit Details
-------------
Semimajor axis 7.05A.U., eccentricity 0.87, inclination 113.60°, Period 18.72Y, LA Sun 138.17°, last Perihelion 2021-07-17

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: 2459437.401715010405
Time: 2021-08-10 21:38:28.176899 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0006 and UK0020
 Convergence angle = 13.51069 deg
 R.A. =  46.76797  Dec = +58.49371 deg
Intersection 2 - Stations: UK0006 and UK003H
 Convergence angle = 4.63003 deg
 R.A. =  47.10142  Dec = +56.57952 deg
Intersection 3 - Stations: UK0020 and UK003H
 Convergence angle = 8.88460 deg
 R.A. =  46.12483  Dec = +59.44213 deg

Best intersection: Stations UK0006 and UK0020 with Qconv = 13.51 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =    772079.59 +/- 232.64 m
 Y =  -3985406.33 +/- 359.21 m
 Z =   5040696.15 +/- 186.13 m
 Vx =    21636.82 +/- 1494.14 m/s
 Vy =    23462.66 +/- 2271.83 m/s
 Vz =    50119.14 +/- 2563.46 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+4.247276e+04, +6.814587e+04, -3.630922e+04, +9.005443e+04, +1.951018e+05, -3.979751e+05
+6.814587e+04, +1.119148e+05, -6.733147e+04, +1.612804e+05, +3.518428e+05, -6.761631e+05
-3.630922e+04, -6.733147e+04, +7.527470e+04, -1.575196e+05, -3.292611e+05, +5.074356e+05
+9.005443e+04, +1.612804e+05, -1.575196e+05, +7.520469e+05, +1.350890e+06, -1.359603e+06
+1.951018e+05, +3.518428e+05, -3.292611e+05, +1.350890e+06, +2.544226e+06, -2.890790e+06
-3.979751e+05, -6.761631e+05, +5.074356e+05, -1.359603e+06, -2.890790e+06, +5.038776e+06

Timing offsets (from input data):
    UK0006: 0.011849 s
    UK0020: 0.000000 s
    UK003H: 0.008141 s
    UK003J: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-10 21:38:28.176899 UTC
  Lon     = +-3.235443 +/- 0.0042 deg
  Lat     = +51.338679 +/- 0.0015 deg
  Lat geo = +51.153913 +/- 0.0015 deg
  Ht      =  106916.79 +/- 315.44 m

  JD dynamic   = 2459437.402515751310 
  LST apparent = 280.9639096045 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  47.31834 +/- 0.6712 deg
  Dec       = +57.51069 +/- 2.4785 deg
  Azimuth   =  29.15179 +/- 1.1085 deg
  Elevation = +27.36962 +/- 2.2932 deg
  Vavg      =  58.62430 +/- 0.6579 km/s
  Vinit     =  59.41865 +/- 1.1973 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  47.00566 +/- 0.6712 deg
  Dec       = +57.31681 +/- 2.4785 deg
  Azimuth   =  29.43174 +/- 1.1085 deg
  Elevation = +27.30555 +/- 2.2932 deg
  Vavg      =  58.75296 +/- 0.6579 km/s
  Vinit     =  59.54730 +/- 1.1973 km/s
Radiant (geocentric, J2000):
  R.A.   =  47.55198 +/- 0.6697 deg
  Dec    = +56.91718 +/- 2.5233 deg
  Vg     =  58.37298 +/- 1.2201 km/s
  Vinf   =  59.41865 +/- 1.1973 km/s
  Zc     =  62.79178 +/- 2.2913 deg
  Zg     =  63.41261 +/- 2.3383 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  62.33707 +/- 0.5170 deg
  Bg     = +37.48443 +/- 2.5181 deg
  Vh     =  40.30693 +/- 1.9362 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  83.60412 +/- 2.0582 deg
  Bh     = +61.80274 +/- 2.9888 deg
  Vh_x   =  -2.12160 +/- 0.8601 km/s
  Vh_y   = -18.92683 +/- 0.9110 km/s
  Vh_z   = -35.52354 +/- 2.5162 km/s
Orbit:
  La Sun = 138.174337 +/- 0.0000 deg
  a      =   7.051150 +/- 2.5903 AU
  e      =   0.867859 +/- 0.1321
  i      = 113.597888 +/- 3.2985 deg
  peri   = 145.707435 +/- 9.1399 deg
  node   = 138.172374 +/- 0.0003 deg
  Pi     = 283.879809 +/- 9.1401 deg
  q      =   0.931749 +/- 0.0264 AU
  f      =  34.288346 +/- 9.1398 deg
  M      =   1.275983 +/- 8.2543 deg
  Q      =  13.170551 +/- 5.1648 AU
  n      =   0.052640 +/- 0.1542 deg/day
  T      =  18.723652 +/- 10.6654 years
  Last perihelion JD = 2459413.162612 (2021-07-17 15:54:09.669519) +/- 7.3128 days
  Tj     =   0.275081 +/- 0.8268
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.221130e-02, +3.357176e-03, +9.716616e-01, +5.589738e-07, +2.047524e-02, -6.552247e-03
q   , +3.357176e-03, +5.508993e-04, +1.572378e-01, +8.833818e-08, +3.344856e-03, -1.022970e-03
Tp  , +9.716616e-01, +1.572378e-01, +4.514762e+01, +2.468592e-05, +9.581725e-01, -2.862563e-01
node, +5.589738e-07, +8.833818e-08, +2.468592e-05, +2.298606e-11, +5.267216e-07, -2.662417e-07
peri, +2.047524e-02, +3.344856e-03, +9.581725e-01, +5.267216e-07, +2.036074e-02, -6.099520e-03
i   , -6.552247e-03, -1.022970e-03, -2.862563e-01, -2.662417e-07, -6.099520e-03, +3.090033e-03

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 10.057847
 a2 = 13.490748

Mean time residuals from time vs. length:
  Station with reference time: UK0020
  Avg. res. = 3.630e-06 s
  Stddev    = 1.91e-03 s

Begin point on the trajectory:
  Lon =    -3.235172 +/- 0.0040 deg
  Lat =    51.338983 +/- 0.0014 deg
  Ht  = 106937.20 +/- 329.21 m
End point on the trajectory:
  Lon =    -3.346800 +/- 0.0005 deg
  Lat =    51.214744 +/- 0.0038 deg
  Ht  = 98639.71 +/- 640.83 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
    UK0006,   False,    -1.306160,    51.883100,   80.00,  34.131827,   4.274591,   106624.37,   101036.18,          0.031459,     13.70,    100.16,             109.13, 0.8926,    True,    True, {"ff_name": "FF_UK0006_20210810_213821_628_0120832.fits"}
    UK0020,   False,    -3.515726,    50.691998,   17.00,  12.145291,  12.975291,   106937.20,    98639.71,          0.035904,      9.01,     78.03,              30.83, 0.2626,    True,    True, {"ff_name": "FF_UK0020_20210810_213827_825_0116480.fits"}
    UK003H,   False,    -2.379250,    51.361350,  169.00,   3.658766,  18.496583,   105938.20,   100430.10,          0.008450,      1.12,     17.85,              81.36, 0.9775,   False,    True, {"ff_name": "FF_UK003H_20210810_213823_760_0119296.fits"}
    UK003J,    True,    -2.379250,    51.361350,  169.00, 7361.454104,   0.703548,   103150.08,    99250.29,          1.729233,       nan,       nan,              81.36, 0.0000,   False,    True, {"ff_name": "FF_UK003J_20210810_213825_541_0115200.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,     UK0006,       0,  0.012579, 2459437.401715221349, 232.16384,  14.35000,              246.28421,  34.99625,       246.25038,       35.01421,    232.16384,     +14.35000,     232.19797,      +14.34842,   771847.96, -3985657.50,  5040159.61,      51.334317,       -3.239403,  106624.37,  182690.84,       0.00,              636.09,     0.13,      0.00,           61589.72,   -104.34,    -14.25,         118.89,  +1.56,  +0.25
  1,     UK0006,       0,  0.053147, 2459437.401715691201, 232.13240,  13.69615,              245.85179,  34.44659,       245.82140,       34.46267,    232.13240,     +13.69615,     232.16326,      +13.69473,   771046.67, -3986526.41,  5038303.52,      51.319226,       -3.253004,  105613.17,  183392.54,    2200.49,             2836.58,  -209.88,  54242.05,           61589.72,    -94.43,    -12.89,         107.19,  +1.66,  +0.34
  2,     UK0006,       0,  0.093863, 2459437.401716162451, 232.06914,  12.88404,              245.34601,  33.74809,       245.29509,       33.77497,    232.06914,     +12.88404,     232.12094,      +12.88167,   770041.04, -3987616.90,  5035974.09,      51.300277,       -3.270025,  104344.92,  184304.53,    4962.14,             5598.22,   132.48,  67826.99,           61589.72,   -159.82,    -21.89,         180.53,  +0.81,  -0.52
  3,     UK0006,       0,  0.134479, 2459437.401716632303, 232.04609,  12.16570,              244.87429,  33.14676,       244.83778,       33.16598,    232.04609,     +12.16570,     232.08357,      +12.16399,   769144.97, -3988588.59,  5033898.45,      51.283384,       -3.285203,  103215.60,  185149.14,    7422.91,             8059.00,   179.91,  60586.39,           61589.72,   -115.59,    -15.81,         129.97,  +1.82,  +0.48
  4,     UK0006,       0,  0.174883, 2459437.401717099827, 232.05762,  11.68232,              244.53467,  32.75616,       244.53517,       32.75590,    232.05762,     +11.68232,     232.05787,      +11.68234,   768539.14, -3989245.54,  5032495.11,      51.271958,       -3.295516,  102452.46,  185739.37,    9086.64,             9722.72,  -557.12,  41177.22,           57638.85,      1.60,      0.22,           1.79,  +1.44,  +0.10
  5,     UK0006,       0,  0.215639, 2459437.401717571542, 232.02396,  10.79596,              243.97191,  32.00725,       243.98388,       32.00099,    232.02396,     +10.79596,     232.01276,      +10.79653,   767414.07, -3990465.56,  5029889.01,      51.250730,       -3.314517,  101036.18,  186862.57,   12176.29,            12812.38,   110.87,  75808.54,           59112.19,     38.53,      5.24,          42.92,  +2.73,  +1.37
  0,     UK0020,       0,  0.000000, 2459437.401715010405, 342.22844,  80.09534,               15.09606,  54.50226,        15.18836,       54.52777,    342.22844,     +80.09534,     342.17436,      +80.03673,   772095.76, -3985388.80,  5040733.60,      51.338983,       -3.235172,  106937.20,  130741.82,       0.00,               44.40,   155.87,      0.00,           56555.48,   -134.52,     15.50,         213.63,  +1.94,  +1.36
  1,     UK0020,       0,  0.039800, 2459437.401715470944, 339.19455,  80.14874,               14.72844,  54.98042,        14.79204,       54.99802,    339.19455,     +80.14874,     339.16983,      +80.10845,   771234.24, -3986323.02,  5038737.99,      51.322759,       -3.249781,  105849.83,  128687.45,    2365.88,             2321.49,    68.10,  59444.35,           56555.48,    -90.40,     10.46,         145.86,  +1.31,  +0.76
  2,     UK0020,       0,  0.079628, 2459437.401715931948, 336.40203,  80.18354,               14.36889,  55.41230,        14.42068,       55.42667,    336.40203,     +80.18354,     336.39136,      +80.15088,   770470.33, -3987151.39,  5036968.49,      51.308367,       -3.262750,  104886.21,  126874.88,    4463.71,             4419.31,  -200.60,  52672.19,           56555.48,    -71.96,      8.34,         117.78,  +0.95,  +0.43
  3,     UK0020,       0,  0.119440, 2459437.401716392953, 333.17476,  80.20477,               13.93010,  55.90342,        13.98423,       55.91849,    333.17476,     +80.20477,     333.17483,      +80.17089,   769617.20, -3988076.51,  5034992.32,      51.292287,       -3.277208,  103810.66,  124861.55,    6806.56,             6762.16,  -223.33,  58847.79,           56555.48,    -73.34,      8.49,         121.96,  +0.73,  +0.25
  4,     UK0020,       0,  0.159220, 2459437.401716853026, 329.48901,  80.18768,               13.42195,  56.46383,        13.47309,       56.47812,    329.48901,     +80.18768,     329.50099,      +80.15609,   768675.32, -3989097.87,  5032810.55,      51.274526,       -3.293147,  102623.98,  122652.74,    9393.15,             9348.75,    -0.41,  65022.27,           58347.11,    -67.31,      7.79,         113.95,  +0.67,  +0.23
  5,     UK0020,       0,  0.199036, 2459437.401717314031, 326.21130,  80.14664,               12.94216,  56.95939,        13.00229,       56.97627,    326.21130,     +80.14664,     326.23725,      +80.11002,   767861.74, -3989980.11,  5030925.99,      51.259178,       -3.306932,  101599.59,  120756.84,   11627.39,            11582.99,  -131.99,  56114.09,           58540.20,    -77.20,      8.91,         132.75,  +1.07,  +0.66
  6,     UK0020,       0,  0.238812, 2459437.401717774570, 322.93213,  80.02977,               12.50750,  57.48550,        12.50628,       57.48516,    322.93213,     +80.02977,     322.93238,      +80.03051,   767053.17, -3990856.91,  5029053.04,      51.243918,       -3.320629,  100582.10,  118884.45,   13847.86,            13803.46,  -274.95,  55824.48,           58318.44,      1.53,     -0.18,           2.68,  +1.15,  +0.77
  7,     UK0020,       0,  0.278628, 2459437.401718235109, 319.58820,  79.93621,               11.95014,  57.99390,        11.98438,       58.00358,    319.58820,     +79.93621,     319.61630,      +79.91618,   766251.63, -3991726.09,  5027196.36,      51.228783,       -3.334204,   99574.02,  117040.50,   16049.05,            16004.65,  -439.58,  55284.00,           57973.06,    -41.74,      4.83,          74.05,  +1.72,  +1.38
  8,     UK0020,       0,  0.318456, 2459437.401718696114, 316.46168,  79.81334,               11.40678,  58.47898,        11.47045,       58.49710,    316.46168,     +79.81334,     316.52293,      +79.77696,   765508.34, -3992532.10,  5025474.63,      51.214744,       -3.346800,   98639.71,  115341.83,   18090.24,            18045.85,  -764.90,  51250.29,           57363.38,    -75.78,      8.72,         136.41,  +3.34,  +3.03
  0,     UK003H,       0,  0.039242, 2459437.401715517510, 240.01037,  40.87980,              266.41995,  59.66626,       266.42344,       59.66425,    240.01037,     +40.87980,     240.00705,      +40.88012,   771304.28, -3986247.06,  5038900.23,      51.324078,       -3.248624,  105938.20,  122211.26,       0.00,             2129.14,   -91.11,      0.00,           59086.16,      5.68,      0.36,           9.60,  +0.52,  +0.08
  1,     UK003H,       0,  0.079882, 2459437.401715987828, 239.82440,  39.70796,              264.70832,  58.87347,       264.71432,       58.87013,    239.82440,     +39.70796,     239.81886,      +39.70849,   770381.23, -3987248.01,  5036762.09,      51.306688,       -3.264263,  104773.85,  121848.02,    2534.87,             4664.01,    28.98,  62373.67,           59086.16,      9.69,      0.61,          16.43,  +0.21,  -0.22
  2,     UK003H,       0,  0.120478, 2459437.401716457680, 239.65206,  38.64454,              263.23085,  58.12990,       263.23043,       58.13012,    239.65206,     +38.64454,     239.65298,      +38.64451,   769547.78, -3988151.79,  5034831.50,      51.290978,       -3.278394,  103723.17,  121565.29,    4823.67,             6952.82,   -94.37,  56380.13,           59086.16,     -0.66,     -0.04,           1.13,  +0.15,  -0.27
  3,     UK003H,       0,  0.161102, 2459437.401716927998, 239.50168,  37.51587,              261.70493,  57.33966,       261.72545,       57.32873,    239.50168,     +37.51587,     239.48288,      +37.51764,   768669.05, -3989104.67,  5032796.03,      51.274408,       -3.293279,  102616.08,  121313.13,    7236.83,             9365.97,   -95.04,  59402.19,           59086.16,     32.89,      2.06,          56.03,  +0.31,  -0.11
  4,     UK003H,       0,  0.201694, 2459437.401717397384, 239.34126,  36.47588,              260.38100,  56.58004,       260.39397,       56.57326,    239.34126,     +36.47588,     239.32995,      +36.47698,   767860.78, -3989981.14,  5030923.78,      51.259160,       -3.306978,  101598.38,  121123.85,    9456.47,            11585.61,  -287.32,  54681.68,           58147.24,     20.78,      1.31,          35.45,  +0.82,  +0.40
  5,     UK003H,       0,  0.242382, 2459437.401717868634, 239.16799,  35.27726,              258.91448,  55.69193,       258.92474,       55.68667,    239.16799,     +35.27726,     239.15950,      +35.27812,   766932.34, -3990987.93,  5028773.15,      51.241637,       -3.322685,  100430.10,  120955.62,   12006.14,            14135.29,  -155.27,  62664.08,           58525.37,     16.47,      1.04,          28.15,  +1.35,  +0.94
  6,     UK003H,       1,  0.282886, 2459437.401718337554, 239.04319,  34.41343,              257.90174,  55.03968,       257.90818,       55.03642,    239.04319,     +34.41343,     239.03846,      +34.41397,   766265.07, -3991711.52,  5027227.49,      51.229037,       -3.334016,   99590.90,  120869.73,   13838.60,            15967.74,  -729.51,  45241.33,           57241.34,     10.36,      0.65,          17.72,  +3.66,  +3.25
  0,     UK003J,       1,  0.295136, 2459437.401718426496, 241.70167,  37.84329,              260.12056,  58.90138,       262.44998,       57.70067,    241.70167,     +37.84329,     239.54518,      +38.05372,   769093.22, -3988644.71,  5033778.58,      51.282408,       -3.286717,  103150.08,  121451.61,       0.00,             8201.11, -9224.00,      0.00,           56187.19,   3629.82,    165.31,        6171.93,  +0.16,  -0.26
  1,     UK003J,       1,  0.336056, 2459437.401718900073, 241.52602,  36.77636,              258.71430,  58.11505,       261.05508,       56.93283,    241.52602,     +36.77636,     239.38633,      +36.98556,   768261.96, -3989546.11,  5031853.06,      51.266729,       -3.300806,  102103.06,  121235.92,    2282.79,            10483.90, -9372.62,  55786.69,           56187.19,   3646.41,    165.97,        6211.15,  +0.55,  +0.13
  2,     UK003J,       1,  0.377068, 2459437.401719374582, 241.33777,  35.60821,              257.24661,  57.23647,       259.59258,       56.07544,    241.33777,     +35.60821,     239.21788,      +35.81594,   767354.79, -3990529.84,  5029751.70,      51.249611,       -3.316160,  100961.14,  121048.88,    4774.06,            12975.17, -9318.24,  60744.80,           56187.19,   3661.18,    166.57,        6245.95,  +0.80,  +0.39
  3,     UK003J,       1,  0.417916, 2459437.401719847228, 241.17255,  34.63961,              256.09574,  56.48767,       258.42832,       55.35060,    241.17255,     +34.63961,     239.08099,      +34.84486,   766603.89, -3991344.10,  5028012.33,      51.235435,       -3.328894,  100016.47,  120933.92,    6836.16,            15037.28, -9683.26,  50482.47,           56187.19,   3652.02,    166.34,        6236.25,  +1.06,  +0.65
  4,     UK003J,       1,  0.458608, 2459437.401720318478, 241.05126,  33.85078,              255.18133,  55.87667,       257.51380,       54.75284,    241.05126,     +33.85078,     238.97118,      +34.05523,   765994.60, -3992004.80,  5026600.99,      51.223929,       -3.339254,   99250.29,  120867.75,    8509.38,            16710.49, -10427.91,  41118.92,           52774.17,   3664.23,    166.85,        6260.52,  +4.75,  +4.34

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.