Orbital Analysis for matched events on 20210816_015416.165_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 69.42° Bg 41.42° Vg 56.33km/s
mass 0.05372g, abs. mag -1.5
Path Details
------------
start -0.04° 53.05° 106.22km
end   -0.11° 53.02° 96.59km

Orbit Details
-------------
Semimajor axis 8.28A.U., eccentricity 0.89, inclination 106.64°, Period 23.82Y, LA Sun 143.15°, last Perihelion 2021-07-22

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: 2459442.579353763256
Time: 2021-08-16 01:54:16.245491 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002F and UK003A
 Convergence angle = 47.53702 deg
 R.A. =  55.53229  Dec = +62.27758 deg

Best intersection: Stations UK002F and UK003A with Qconv = 47.54 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3879470.89 +/- 22.43 m
 Y =   -460305.38 +/- 89.52 m
 Z =   5162402.68 +/- 127.41 m
 Vx =    15142.30 +/- 348.50 m/s
 Vy =    21717.21 +/- 374.81 m/s
 Vz =    50939.85 +/- 472.29 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+5.407506e+02, -1.726317e+02, +1.983886e+01, +1.566166e+03, -2.298220e+03, -3.628474e+03
-1.726317e+02, +8.604701e+03, +1.166854e+04, -6.669882e+03, +3.214357e+04, +3.495202e+04
+1.983886e+01, +1.166854e+04, +1.742504e+04, -1.069462e+04, +4.015237e+04, +4.566683e+04
+1.566166e+03, -6.669882e+03, -1.069462e+04, +1.437795e+04, -2.898119e+04, -3.909930e+04
-2.298220e+03, +3.214357e+04, +4.015237e+04, -2.898119e+04, +1.495504e+05, +1.602007e+05
-3.628474e+03, +3.495202e+04, +4.566683e+04, -3.909930e+04, +1.602007e+05, +1.791850e+05

Timing offsets (from input data):
    UK0027: 0.000000 s
    UK002F: 0.000000 s
    UK003A: -0.000092 s
    UK003G: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-16 01:54:16.245491 UTC
  Lon     = +-0.019492 +/- 0.0013 deg
  Lat     = +53.065029 +/- 0.0008 deg
  Lat geo = +52.883137 +/- 0.0008 deg
  Ht      =  109430.88 +/- 96.90 m

  JD dynamic   = 2459442.580155434087 
  LST apparent = 353.2334003687 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  55.11391 +/- 0.6078 deg
  Dec       = +62.53771 +/- 0.0992 deg
  Azimuth   =  48.53044 +/- 0.1808 deg
  Elevation = +57.12485 +/- 0.2790 deg
  Vavg      =  56.70393 +/- 0.5105 km/s
  Vinit     =  57.40901 +/- 0.4808 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  55.40175 +/- 0.6078 deg
  Dec       = +62.31536 +/- 0.0992 deg
  Azimuth   =  48.87494 +/- 0.1808 deg
  Elevation = +56.94582 +/- 0.2790 deg
  Vavg      =  56.82039 +/- 0.5105 km/s
  Vinit     =  57.52547 +/- 0.4808 km/s
Radiant (geocentric, J2000):
  R.A.   =  55.32972 +/- 0.5993 deg
  Dec    = +62.39952 +/- 0.1001 deg
  Vg     =  56.32637 +/- 0.4900 km/s
  Vinf   =  57.40901 +/- 0.4808 km/s
  Zc     =  32.99585 +/- 0.2791 deg
  Zg     =  33.31892 +/- 0.2765 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  69.42474 +/- 0.3431 deg
  Bg     = +41.41616 +/- 0.1437 deg
  Vh     =  40.55754 +/- 0.4188 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  99.07718 +/- 0.3023 deg
  Bh     = +66.74059 +/- 0.5295 deg
  Vh_x   =   2.52675 +/- 0.1097 km/s
  Vh_y   = -15.81539 +/- 0.5058 km/s
  Vh_z   = -37.26128 +/- 0.2382 km/s
Orbit:
  La Sun = 143.146472 +/- 0.0000 deg
  a      =   8.278143 +/- 5.6382 AU
  e      =   0.888138 +/- 0.0358
  i      = 106.644549 +/- 0.4243 deg
  peri   = 144.890391 +/- 0.0497 deg
  node   = 143.146847 +/- 0.0000 deg
  Pi     = 288.037238 +/- 0.0496 deg
  q      =   0.926007 +/- 0.0019 AU
  f      =  35.106144 +/- 0.0497 deg
  M      =   1.015721 +/- 0.4455 deg
  Q      =  15.630280 +/- 11.2782 AU
  n      =   0.041381 +/- 0.0178 deg/day
  T      =  23.817713 +/- 32.1291 years
  Last perihelion JD = 2459418.034771 (2021-07-22 12:50:04.250492) +/- 0.2680 days
  Tj     =   0.296630 +/- 0.2109
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.373478e-03, -7.053983e-05, +1.021850e-02, -1.661405e-08, -2.626434e-06, +2.633259e-04
q   , -7.053983e-05, +3.680726e-06, -5.174273e-04, +8.170769e-10, +3.479265e-07, -1.294961e-05
Tp  , +1.021850e-02, -5.174273e-04, +7.702110e-02, -1.281889e-07, +8.427340e-06, +2.031962e-03
node, -1.661405e-08, +8.170769e-10, -1.281889e-07, +2.333669e-13, -1.010783e-10, -3.699748e-09
peri, -2.626434e-06, +3.479265e-07, +8.427340e-06, -1.010783e-10, +8.006674e-07, +1.606578e-06
i   , +2.633259e-04, -1.294961e-05, +2.031962e-03, -3.699748e-09, +1.606578e-06, +5.865537e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.000000
 a2 = 0.000000

Mean time residuals from time vs. length:
  Station with reference time: UK002F
  Avg. res. = 1.032e-05 s
  Stddev    = 3.21e-03 s

Begin point on the trajectory:
  Lon =    -0.042332 +/- 0.0008 deg
  Lat =    53.052864 +/- 0.0005 deg
  Ht  = 106216.01 +/- 45.43 m
End point on the trajectory:
  Lon =    -0.111621 +/- 0.0006 deg
  Lat =    53.016342 +/- 0.0004 deg
  Ht  = 96593.68 +/- 33.19 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
    UK0027,    True,    -2.374601,    51.371449,   48.00,   0.000000,   0.000000,   106169.87,    96904.68,          0.071733,       nan,       nan,              32.60, 0.0000,    True,    True, {"ff_name": "FF_UK0027_20210816_015415_300_0515584.fits"}
    UK002F,   False,    -1.306160,    51.883100,   80.00,   0.000000,   0.000000,   106216.01,    96593.68,          0.006622,     20.54,      6.28,              23.87, 1.0000,    True,    True, {"ff_name": "FF_UK002F_20210816_015411_308_0518912.fits"}
    UK003A,   False,    -2.395630,    52.113500,   85.00,   3.518490,   6.694975,   105003.90,    97374.21,          0.006418,     20.75,     12.03,              27.41, 1.0000,    True,    True, {"ff_name": "FF_UK003A_20210816_015412_301_0514816.fits"}
    UK003G,    True,    -1.802002,    51.351948,  130.00,   0.000000,   0.000000,   120281.63,   109708.90,          0.582587,       nan,       nan,              32.24, 0.0000,    True,    True, {"ff_name": "FF_UK003G_20210816_015406_997_0522752.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,     UK0027,       1,  0.071978, 2459442.579354596324, 109.55028,  47.65792,               39.61839,  22.06600,        39.51499,       22.07769,    109.55028,     +47.65792,     109.65517,      +47.72395,  3878446.67,  -461774.33,  5158957.10,      53.052690,       -0.042625,  106169.87,  269538.03,       0.00,             3883.15,   444.22,      0.00,           56422.32,      9.80,   -453.99,         347.50,  +3.84,  +1.69
  1,     UK0027,       1,  0.112134, 2459442.579355061054, 109.75279,  47.53621,               39.57693,  21.88716,        39.48874,       21.89717,    109.75279,     +47.53621,     109.84254,      +47.59249,  3878035.23,  -462364.41,  5157573.01,      53.047728,       -0.052103,  104860.08,  268227.65,    1559.87,             5443.02,  -301.22,  38845.34,           56422.32,      8.13,   -385.84,         296.77,  +2.98,  +0.84
  2,     UK0027,       1,  0.152402, 2459442.579355527181, 110.09114,  47.30744,               39.52219,  21.56754,        39.44383,       21.57645,    110.09114,     +47.30744,     110.17123,      +47.35734,  3877315.18,  -463397.12,  5155150.69,      53.039038,       -0.068568,  102568.09,  265946.12,    4289.81,             8172.96,   116.97,  67794.20,           56422.32,      7.05,   -340.69,         264.29,  +1.43,  -0.69
  3,     UK0027,       1,  0.192646, 2459442.579355992842, 110.39566,  47.11094,               39.46525,  21.28719,        39.40419,       21.29415,    110.39566,     +47.11094,     110.45845,      +47.14976,  3876691.26,  -464291.94,  5153051.79,      53.031502,       -0.082861,  100582.36,  263975.25,    6655.26,            10538.41,   172.05,  58777.78,           56422.32,      5.31,   -264.00,         206.32,  +1.74,  -0.37
  4,     UK0027,       1,  0.232862, 2459442.579356458504, 110.64219,  46.90425,               39.44757,  21.02128,        39.36713,       21.03043,    110.64219,     +46.90425,     110.72494,      +46.95528,  3876116.58,  -465116.15,  5151118.52,      53.024555,       -0.096043,   98753.54,  262165.21,    8834.05,            12717.20,    42.08,  54177.18,           56587.93,      7.13,   -346.04,         272.31,  +1.43,  -0.66
  5,     UK0027,       1,  0.273102, 2459442.579356924165, 110.97435,  46.74240,               39.34956,  20.75771,        39.32929,       20.76004,    110.97435,     +46.74240,     110.99611,      +46.75525,  3875535.54,  -465949.49,  5149163.85,      53.017525,       -0.109372,   96904.68,  260341.02,   11036.96,            14920.11,   -65.15,  54744.25,           56371.78,      1.63,    -86.75,          68.74,  +2.03,  -0.05
  0,     UK002F,       1,  0.000000, 2459442.579353763256, 106.17005,  60.08326,               33.16360,  33.75243,        33.11489,       33.76661,    106.17005,     +60.08326,     106.21059,      +60.12112,  3879491.00,  -460276.54,  5162470.31,      53.065271,       -0.018701,  109494.90,  193274.75,       0.00,               76.22,   769.48,      0.00,           51991.02,    -42.00,   -138.53,         154.48,  +4.95,  +3.52
  1,     UK002F,       1,  0.040160, 2459442.579354227986, 106.61445,  60.00196,               33.03285,  33.54265,        33.01829,       33.54690,    106.61445,     +60.00196,     106.62685,      +60.01328,  3878983.41,  -461004.54,  5160762.73,      53.059158,       -0.030350,  107878.69,  191512.83,    1924.44,             1848.22,   235.93,  47919.26,           51991.02,    -12.53,    -41.12,          46.30,  +4.43,  +3.02
  2,     UK002F,       0,  0.080336, 2459442.579354693182, 107.06137,  59.90016,               32.91585,  33.31702,        32.91765,       33.31649,    107.06137,     +59.90016,     107.06018,      +59.89876,  3878461.16,  -461753.54,  5159005.87,      53.052864,       -0.042332,  106216.01,  189703.60,    3904.42,             3828.19,   -90.56,  49282.60,           51991.02,      1.54,      5.05,           5.74,  +1.67,  +0.28
  3,     UK002F,       0,  0.120560, 2459442.579355158843, 107.60081,  59.76307,               32.78345,  33.03417,        32.79454,       33.03093,    107.60081,     +59.76307,     107.59178,      +59.75448,  3877828.20,  -462661.34,  5156876.52,      53.045230,       -0.056823,  104201.04,  187516.66,    6304.17,             6227.95,    -0.02,  59659.87,           51991.02,      9.43,     30.81,          35.45,  +1.22,  -0.15
  4,     UK002F,       0,  0.160796, 2459442.579355624504, 108.10417,  59.59897,               32.68566,  32.74304,        32.67278,       32.74680,    108.10417,     +59.59897,     108.11606,      +59.60893,  3877212.92,  -463543.78,  5154806.69,      53.037804,       -0.070918,  102242.61,  185395.83,    8636.87,             8560.65,    22.77,  57975.39,           53866.59,    -10.84,    -35.50,          41.29,  +0.73,  -0.61
  5,     UK002F,       0,  0.201028, 2459442.579356090166, 108.67044,  59.45643,               32.53939,  32.44708,        32.54471,       32.44552,    108.67044,     +59.45643,     108.66659,      +59.45232,  3876575.86,  -464457.46,  5152663.55,      53.030107,       -0.085509,  100215.08,  183205.64,   11052.19,            10975.96,   128.40,  60034.63,           55283.89,      4.44,     14.52,          17.10,  +0.84,  -0.47
  6,     UK002F,       0,  0.241248, 2459442.579356555361, 109.15853,  59.30576,               32.43215,  32.17088,        32.42873,       32.17188,    109.15853,     +59.30576,     109.16258,      +59.30840,  3876010.09,  -465268.89,  5150760.27,      53.023267,       -0.098490,   98414.67,  181264.88,   13197.17,            13120.95,   -35.61,  53331.24,           55580.45,     -2.83,     -9.26,          11.02,  +0.68,  -0.61
  7,     UK002F,       0,  0.281472, 2459442.579357021023, 109.66991,  59.15794,               32.30924,  31.88904,        32.30963,       31.88893,    109.66991,     +59.15794,     109.67074,      +59.15765,  3875437.80,  -466089.68,  5148835.03,      53.016342,       -0.111621,   96593.68,  179306.63,   15366.90,            15290.68,  -175.09,  53941.34,           55567.34,      0.32,      1.03,           1.24,  +1.19,  -0.08
  0,     UK003A,       0,  0.101129, 2459442.579354934860,  88.98460,  42.33774,               55.86598,  27.86360,        55.86688,       27.86375,     88.98460,     +42.33774,      88.98411,      +42.33730,  3878080.41,  -462299.62,  5157724.98,      53.048273,       -0.051035,  105003.90,  218338.56,       0.00,             5271.74,   159.30,      0.00,           56158.05,     -1.55,      2.66,           2.91,  +1.77,  +0.07
  1,     UK003A,       0,  0.141381, 2459442.579355400521,  89.18235,  42.11312,               55.91996,  27.59976,        55.92099,       27.59993,     89.18235,     +42.11312,      89.18189,      +42.11262,  3877513.29,  -463112.99,  5155817.14,      53.041430,       -0.064038,  103198.65,  216438.99,    2150.13,             7421.88,    -1.39,  53416.79,           56158.05,     -1.76,      3.04,           3.35,  +1.48,  -0.20
  2,     UK003A,       0,  0.181621, 2459442.579355866648,  89.38396,  41.90310,               55.95897,  27.34411,        55.97266,       27.34637,     89.38396,     +41.90310,      89.37073,      +41.89643,  3876977.34,  -463881.66,  5154014.15,      53.034958,       -0.076339,  101492.79,  214647.77,    4182.09,             9453.83,  -279.58,  50495.92,           56158.05,    -23.23,     40.07,          44.51,  +0.80,  -0.86
  3,     UK003A,       0,  0.221949, 2459442.579356333241,  89.61332,  41.60092,               56.05020,  27.00646,        56.04231,       27.00516,     89.61332,     +41.60092,      89.62232,      +41.60475,  3876270.81,  -464894.96,  5151637.35,      53.026420,       -0.092505,   99244.32,  212295.95,    6860.74,            12132.48,    83.88,  66421.52,           56158.05,     13.30,    -22.90,          25.73,  +0.65,  -0.98
  4,     UK003A,       0,  0.262225, 2459442.579356799368,  89.83392,  41.35745,               56.10001,  26.71558,        56.10080,       26.71571,     89.83392,     +41.35745,      89.83421,      +41.35707,  3875683.11,  -465737.85,  5149660.27,      53.019311,       -0.105984,   97374.21,  210344.26,    9088.89,            14360.64,    -0.17,  55322.24,           56829.81,     -1.31,      2.26,           2.56,  +0.98,  -0.63
  0,     UK003G,       1,  0.012311, 2459442.579353905749, 114.37124,  54.31704,               32.96899,  25.87354,        32.33464,       26.02403,    114.37124,     +54.31704,     115.02102,      +54.77087,  3882877.40,  -455419.73,  5173862.44,      53.105948,       +0.057778,  120281.63,  263978.88,       0.00,            12915.11, 12901.59,      0.00,           71071.84,   -557.81,  -2660.02,        2123.70,  +2.70,  +0.59
  1,     UK003G,       1,  0.052595, 2459442.579354371876, 114.79155,  54.12343,               32.87164,  25.57324,        32.23880,       25.72345,    114.79155,     +54.12343,     115.44288,      +54.57510,  3882143.69,  -456472.02,  5171394.18,      53.097150,       +0.041038,  117943.89,  261589.90,    2781.72,            10133.39,  7807.20,  69052.77,           71071.84,   -553.46,  -2635.86,        2123.75,  +1.35,  -0.74
  2,     UK003G,       1,  0.092891, 2459442.579354838468, 115.22181,  53.92201,               32.77143,  25.26297,        32.14033,       25.41285,    115.22181,     +53.92201,     115.87442,      +54.37131,  3881399.50,  -457539.35,  5168890.66,      53.088218,       +0.024055,  115573.10,  259174.96,    5603.18,             7311.93,  2672.39,  70018.43,           71071.84,   -548.88,  -2610.57,        2123.09,  +1.14,  -0.93
  3,     UK003G,       1,  0.133211, 2459442.579355305061, 115.68615,  53.70313,               32.66123,  24.92665,        32.03420,       25.07568,    115.68615,     +53.70313,     116.33771,      +54.14833,  3880607.29,  -458675.55,  5166225.59,      53.078700,       +0.005982,  113049.71,  256613.80,    8606.70,             4308.41, -2645.86,  74492.00,           71071.84,   -542.27,  -2574.69,        2114.96,  +0.60,  -1.45
  4,     UK003G,       1,  0.173455, 2459442.579355770722, 116.04742,  53.53924,               32.56935,  24.67010,        31.95253,       24.81690,    116.04742,     +53.53924,     116.69068,      +53.97635,  3880009.53,  -459532.85,  5164214.71,      53.071512,       -0.007700,  111145.96,  254686.39,   10872.96,             2042.15, -7222.49,  56313.04,           68431.19,   -531.77,  -2518.59,        2084.76,  +0.92,  -1.11
  5,     UK003G,       1,  0.213639, 2459442.579356235918, 116.33815,  53.42399,               32.48381,  24.47733,        31.88970,       24.61905,    116.33815,     +53.42399,     116.95938,      +53.84451,  3879558.27,  -460180.06,  5162696.63,      53.066081,       -0.018072,  109708.90,  253233.73,   12583.83,              331.28, -11240.28,  42575.82,           63992.99,   -512.16,  -2415.51,        2011.26,  +3.30,  +1.28

Notes
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- 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.