Orbital Analysis for matched events on 20210813_004240.380_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 66.57° Bg 39.72° Vg 58.13km/s
mass 0.25681g, abs. mag -2.5
Path Details
------------
start 0.62° 49.81° 106.54km
end   0.44° 49.70° 87.65km

Orbit Details
-------------
Semimajor axis 23.29A.U., eccentricity 0.96, inclination 109.98°, Period 112.38Y, LA Sun 140.22°, last Perihelion 2021-07-19

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: 2459439.529634038918
Time: 2021-08-13 00:42:40.461831 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002C and UK002N
 Convergence angle = 13.26875 deg
 R.A. =  50.44806  Dec = +59.53075 deg

Best intersection: Stations UK002C and UK002N with Qconv = 13.27 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3736045.14 +/- 470.61 m
 Y =  -1903884.53 +/- 66.84 m
 Z =   4935083.15 +/- 87.69 m
 Vx =    18097.17 +/- 1255.32 m/s
 Vy =    23013.89 +/- 236.98 m/s
 Vz =    51429.97 +/- 724.61 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.270170e+05, +2.182784e+04, -2.714796e+04, +5.775642e+05, +3.680771e+04, -1.156678e+05
+2.182784e+04, +4.592151e+03, -1.757662e+03, +5.725475e+04, +8.878889e+03, -1.256505e+04
-2.714796e+04, -1.757662e+03, +7.899543e+03, -6.863039e+04, -8.556998e+03, +1.173263e+04
+5.775642e+05, +5.725475e+04, -6.863039e+04, +1.625154e+06, +9.844432e+04, -3.390292e+05
+3.680771e+04, +8.878889e+03, -8.556998e+03, +9.844432e+04, +3.000359e+04, -1.429950e+04
-1.156678e+05, -1.256505e+04, +1.173263e+04, -3.390292e+05, -1.429950e+04, +9.157567e+04

Timing offsets (from input data):
    UK002C: 0.000102 s
    UK002N: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 00:42:40.461831 UTC
  Lon     = ++0.648795 +/- 0.0035 deg
  Lat     = +49.833050 +/- 0.0030 deg
  Lat geo = +49.646483 +/- 0.0030 deg
  Ht      =  110206.80 +/- 219.21 m

  JD dynamic   = 2459439.530435715802 
  LST apparent = 332.9966586886 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  51.81996 +/- 1.6495 deg
  Dec       = +60.34883 +/- 0.8749 deg
  Azimuth   =  44.88572 +/- 1.6742 deg
  Elevation = +46.54845 +/- 0.4740 deg
  Vavg      =  57.96948 +/- 0.3212 km/s
  Vinit     =  59.17929 +/- 0.2941 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  51.93478 +/- 1.6495 deg
  Dec       = +60.09702 +/- 0.8749 deg
  Azimuth   =  45.18910 +/- 1.6742 deg
  Elevation = +46.39677 +/- 0.4740 deg
  Vavg      =  58.11849 +/- 0.3212 km/s
  Vinit     =  59.32830 +/- 0.2941 km/s
Radiant (geocentric, J2000):
  R.A.   =  52.13650 +/- 1.6706 deg
  Dec    = +60.11390 +/- 0.8735 deg
  Vg     =  58.12994 +/- 0.2993 km/s
  Vinf   =  59.17929 +/- 0.2941 km/s
  Zc     =  43.58389 +/- 0.4778 deg
  Zg     =  43.99371 +/- 0.4855 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  66.57156 +/- 1.4266 deg
  Bg     = +39.71850 +/- 0.5365 deg
  Vh     =  41.38836 +/- 0.2480 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  92.49787 +/- 3.9250 deg
  Bh     = +63.83250 +/- 0.3708 deg
  Vh_x   =   0.79547 +/- 1.2533 km/s
  Vh_y   = -18.23479 +/- 0.1674 km/s
  Vh_z   = -37.14641 +/- 0.2891 km/s
Orbit:
  La Sun = 140.216956 +/- -0.0000 deg
  a      =  23.287619 +/- 5.5906 AU
  e      =   0.960398 +/- 0.0223
  i      = 109.977775 +/- 1.1890 deg
  peri   = 144.750632 +/- 2.5154 deg
  node   = 140.216653 +/- 0.0001 deg
  Pi     = 284.967285 +/- 2.5154 deg
  q      =   0.922235 +/- 0.0112 AU
  f      =  35.245669 +/- 2.5155 deg
  M      =   0.211484 +/- 0.1749 deg
  Q      =  45.653003 +/- 11.1901 AU
  n      =   0.008770 +/- 0.0090 deg/day
  T      = 112.379805 +/- 34.7527 years
  Last perihelion JD = 2459415.416926 (2021-07-19 22:00:22.414148) +/- 1.4884 days
  Tj     =  -0.179269 +/- 0.1049
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +5.246803e-04, -2.059915e-04, -2.366079e-02, +2.531361e-08, -7.536770e-04, -3.597891e-04
q   , -2.059915e-04, +1.291347e-04, +1.679458e-02, -1.627728e-08, +5.017172e-04, +2.302436e-04
Tp  , -2.366079e-02, +1.679458e-02, +2.245743e+00, -2.151491e-06, +6.622084e-02, +3.039043e-02
node, +2.531361e-08, -1.627728e-08, -2.151491e-06, +2.192235e-12, -6.386655e-08, -3.097577e-08
peri, -7.536770e-04, +5.017172e-04, +6.622084e-02, -6.386655e-08, +1.964780e-03, +9.026941e-04
i   , -3.597891e-04, +2.302436e-04, +3.039043e-02, -3.097577e-08, +9.026941e-04, +4.377176e-04

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: UK002N
  Avg. res. = 8.800e-06 s
  Stddev    = 2.97e-03 s

Begin point on the trajectory:
  Lon =     0.615310 +/- 0.0027 deg
  Lat =    49.811290 +/- 0.0024 deg
  Ht  = 106542.51 +/- 160.55 m
End point on the trajectory:
  Lon =     0.440371 +/- 0.0020 deg
  Lat =    49.698373 +/- 0.0019 deg
  Ht  = 87647.91 +/- 123.99 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
    UK002C,   False,    -1.801980,    51.351940,  130.00,   0.000000,   0.000000,   106187.19,    87647.91,          0.024331,     81.44,     76.26,              69.57, 1.0000,    True,    True, {"ff_name": "FF_UK002C_20210813_004235_300_0404480.fits"}
    UK002N,   False,    -0.727590,    51.263100,   57.00,   0.000000,   0.000000,   106542.51,    87834.97,          0.017629,     57.41,     33.01,              74.03, 1.0000,    True,    True, {"ff_name": "FF_UK002N_20210813_004233_916_0412672.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,     UK002C,       0,  0.091677, 2459439.529635098297,  12.35853,  -6.02180,              134.18406,  22.39447,       134.17013,       22.38116,     12.35853,      -6.02180,      12.37650,       -6.02787,  3734351.47, -1906038.34,  4930269.95,      49.809178,       +0.612017,  106187.19,  266257.82,       0.00,             5538.45,   128.18,      0.00,           60438.52,     58.79,     62.81,          66.64,  +1.72,  -0.41
  1,     UK002C,       0,  0.131873, 2459439.529635563493,  12.20577,  -6.45863,              134.54260,  22.07238,       134.53012,       22.06049,     12.20577,      -6.45863,      12.22209,       -6.46408,  3733667.94, -1906907.57,  4928327.44,      49.799532,       +0.597021,  104565.57,  265613.45,    2235.20,             7773.64,   -15.39,  55607.44,           60438.52,     52.56,     56.16,          59.73,  +1.28,  -0.84
  2,     UK002C,       0,  0.172097, 2459439.529636029154,  12.02299,  -6.96095,              134.95939,  21.70400,       134.94359,       21.68899,     12.02299,      -6.96095,      12.04369,       -6.96786,  3732882.44, -1907906.48,  4926095.14,      49.788439,       +0.579812,  102702.47,  264895.57,    4803.85,            10342.30,   172.84,  63858.85,           60438.52,     66.33,     70.88,          75.59,  +0.76,  -1.36
  3,     UK002C,       0,  0.212297, 2459439.529636494350,  11.83513,  -7.43617,              135.36569,  21.36088,       135.33658,       21.33329,     11.83513,      -7.43617,      11.87286,       -7.44891,  3732136.17, -1908855.50,  4923974.34,      49.777892,       +0.563452,  100932.85,  264234.59,    7244.21,            12782.66,   234.19,  60705.39,           60438.52,    121.85,    130.31,         139.27,  +0.67,  -1.44
  4,     UK002C,       0,  0.252493, 2459439.529636959545,  11.70089,  -7.85491,              135.69201,  21.04388,       135.67362,       21.02649,     11.70089,      -7.85491,      11.72524,       -7.86297,  3731496.75, -1909668.64,  4922157.18,      49.768848,       +0.549409,   99416.91,  263683.87,    9335.18,            14873.63,   -53.62,  52019.35,           58895.92,     76.84,     82.13,          87.98,  +0.26,  -1.85
  5,     UK002C,       0,  0.292729, 2459439.529637425207,  11.55073,  -8.34695,              136.06618,  20.66712,       136.06572,       20.66670,     11.55073,      -8.34695,      11.55252,       -8.34715,  3730752.19, -1910615.48,  4920041.24,      49.758310,       +0.533082,   97652.13,  263063.46,   11769.94,            17308.38,     0.00,  60511.89,           58686.10,      1.89,      2.02,           2.17,  +0.08,  -2.02
  6,     UK002C,       0,  0.332921, 2459439.529637890402,  11.37149,  -8.79667,              136.44608,  20.33995,       136.43293,       20.32756,     11.37149,      -8.79667,      11.38957,       -8.80245,  3730055.10, -1911501.97,  4918060.18,      49.748436,       +0.517785,   96000.20,  262501.34,   14049.51,            19587.95,   -98.96,  56716.95,           58400.30,     54.71,     58.47,          62.92,  -0.06,  -2.16
  7,     UK002C,       0,  0.373173, 2459439.529638356529,  11.24562,  -9.29622,              136.79645,  19.94397,       136.82074,       19.96678,     11.24562,      -9.29622,      11.21632,       -9.28555,  3729318.50, -1912438.69,  4915966.86,      49.737996,       +0.501627,   94255.08,  261928.15,   16458.23,            21996.68,   -72.32,  59841.18,           58401.41,   -100.91,   -107.66,         116.20,  -0.43,  -2.52
  8,     UK002C,       0,  0.413409, 2459439.529638822190,  11.06178,  -9.81395,              137.20777,  19.55532,       137.23373,       19.57965,     11.06178,      -9.81395,      11.03047,       -9.80252,  3728533.57, -1913436.87,  4913736.18,      49.726861,       +0.484419,   92395.90,  261341.00,   19025.03,            24563.47,   113.34,  63793.50,           58761.66,   -107.61,   -114.81,         124.19,  -0.31,  -2.40
  9,     UK002C,       0,  0.453629, 2459439.529639287386,  10.87214, -10.31687,              137.61535,  19.18124,       137.63568,       19.20023,     10.87214,     -10.31687,      10.84814,      -10.30791,  3727769.41, -1914408.64,  4911564.54,      49.716013,       +0.467660,   90586.38,  260792.31,   21523.88,            27062.33,   232.00,  62129.63,           59128.75,    -84.05,    -89.70,          97.22,  -0.20,  -2.28
 10,     UK002C,       0,  0.493837, 2459439.529639753047,  10.66102, -10.82309,              138.04223,  18.81189,       138.04321,       18.81281,     10.66102,     -10.82309,      10.66182,      -10.82266,  3726994.18, -1915394.50,  4909361.41,      49.704998,       +0.450659,   88751.07,  260259.21,   24058.98,            29597.42,   387.61,  63049.52,           59507.13,     -4.07,     -4.34,           4.72,  +0.01,  -2.07
 11,     UK002C,       0,  0.533993, 2459439.529640217777,  10.57123, -11.14186,              138.26930,  18.56067,       138.28895,       18.57898,     10.57123,     -11.14186,      10.54835,      -11.13317,  3726528.14, -1915987.14,  4908037.00,      49.698373,       +0.440371,   87647.91,  259947.20,   25582.94,            31121.39,  -464.83,  37951.14,           58897.67,    -81.03,    -86.49,          94.05,  +0.62,  -1.45
  0,     UK002N,       1,  0.000000, 2459439.529634038918, 359.20480,  -4.44028,              147.96159,  29.50897,       147.94409,       29.49462,    359.20480,      -4.44028,     359.22400,       -4.44874,  3736043.16, -1903887.05,  4935077.52,      49.833022,       +0.649090,  110202.09,  218074.85,       0.00,                6.48,    21.59,      0.00,           60399.34,     39.69,     69.07,          75.34,  +4.12,  +2.43
  1,     UK002N,       1,  0.040428, 2459439.529634506907, 358.92017,  -5.05720,              148.50223,  29.02050,       148.47853,       29.00115,    358.92017,      -5.05720,     358.94638,       -5.06867,  3735234.54, -1904915.35,  4932779.53,      49.821630,       +0.631384,  108282.73,  217470.69,    2644.24,             2650.73,   273.33,  65406.26,           60399.34,     53.61,     93.33,         102.09,  +3.32,  +1.63
  2,     UK002N,       0,  0.080852, 2459439.529634974897, 358.71134,  -5.64211,              148.94421,  28.53545,       148.96158,       28.54957,    358.71134,      -5.64211,     358.69258,       -5.63369,  3734501.22, -1905847.91,  4930695.52,      49.811290,       +0.615310,  106542.51,  216948.81,    5042.27,             5048.76,   279.10,  59321.83,           60399.34,    -39.26,    -68.22,          74.84,  +1.47,  -0.21
  3,     UK002N,       0,  0.121224, 2459439.529635441955, 358.45783,  -6.18112,              149.41274,  28.10648,       149.42204,       28.11402,    358.45783,      -6.18112,     358.44809,       -6.17661,  3733799.70, -1906740.02,  4928701.89,      49.801392,       +0.599924,  104878.14,  216473.15,    7336.29,             7342.78,   183.93,  56822.16,           60399.34,    -21.00,    -36.50,          40.12,  +0.82,  -0.86
  4,     UK002N,       0,  0.161556, 2459439.529635908548, 358.19023,  -6.67384,              149.87548,  27.72400,       149.85082,       27.70409,    358.19023,      -6.67384,     358.21809,       -6.68583,  3733144.32, -1907573.45,  4926839.38,      49.792138,       +0.585537,  103323.57,  216049.60,    9479.43,             9485.92,   -59.75,  53137.41,           58556.34,     55.48,     96.61,         106.36,  +0.46,  -1.21
  5,     UK002N,       0,  0.202004, 2459439.529636377003, 357.97513,  -7.29145,              150.32266,  27.20477,       150.34655,       27.22400,    357.97513,      -7.29145,     357.94957,       -7.27982,  3732382.78, -1908541.89,  4924675.18,      49.781378,       +0.568845,  101517.59,  215584.12,   11969.73,            11976.22,    36.87,  61567.97,           58459.87,    -53.79,    -93.47,         103.18,  +0.22,  -1.45
  6,     UK002N,       0,  0.242380, 2459439.529636844061, 357.69536,  -7.84708,              150.81193,  26.76258,       150.81502,       26.76506,    357.69536,      -7.84708,     357.69295,       -7.84557,  3731660.23, -1909460.75,  4922621.76,      49.771161,       +0.552998,   99804.45,  215168.05,   14332.56,            14339.04,    10.27,  58520.53,           58431.92,     -6.94,    -12.07,          13.34,  +0.03,  -1.63
  7,     UK002N,       0,  0.282764, 2459439.529637311585, 357.42999,  -8.40330,              151.28173,  26.31342,       151.27571,       26.30861,    357.42999,      -8.40330,     357.43784,       -8.40625,  3730946.63, -1910368.23,  4920593.80,      49.761063,       +0.537343,   98112.94,  214781.91,   16666.09,            16672.57,   -46.10,  57783.51,           58366.26,     13.49,     23.48,          26.01,  -0.04,  -1.70
  8,     UK002N,       0,  0.323200, 2459439.529637779575, 357.12896,  -9.03313,              151.80900,  25.80267,       151.79277,       25.78974,    357.12896,      -9.03313,     357.14835,       -9.04110,  3730141.31, -1911392.34,  4918305.18,      49.749658,       +0.519696,   96204.49,  214376.61,   19299.55,            19306.03,   194.39,  65126.62,           58786.83,     36.36,     63.32,          70.26,  -0.20,  -1.86
  9,     UK002N,       0,  0.363612, 2459439.529638247564, 356.90560,  -9.60916,              152.23221,  25.31830,       152.24647,       25.32962,    356.90560,      -9.60916,     356.89124,       -9.60215,  3729431.84, -1912294.56,  4916288.94,      49.739603,       +0.504127,   94523.58,  214045.27,   21619.58,            21626.07,   122.87,  57409.53,           58925.74,    -31.95,    -55.56,          61.76,  -0.29,  -1.94
 10,     UK002N,       0,  0.404004, 2459439.529638715088, 356.65386, -10.17269,              152.67673,  24.85247,       152.69663,       24.86824,    356.65386,     -10.17269,     356.63333,      -10.16288,  3728724.64, -1913193.89,  4914279.18,      49.729572,       +0.488606,   92848.42,  213739.65,   23932.18,            23938.66,    45.10,  57253.78,           58925.49,    -44.58,    -77.52,          86.30,  -0.45,  -2.10
 11,     UK002N,       0,  0.444420, 2459439.529639182612, 356.35467, -10.78023,              153.17997,  24.35617,       153.18593,       24.36088,    356.35467,     -10.78023,     356.34985,      -10.77728,  3727951.64, -1914176.90,  4912082.41,      49.718601,       +0.471655,   91017.86,  213434.36,   26459.94,            26466.43,   181.07,  62543.66,           59064.59,    -13.34,    -23.21,          25.87,  -0.47,  -2.12
 12,     UK002N,       0,  0.484792, 2459439.529639650136, 356.10885, -11.31777,              153.60153,  23.90992,       153.61028,       23.91680,    356.10885,     -11.31777,     356.10107,      -11.31343,  3727278.60, -1915032.80,  4910169.70,      49.709040,       +0.456872,   89424.33,  213192.08,   28660.85,            28667.34,    -7.21,  54515.79,           58998.78,    -19.55,    -34.02,          37.97,  -0.22,  -1.86
 13,     UK002N,       0,  0.525156, 2459439.529640117195, 355.84934, -11.84931,              154.03149,  23.47158,       154.03161,       23.47167,    355.84934,     -11.84931,     355.85140,      -11.84925,  3726607.17, -1915886.65,  4908261.58,      49.699497,       +0.442123,   87834.97,  212972.87,   30856.49,            30862.97,  -200.28,  54395.92,           58826.03,     -0.26,     -0.46,           0.51,  -0.16,  -1.80

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.