Orbital Analysis for matched events on 20210813_003753.487_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 63.12° Bg 38.79° Vg 58.90km/s
mass 0.02834g, abs. mag -0.7
Path Details
------------
start 0.74° 52.18° 110.33km
end   0.62° 52.12° 98.39km

Orbit Details
-------------
Semimajor axis 16.05A.U., eccentricity 0.94, inclination 112.58°, Period 64.33Y, LA Sun 140.21°, last Perihelion 2021-07-23

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: 2459439.526313509792
Time: 2021-08-13 00:37:53.525307 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000C and UK002F
 Convergence angle = 87.17585 deg
 R.A. =  54.04218  Dec = +58.77739 deg
Intersection 2 - Stations: UK000C and UK002K
 Convergence angle = 42.54331 deg
 R.A. =  52.62622  Dec = +58.98086 deg
Intersection 3 - Stations: UK000C and UK0032
 Convergence angle = 34.63947 deg
 R.A. =  51.18048  Dec = +59.17040 deg
Intersection 4 - Stations: UK002F and UK002K
 Convergence angle = 44.63738 deg
 R.A. =  54.50982  Dec = +59.46783 deg
Intersection 5 - Stations: UK002F and UK0032
 Convergence angle = 52.55093 deg
 R.A. =  54.74842  Dec = +59.80894 deg
Intersection 6 - Stations: UK002K and UK0032
 Convergence angle = 7.91817 deg
 R.A. =  58.29838  Dec = +60.32830 deg

Best intersection: Stations UK000C and UK002F with Qconv = 87.18 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3516346.69 +/- 95.53 m
 Y =  -1878393.34 +/- 360.97 m
 Z =   5102453.24 +/- 697.10 m
 Vx =    21069.67 +/- 1255.42 m/s
 Vy =    23048.70 +/- 636.02 m/s
 Vz =    51154.22 +/- 810.92 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+8.539602e+03, +2.693707e+04, +5.032593e+04, -6.338391e+04, +3.063425e+04, +2.438907e+03
+2.693707e+04, +1.123284e+05, +2.157503e+05, -3.016326e+05, +9.956110e+04, +1.601270e+04
+5.032593e+04, +2.157503e+05, +4.170024e+05, -5.850275e+05, +1.846355e+05, +3.514922e+04
-6.338391e+04, -3.016326e+05, -5.850275e+05, +1.077261e+06, -2.839424e+05, -8.015654e+04
+3.063425e+04, +9.956110e+04, +1.846355e+05, -2.839424e+05, +1.301883e+05, +1.429465e+04
+2.438907e+03, +1.601270e+04, +3.514922e+04, -8.015654e+04, +1.429465e+04, +1.874472e+04

Timing offsets (from input data):
    UK000C: 0.000000 s
    UK002F: 0.006582 s
    UK002K: 0.005501 s
    UK0032: 0.001776 s

Reference point on the trajectory:
  Time: 2021-08-13 00:37:53.525307 UTC
  Lon     = ++0.740341 +/- 0.0051 deg
  Lat     = +52.182434 +/- 0.0045 deg
  Lat geo = +51.999051 +/- 0.0045 deg
  Ht      =  110310.72 +/- 487.83 m

  JD dynamic   = 2459439.527114691213 
  LST apparent = 331.8893623961 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  47.56842 +/- 1.8918 deg
  Dec       = +58.59748 +/- 0.4782 deg
  Azimuth   =  50.13998 +/- 1.2253 deg
  Elevation = +48.87559 +/- 0.6779 deg
  Vavg      =  58.10110 +/- 0.7725 km/s
  Vinit     =  59.93269 +/- 0.6521 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  47.69917 +/- 1.8918 deg
  Dec       = +58.36813 +/- 0.4782 deg
  Azimuth   =  50.40928 +/- 1.2253 deg
  Elevation = +48.71497 +/- 0.6779 deg
  Vavg      =  58.24839 +/- 0.7725 km/s
  Vinit     =  60.07998 +/- 0.6521 km/s
Radiant (geocentric, J2000):
  R.A.   =  47.79604 +/- 1.9065 deg
  Dec    = +58.35530 +/- 0.4738 deg
  Vg     =  58.89665 +/- 0.6632 km/s
  Vinf   =  59.93269 +/- 0.6521 km/s
  Zc     =  41.24214 +/- 0.6805 deg
  Zg     =  41.61810 +/- 0.6907 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  63.11594 +/- 1.3599 deg
  Bg     = +38.79212 +/- 0.2472 deg
  Vh     =  41.18053 +/- 0.5488 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  83.14290 +/- 3.3731 deg
  Bh     = +63.64102 +/- 0.4913 deg
  Vh_x   =  -2.18298 +/- 1.1186 km/s
  Vh_y   = -18.15312 +/- 0.4922 km/s
  Vh_z   = -36.89898 +/- 0.4358 km/s
Orbit:
  La Sun = 140.213767 +/- nan deg
  a      =  16.054863 +/- 11.1460 AU
  e      =   0.940680 +/- 0.0493
  i      = 112.582554 +/- 0.8403 deg
  peri   = 151.170124 +/- 2.9721 deg
  node   = 140.213233 +/- 0.0001 deg
  Pi     = 291.383357 +/- 2.9721 deg
  q      =   0.952371 +/- 0.0141 AU
  f      =  28.826053 +/- 2.9721 deg
  M      =   0.311724 +/- nan deg
  Q      =  31.157355 +/- 22.2998 AU
  n      =   0.015321 +/- 0.0145 deg/day
  T      =  64.329556 +/- 249443791.8711 years
  Last perihelion JD = 2459419.181271 (2021-07-23 16:21:01.827663) +/- 1.6400 days
  Tj     =  -0.133541 +/- 0.2863
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.291286e-04, -7.829615e-05, -8.900514e-03, +5.395014e-09, -2.799414e-04, -7.544660e-05
q   , -7.829615e-05, +1.705427e-04, +2.080121e-02, -8.596019e-09, +6.218465e-04, +1.199488e-04
Tp  , -8.900514e-03, +2.080121e-02, +2.552961e+00, -1.017880e-06, +7.609952e-02, +1.419623e-02
node, +5.395014e-09, -8.596019e-09, -1.017880e-06, +6.245845e-13, -3.087081e-08, -8.724992e-09
peri, -2.799414e-04, +6.218465e-04, +7.609952e-02, -3.087081e-08, +2.271804e-03, +4.306456e-04
i   , -7.544660e-05, +1.199488e-04, +1.419623e-02, -8.724992e-09, +4.306456e-04, +1.218862e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 1.310835
 a2 = 23.413304

Mean time residuals from time vs. length:
  Station with reference time: UK000C
  Avg. res. = 7.321e-06 s
  Stddev    = 2.71e-03 s

Begin point on the trajectory:
  Lon =     0.740488 +/- 0.0054 deg
  Lat =    52.182509 +/- 0.0048 deg
  Ht  = 110326.04 +/- 525.43 m
End point on the trajectory:
  Lon =     0.624220 +/- 0.0049 deg
  Lat =    52.123306 +/- 0.0043 deg
  Ht  = 98391.18 +/- 449.86 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
    UK000C,   False,    -0.727590,    51.263100,   57.00,   2.540539,  21.336644,   110326.04,    98391.18,          0.036513,    103.07,     40.72,              10.74, 0.0347,    True,    True, {"ff_name": "FF_UK000C_20210813_003747_722_0401920.fits"}
    UK002F,   False,    -1.306160,    51.883100,   80.00,   0.000000,   0.000000,   106693.33,   101294.01,          0.025489,     28.94,     72.75,              23.22, 0.1555,    True,    True, {"ff_name": "FF_UK002F_20210813_003746_969_0367872.fits"}
    UK002K,   False,    -0.382860,    53.537770,   34.00,   0.000000,   0.000000,   106709.18,   101307.38,          0.022187,     74.11,     22.25,              74.08, 0.9248,    True,    True, {"ff_name": "FF_UK002K_20210813_003749_739_0392960.fits"}
    UK0032,   False,    -0.023645,    52.984073,    6.00,   0.000000,   0.000000,   109412.30,   100826.38,          0.011415,     28.97,      4.44,              62.44, 0.7859,    True,    True, {"ff_name": "FF_UK0032_20210813_003745_951_0398848.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,     UK000C,       0,  0.000000, 2459439.526313950308,  68.26743,  55.63688,               44.11792,  36.56121,        44.18555,       36.54545,     68.26743,     +55.63688,      68.22761,      +55.58493,  3516353.84, -1878385.52,  5102470.59,      52.182509,       +0.740488,  110326.04,  182404.89,       0.00,               20.33,   161.22,      0.00,           61471.41,    -65.40,    167.82,         203.67,  +4.58,  +3.27
  1,     UK000C,       0,  0.040124, 2459439.526314415038,  68.46523,  55.55020,               44.11248,  36.41984,        44.13533,       36.41457,     68.46523,     +55.55020,      68.45164,      +55.53267,  3515593.94, -1879216.79,  5100625.68,      52.174457,       +0.724636,  108697.94,  180281.24,    2161.52,             2141.18,  -122.67,  53870.96,           61471.41,    -22.03,     56.03,          68.88,  +2.89,  +1.61
  2,     UK000C,       0,  0.080264, 2459439.526314879302,  68.73960,  55.47836,               44.05774,  36.25446,        44.07359,       36.25081,     68.73960,     +55.47836,      68.73025,      +55.46621,  3514669.87, -1880227.66,  5098382.15,      52.164657,       +0.705392,  106718.48,  177701.61,    4790.05,             4769.72,   100.16,  65484.08,           61471.41,    -15.10,     38.37,          47.87,  +2.11,  +0.86
  3,     UK000C,       0,  0.120412, 2459439.526315344032,  68.99944,  55.38825,               44.02608,  36.08358,        44.01193,       36.08682,     68.99944,     +55.38825,      69.00835,      +55.39910,  3513770.55, -1881211.45,  5096198.73,      52.155111,       +0.686656,  104792.48,  175192.47,    7348.16,             7327.83,   252.10,  63717.08,           61471.41,     13.37,    -33.80,          42.80,  +1.99,  +0.77
  4,     UK000C,       0,  0.160560, 2459439.526315808762,  69.25283,  55.28986,               44.00425,  35.90998,        43.95021,       35.92224,     69.25283,     +55.28986,      69.28653,      +55.33119,  3512893.15, -1882171.26,  5094068.52,      52.145789,       +0.668369,  102913.82,  172745.85,    9843.94,             9823.60,   341.69,  62164.32,           61968.36,     50.73,   -127.29,         163.62,  +2.10,  +0.91
  5,     UK000C,       0,  0.200640, 2459439.526316272561,  69.43620,  55.26830,               43.94121,  35.81637,        43.91155,       35.82315,     69.43620,     +55.26830,      69.45512,      +55.29101,  3512373.15, -1882740.10,  5092806.04,      52.140260,       +0.657462,  101800.59,  171293.92,   11323.07,            11302.73,  -581.28,  36904.47,           58535.40,     27.51,    -69.44,          89.94,  +1.90,  +0.73
  6,     UK000C,       0,  0.240780, 2459439.526316737290,  69.71619,  55.20045,               43.87723,  35.65085,        43.84958,       35.65717,     69.71619,     +55.20045,      69.73418,      +55.22163,  3511526.99, -1883665.74,  5090751.69,      52.131258,       +0.639816,   99989.43,  168936.64,   13729.96,            13709.63,  -580.08,  59962.51,           57461.52,     25.32,    -63.99,          84.03,  +2.15,  +1.01
  7,     UK000C,       0,  0.280916, 2459439.526317202020,  69.94105,  55.10470,               43.86371,  35.49100,        43.79324,       35.50696,     69.94105,     +55.10470,      69.98633,      +55.15860,  3510780.17, -1884482.71,  5088938.50,      52.123306,       +0.624220,   98391.18,  166856.62,   15854.31,            15833.97,  -861.19,  52928.70,           56636.22,     64.24,   -161.09,         214.38,  +4.93,  +3.82
  8,     UK000C,       1,  0.320972, 2459439.526317665353,  70.02850,  55.06423,               43.86124,  35.42666,        43.76854,       35.44757,     70.02850,     +55.06423,      70.08821,      +55.13508,  3510485.02, -1884805.58,  5088221.92,      52.120161,       +0.617955,   97759.56,  166030.91,   16693.86,            16673.53, -2422.30,  20959.55,           53877.51,     84.37,   -210.84,         282.13,  +5.17,  +4.07
  0,     UK002F,       0,  0.081819, 2459439.526314463466,  44.57381,  35.50157,               76.41472,  36.10223,        76.42938,       36.11709,     44.57381,     +35.50157,      44.55052,      +35.50288,  3514658.12, -1880240.50,  5098353.64,      52.164533,       +0.705300,  106693.33,  178164.72,       0.00,             4803.12,    40.38,      0.00,           60088.50,    -54.89,    -21.88,          68.41,  +3.17,  +1.92
  1,     UK002F,       0,  0.121951, 2459439.526314927731,  44.57767,  35.20786,               76.67932,  35.90111,        76.71331,       35.93538,     44.57767,     +35.20786,      44.52416,      +35.21085,  3513849.03, -1881125.60,  5096389.27,      52.155944,       +0.688427,  104960.53,  176042.26,    2301.47,             7104.59,   -63.36,  57347.58,           60088.50,   -125.51,    -49.88,         158.24,  +1.69,  +0.46
  2,     UK002F,       0,  0.162059, 2459439.526315391995,  44.51247,  34.87275,               77.02737,  35.71277,        77.03923,       35.72471,     44.51247,     +34.87275,      44.49415,      +34.87381,  3512939.55, -1882120.49,  5094181.19,      52.146282,       +0.669478,  103013.17,  173663.24,    4888.47,             9691.59,   119.85,  64500.84,           60088.50,    -43.19,    -17.23,          55.22,  +1.88,  +0.68
  3,     UK002F,       0,  0.202171, 2459439.526315856259,  44.47667,  34.56811,               77.32644,  35.52685,        77.33293,       35.53335,     44.47667,     +34.56811,      44.46702,      +34.56868,  3512136.49, -1882998.99,  5092231.46,      52.137743,       +0.652724,  101294.01,  171566.63,    7172.79,            11975.91,     0.15,  56948.55,           60088.50,    -23.30,     -9.30,          30.16,  +2.34,  +1.17
  0,     UK002K,       0,  0.081592, 2459439.526314604096, 352.84887,  -2.27984,              153.94475,  31.21616,       153.93560,       31.20928,    352.84887,      -2.27984,     352.85828,       -2.28444,  3514665.52, -1880232.41,  5098371.61,      52.164611,       +0.705402,  106709.18,  201451.86,       0.00,             4782.07,    32.91,      0.00,           59960.10,     10.56,     35.09,          37.52,  +1.21,  -0.31
  1,     UK002K,       0,  0.121844, 2459439.526315069757, 352.56625,  -2.85612,              154.43688,  30.73268,       154.43107,       30.72832,    352.56625,      -2.85612,     352.57242,       -2.85904,  3513846.82, -1881128.01,  5096383.92,      52.155921,       +0.688330,  104955.81,  200839.03,    2328.79,             7110.86,   -50.71,  57855.36,           59960.10,      6.69,     22.24,          23.85,  +0.93,  -0.58
  2,     UK002K,       0,  0.162120, 2459439.526315535884, 352.23797,  -3.50051,              154.99471,  30.19278,       154.98304,       30.18407,    352.23797,      -3.50051,     352.25033,       -3.50640,  3512930.15, -1882130.79,  5094158.35,      52.146182,       +0.669232,  102993.03,  200183.42,    4936.28,             9718.35,   142.93,  64740.47,           59960.10,     13.40,     44.57,          47.95,  +0.92,  -0.59
  3,     UK002K,       0,  0.202344, 2459439.526316001546, 351.93428,  -4.04780,              155.49101,  29.73836,       155.45560,       29.71203,    351.93428,      -4.04780,     351.97124,       -4.06571,  3512142.74, -1882992.16,  5092246.63,      52.137810,       +0.652801,  101307.38,  199645.27,    7176.07,            11958.14,   -28.01,  55682.97,           59960.10,     40.55,    135.12,         145.75,  +1.46,  -0.04
  0,     UK0032,       0,  0.018428, 2459439.526313895360, 351.98297,  12.19361,              149.97439,  45.93424,       149.98218,       45.94006,    351.98297,     +12.19361,     351.97566,      +12.19748,  3515927.38, -1878852.03,  5101435.21,      52.177991,       +0.731706,  109412.30,  151062.11,       0.00,             1192.73,   229.15,      0.00,           57837.13,     -3.18,    -20.73,          28.64,  +3.61,  +2.71
  1,     UK0032,       0,  0.058472, 2459439.526314359158, 351.63042,  11.57841,              150.71298,  45.45325,       150.72200,       45.45992,    351.63042,     +11.57841,     351.62217,      +11.58287,  3515194.13, -1879654.15,  5099654.99,      52.170218,       +0.716403,  107841.45,  150093.20,    2085.72,             3278.45,   -85.08,  52085.67,           57837.13,     -3.65,    -23.80,          33.09,  +1.47,  +0.59
  2,     UK0032,       0,  0.098520, 2459439.526314822491, 351.19268,  10.84227,              151.60380,  44.87723,       151.59823,       44.87315,    351.19268,     +10.84227,     351.19787,      +10.83952,  3514320.33, -1880610.02,  5097533.53,      52.160948,       +0.698196,  105969.86,  148969.40,    4571.24,             5763.96,     0.25,  62063.45,           57837.13,      2.23,     14.59,          20.44,  +0.56,  -0.31
  3,     UK0032,       0,  0.138580, 2459439.526315286290, 350.79697,  10.13474,              152.41269,  44.31135,       152.41247,       44.31119,    350.79697,     +10.13474,     350.79747,      +10.13463,  3513504.17, -1881502.85,  5095552.00,      52.152281,       +0.681176,  104222.07,  147949.65,    6892.82,             8085.55,   -79.07,  57952.59,           57837.13,      0.09,      0.58,           0.82,  +0.53,  -0.32
  4,     UK0032,       0,  0.178636, 2459439.526315749623, 350.35559,   9.37098,              153.28949,  43.69911,       153.28080,       43.69289,    350.35559,      +9.37098,     350.36391,       +9.36672,  3512628.11, -1882461.19,  5093425.06,      52.142971,       +0.662917,  102346.41,  146888.48,    9384.76,            10577.49,    12.20,  62211.43,           58864.51,      3.42,     22.42,          31.85,  +0.66,  -0.17
  5,     UK0032,       0,  0.218720, 2459439.526316213887, 350.02823,   8.72486,              153.95901,  43.16470,       153.98148,       43.18066,    350.02823,      +8.72486,     350.00856,       +8.73587,  3511918.03, -1883237.97,  5091701.07,      52.135419,       +0.648083,  100826.38,  146053.34,   11404.59,            12597.32,  -370.30,  50390.11,           57946.38,     -8.83,    -57.65,          82.37,  +1.20,  +0.38

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.