Orbital Analysis for matched events on 20210813_003311.566_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 63.60° Bg 38.32° Vg 57.86km/s
mass 0.00797g, abs. mag 0.2
Path Details
------------
start -0.32° 51.08° 110.19km
end   -0.42° 51.02° 100.25km

Orbit Details
-------------
Semimajor axis 6.26A.U., eccentricity 0.85, inclination 112.36°, Period 15.66Y, LA Sun 140.21°, last Perihelion 2021-07-20

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: 2459439.523050534073
Time: 2021-08-13 00:33:11.566144 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0001 and UK000F
 Convergence angle = 25.23331 deg
 R.A. =  48.60347  Dec = +57.86086 deg
Intersection 2 - Stations: UK0001 and UK002C
 Convergence angle = 9.93488 deg
 R.A. =  49.76010  Dec = +58.63202 deg
Intersection 3 - Stations: UK000F and UK002C
 Convergence angle = 15.30078 deg
 R.A. =  47.53616  Dec = +57.56504 deg

Best intersection: Stations UK0001 and UK000F with Qconv = 25.23 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3524927.65 +/- 194.66 m
 Y =  -2063880.98 +/- 54.39 m
 Z =   5024629.74 +/- 67.53 m
 Vx =    20513.78 +/- 1251.69 m/s
 Vy =    23180.28 +/- 330.75 m/s
 Vz =    50129.45 +/- 965.78 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+3.352593e+04, +7.536742e+03, +5.991863e+03, +1.875423e+05, +3.263011e+04, +1.285014e+04
+7.536742e+03, +2.162567e+03, +1.888475e+03, +3.830921e+04, +7.781004e+03, +2.183857e+03
+5.991863e+03, +1.888475e+03, +2.458854e+03, +2.972943e+04, +5.002391e+03, +1.943813e+03
+1.875423e+05, +3.830921e+04, +2.972943e+04, +1.388454e+06, +2.185367e+05, +1.004738e+05
+3.263011e+04, +7.781004e+03, +5.002391e+03, +2.185367e+05, +4.036452e+04, +1.426640e+04
+1.285014e+04, +2.183857e+03, +1.943813e+03, +1.004738e+05, +1.426640e+04, +9.288918e+03

Timing offsets (from input data):
    UK0001: -0.004153 s
    UK000F: 0.000000 s
    UK002B: 0.000000 s
    UK002C: -0.001602 s

Reference point on the trajectory:
  Time: 2021-08-13 00:33:11.566144 UTC
  Lon     = +-0.320382 +/- 0.0020 deg
  Lat     = +51.076199 +/- 0.0008 deg
  Lat geo = +50.891159 +/- 0.0008 deg
  Ht      =  110181.61 +/- 130.90 m

  JD dynamic   = 2459439.523851274978 
  LST apparent = 329.6505930375 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  48.49223 +/- 1.4353 deg
  Dec       = +58.30557 +/- 0.7681 deg
  Azimuth   =  48.53452 +/- 1.4984 deg
  Elevation = +46.53844 +/- 0.3538 deg
  Vavg      =  58.44787 +/- 1.7140 km/s
  Vinit     =  58.91606 +/- 0.6388 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  48.59793 +/- 1.4353 deg
  Dec       = +58.06435 +/- 0.7681 deg
  Azimuth   =  48.81184 +/- 1.4984 deg
  Elevation = +46.38096 +/- 0.3538 deg
  Vavg      =  58.60196 +/- 1.7140 km/s
  Vinit     =  59.07015 +/- 0.6388 km/s
Radiant (geocentric, J2000):
  R.A.   =  48.77253 +/- 1.4619 deg
  Dec    = +58.04241 +/- 0.7640 deg
  Vg     =  57.86186 +/- 0.6502 km/s
  Vinf   =  58.91606 +/- 0.6388 km/s
  Zc     =  43.58426 +/- 0.3574 deg
  Zg     =  43.99785 +/- 0.3696 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  63.59971 +/- 1.2646 deg
  Bg     = +38.32353 +/- 0.4557 deg
  Vh     =  40.11650 +/- 0.2358 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  84.85873 +/- 3.8146 deg
  Bh     = +63.43291 +/- 0.5171 deg
  Vh_x   =  -1.60781 +/- 1.2655 km/s
  Vh_y   = -17.86974 +/- 0.2466 km/s
  Vh_z   = -35.88064 +/- 0.0847 km/s
Orbit:
  La Sun = 140.210633 +/- 0.0000 deg
  a      =   6.258118 +/- 1.3830 AU
  e      =   0.849490 +/- 0.0190
  i      = 112.360478 +/- 1.3120 deg
  peri   = 147.856340 +/- 3.0957 deg
  node   = 140.210059 +/- 0.0001 deg
  Pi     = 288.066398 +/- 3.0956 deg
  q      =   0.941910 +/- 0.0119 AU
  f      =  32.139843 +/- 3.0958 deg
  M      =   1.449867 +/- 0.3483 deg
  Q      =  11.574326 +/- 2.7565 AU
  n      =   0.062956 +/- 0.0115 deg/day
  T      =  15.655476 +/- 6.0538 years
  Last perihelion JD = 2459416.494078 (2021-07-20 23:51:28.311808) +/- 2.1060 days
  Tj     =   0.391394 +/- 0.1400
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.126205e-04, +1.557854e-04, +2.729045e-02, -2.148541e-08, +7.027228e-04, +2.941196e-04
q   , +1.557854e-04, +1.259138e-04, +2.168034e-02, -1.721604e-08, +5.615329e-04, +2.360906e-04
Tp  , +2.729045e-02, +2.168034e-02, +3.748823e+00, -2.978021e-06, +9.697223e-02, +4.081789e-02
node, -2.148541e-08, -1.721604e-08, -2.978021e-06, +2.408756e-12, -7.704187e-08, -3.300791e-08
peri, +7.027228e-04, +5.615329e-04, +9.697223e-02, -7.704187e-08, +2.509426e-03, +1.056121e-03
i   , +2.941196e-04, +2.360906e-04, +4.081789e-02, -3.300791e-08, +1.056121e-03, +4.523481e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = -0.003629
 a2 = 44.572499

Mean time residuals from time vs. length:
  Station with reference time: UK000F
  Avg. res. = 1.102e-06 s
  Stddev    = 1.05e-03 s

Begin point on the trajectory:
  Lon =    -0.320277 +/- 0.0021 deg
  Lat =    51.076258 +/- 0.0008 deg
  Ht  = 110192.21 +/- 145.79 m
End point on the trajectory:
  Lon =    -0.420381 +/- 0.0013 deg
  Lat =    51.020992 +/- 0.0008 deg
  Ht  = 100254.57 +/- 82.63 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
    UK0001,   False,    -1.778230,    50.857470,   24.00,  40.824829,   0.000000,   109870.84,   100917.61,          0.015986,     30.95,     26.50,              18.62, 0.1019,    True,    True, {"ff_name": "FF_UK0001_20210813_003307_515_0395008.fits"}
    UK000F,   False,    -1.306160,    51.883100,   80.00,   0.000000,   0.000000,   110192.21,   100254.57,          0.017252,     45.01,     11.74,              61.06, 0.7659,    True,    True, {"ff_name": "FF_UK000F_20210813_003307_969_0370432.fits"}
    UK002B,    True,    -1.367130,    50.815550,   22.00,  28.900116,  11.530906,   109790.60,    98703.29,          0.043689,       nan,       nan,              14.26, 0.0000,    True,    True, {"ff_name": "FF_UK002B_20210813_003309_183_0397568.fits"}
    UK002C,   False,    -1.801980,    51.351940,  130.00,   0.001788,  49.043333,   105686.74,   100682.88,          0.001651,      3.72,      2.14,              38.63, 0.3898,    True,    True, {"ff_name": "FF_UK002C_20210813_003311_667_0390400.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,     UK0001,       0,  0.023621, 2459439.523050855380,  32.91419,  41.28191,               76.14474,  45.58285,        76.14286,       45.57580,     32.91419,     +41.28191,      32.92298,      +41.27890,  3524778.57, -2064049.44,  5024265.44,      51.074476,       -0.323594,  109870.84,  152577.63,       0.00,              428.16,  -536.02,      0.00,           63846.36,     12.42,     14.54,          25.84,  +3.92,  +3.00
  1,     UK0001,       0,  0.063697, 2459439.523051319178,  32.71039,  40.93754,               76.67242,  45.50804,        76.67248,       45.50826,     32.71039,     +40.93754,      32.71041,      +40.93763,  3523754.33, -2065206.82,  5021762.51,      51.062629,       -0.345032,  107736.08,  149802.76,    2941.63,             3369.79,    44.50,  73401.39,           63846.36,     -0.38,     -0.44,           0.80,  +1.99,  +1.11
  2,     UK0001,       0,  0.103773, 2459439.523051782977,  32.54843,  40.62422,               77.13724,  45.42473,        77.14344,       45.44643,     32.54843,     +40.62422,      32.52235,      +40.63339,  3522871.95, -2066203.89,  5019606.25,      51.052414,       -0.363527,  105897.48,  147416.48,    5475.84,             5904.00,   217.58,  63235.10,           63846.36,    -37.02,    -43.24,          79.65,  +1.33,  +0.49
  3,     UK0001,       0,  0.143829, 2459439.523052246775,  32.38815,  40.34860,               77.55693,  45.36175,        77.56513,       45.38971,     32.38815,     +40.34860,      32.35465,      +40.36037,  3522103.47, -2067072.27,  5017728.30,      51.043510,       -0.379658,  104296.56,  145341.41,    7682.95,             8111.11,    64.75,  55100.49,           63846.36,    -47.10,    -54.99,         102.76,  +1.26,  +0.45
  4,     UK0001,       0,  0.183869, 2459439.523052710108,  32.20266,  40.08060,               77.98371,  45.31825,        77.98762,       45.33128,     32.20266,     +40.08060,      32.18758,      +40.08609,  3521353.34, -2067919.90,  5015895.23,      51.034813,       -0.395409,  102734.21,  143319.70,    9837.32,            10265.48,  -139.88,  53805.56,           60944.97,    -21.65,    -25.33,          47.95,  +1.41,  +0.63
  5,     UK0001,       0,  0.223921, 2459439.523053173907,  31.98823,  39.75654,               78.49331,  45.25885,        78.49323,       45.25862,     31.98823,     +39.75654,      31.98947,      +39.75645,  3520480.94, -2068905.70,  5013763.34,      51.024690,       -0.413703,  100917.61,  140974.92,   12342.88,            12771.04,     5.98,  62557.68,           60345.90,      0.38,      0.44,           0.85,  +4.51,  +3.76
  0,     UK000F,       0,  0.000000, 2459439.523050534073, 355.53001,  10.82124,              142.26071,  43.51664,       142.27167,       43.52645,    355.53001,     +10.82124,     355.51870,      +10.82724,  3524932.73, -2063875.24,  5024642.17,      51.076258,       -0.320277,  110192.21,  158407.57,       0.00,               14.60,   442.09,      0.00,           55612.14,     -8.84,    -33.77,          45.46,  +2.66,  +1.66
  1,     UK000F,       0,  0.040340, 2459439.523051001132, 355.19297,  10.28378,              142.96352,  43.14609,       142.94604,       43.13060,    355.19297,     +10.28378,     355.21109,      +10.27426,  3524250.72, -2064645.90,  5022975.54,      51.068372,       -0.334608,  108770.60,  157490.18,    1958.75,             1944.15,    -5.03,  48556.08,           55612.14,     13.94,     53.37,          72.24,  +1.21,  +0.22
  2,     UK000F,       0,  0.080784, 2459439.523051469121, 354.85818,   9.61662,              143.72172,  42.65076,       143.73003,       42.65805,    354.85818,      +9.61662,     354.85003,       +9.62112,  3523455.69, -2065544.27,  5021032.73,      51.059173,       -0.351289,  107113.75,  156445.96,    4242.10,             4227.49,  -104.49,  56456.95,           55612.14,     -6.57,    -25.11,          34.22,  +0.77,  -0.20
  3,     UK000F,       0,  0.121240, 2459439.523051937111, 354.44079,   8.90514,              144.59361,  42.13957,       144.58209,       42.12959,    354.44079,      +8.90514,     354.45301,       +8.89893,  3522589.17, -2066523.43,  5018915.21,      51.049139,       -0.369456,  105308.34,  155338.71,    6730.77,             6716.16,     0.67,  61515.47,           55612.14,      9.00,     34.45,          47.28,  +0.66,  -0.30
  4,     UK000F,       0,  0.161712, 2459439.523052405566, 354.04182,   8.17985,              145.43694,  41.60352,       145.42396,       41.59240,    354.04182,      +8.17985,     354.05564,       +8.17289,  3521730.63, -2067493.57,  5016817.19,      51.039188,       -0.387461,  103519.97,  154273.55,    9196.52,             9181.92,    81.98,  60925.00,           57294.94,     10.03,     38.44,          53.11,  +0.53,  -0.41
  5,     UK000F,       0,  0.202164, 2459439.523052874021, 353.69388,   7.49977,              146.18419,  41.08717,       146.18909,       41.09133,    353.69388,      +7.49977,     353.68978,       +7.50239,  3520948.38, -2068377.50,  5014905.61,      51.030115,       -0.403882,  101890.90,  153330.85,   11443.16,            11428.56,   -54.66,  55538.28,           57524.11,     -3.76,    -14.40,          20.03,  +1.29,  +0.36
  6,     UK000F,       0,  0.242584, 2459439.523053341545, 353.28964,   6.83517,              146.98329,  40.60021,       146.95522,       40.57664,    353.28964,      +6.83517,     353.31889,       +6.82022,  3520162.48, -2069265.56,  5012985.11,      51.020992,       -0.420381,  100254.57,  152411.43,   13700.29,            13685.68,  -178.92,  55841.87,           57425.76,     21.31,     81.80,         114.40,  +3.19,  +2.27
  0,     UK002B,       1,  0.012208, 2459439.523050675169,  26.94531,  49.77533,               68.21579,  53.70372,        68.17202,       53.76506,     26.94531,     +49.77533,      26.87574,      +49.82445,  3524740.07, -2064092.94,  5024171.37,      51.074031,       -0.324328,  109790.60,  135475.00,       0.00,              538.72,   246.93,      0.00,           54624.81,    -33.37,   -153.84,         239.67,  +3.12,  +2.46
  1,     UK002B,       1,  0.052120, 2459439.523051137105,  26.66053,  49.61660,               68.59002,  53.80459,        68.54810,       53.86397,     26.66053,     +49.61660,      26.59345,      +49.66392,  3523986.01, -2064945.02,  5022328.67,      51.065310,       -0.340155,  108218.91,  133379.37,    2165.68,             2704.40,    61.15,  54261.36,           54624.81,    -31.67,   -146.36,         231.58,  +1.73,  +1.10
  2,     UK002B,       1,  0.092004, 2459439.523051599041,  26.34335,  49.48839,               68.93381,  53.93760,        68.91811,       53.95992,     26.34335,     +49.48839,      26.31850,      +49.50615,  3523269.55, -2065754.61,  5020577.86,      51.057018,       -0.355202,  106725.89,  131390.20,    4223.37,             4762.08,  -230.97,  51591.81,           54624.81,    -11.56,    -54.19,          86.99,  +1.58,  +0.99
  3,     UK002B,       1,  0.131908, 2459439.523052060977,  26.02724,  49.29618,               69.37764,  54.04338,        69.35828,       54.07133,     26.02724,     +49.29618,      25.99626,      +49.31826,  3522449.39, -2066681.38,  5018573.63,      51.047519,       -0.372405,  105017.14,  129116.89,    6578.90,             7117.62,  -226.42,  59030.05,           54624.81,    -14.19,    -66.49,         108.61,  +1.26,  +0.71
  4,     UK002B,       1,  0.171796, 2459439.523052522447,  25.69133,  49.12029,               69.80768,  54.16799,        69.79889,       54.18083,     25.69133,     +49.12029,      25.67760,      +49.13038,  3521660.25, -2067573.09,  5016645.22,      51.038372,       -0.388965,  103373.39,  126932.39,    8845.32,             9384.03,  -310.05,  56819.49,           55403.14,     -6.35,    -29.97,          49.78,  +1.12,  +0.60
  5,     UK002B,       1,  0.211724, 2459439.523052984383,  25.41145,  48.89674,               70.28698,  54.23930,        70.25221,       54.29127,     25.41145,     +48.89674,      25.35391,      +48.93723,  3520879.76, -2068455.04,  5014737.94,      51.029319,       -0.405347,  101748.01,  124774.82,   11086.91,            11625.62,  -420.86,  56140.75,           55731.02,    -25.48,   -118.81,         200.87,  +1.40,  +0.92
  6,     UK002B,       1,  0.251600, 2459439.523053446319,  25.02778,  48.68148,               70.80561,  54.37595,        70.77910,       54.41620,     25.02778,     +48.68148,      24.98371,      +48.71264,  3520010.72, -2069437.05,  5012614.25,      51.019230,       -0.423572,   99938.63,  122377.00,   13582.83,            14121.55,  -274.27,  62592.11,           56582.73,    -19.20,    -90.05,         155.18,  +2.08,  +1.64
  7,     UK002B,       1,  0.291484, 2459439.523053907789,  24.72857,  48.54984,               71.15586,  54.49826,        71.15187,       54.50436,     24.72857,     +48.54984,      24.72297,      +48.55455,  3519417.28, -2070107.62,  5011164.07,      51.012336,       -0.436071,   98703.29,  120739.98,   15287.20,            15825.91,  -919.71,  42733.09,           55783.99,     -2.83,    -13.45,          23.48,  +3.82,  +3.41
  0,     UK002C,       0,  0.111644, 2459439.523051844910,  16.49171,  24.03507,              107.86873,  44.21602,       107.86995,       44.21795,     16.49171,     +24.03507,      16.49008,      +24.03596,  3522770.81, -2066318.19,  5019359.07,      51.051243,       -0.365650,  105686.74,  150079.21,       0.00,             6194.50,    44.37,      0.00,           57299.82,     -2.77,     -4.81,           7.63,  +1.13,  +0.25
  1,     UK002C,       0,  0.151816, 2459439.523052309640,  16.20948,  23.50023,              108.62527,  43.97611,       108.62381,       43.97383,     16.20948,     +23.50023,      16.21261,      +23.49917,  3521956.80, -2067238.00,  5017369.89,      51.041810,       -0.382727,  103991.05,  148317.65,    2337.84,             8532.35,    15.44,  58195.86,           57299.82,      3.25,      5.63,           9.04,  +1.08,  +0.22
  2,     UK002C,       0,  0.192000, 2459439.523052774835,  15.93177,  22.95279,              109.38420,  43.72063,       109.38413,       43.72053,     15.93177,     +22.95279,      15.93269,      +22.95274,  3521148.20, -2068151.70,  5015393.92,      51.032433,       -0.399694,  102307.01,  146583.89,    4660.15,            10854.66,   -29.73,  57791.90,           57299.82,      0.15,      0.26,           0.41,  +1.40,  +0.57
  3,     UK002C,       0,  0.232184, 2459439.523053240031,  15.65778,  22.41275,              110.12827,  43.46540,       110.12846,       43.46568,     15.65778,     +22.41275,      15.65845,      +22.41288,  3520368.20, -2069033.09,  5013487.84,      51.023381,       -0.416069,  100682.88,  144926.94,    6900.33,            13094.84,  -157.04,  55748.03,           57299.82,     -0.39,     -0.68,           1.12,  +2.82,  +2.01

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.