Orbital Analysis for matched events on 20210813_220442.440_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 67.08° Bg 37.20° Vg 59.06km/s
mass 0.00534g, abs. mag 1.2
Path Details
------------
start -0.84° 50.46° 107.94km
end   -0.95° 50.33° 98.90km

Orbit Details
-------------
Semimajor axis 13.46A.U., eccentricity 0.93, inclination 113.88°, Period 49.38Y, LA Sun 141.07°, 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: 2459440.419935659505
Time: 2021-08-13 22:04:42.480732 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0001 and UK002D
 Convergence angle = 2.82257 deg
 R.A. =  60.78191  Dec = +57.13077 deg
Intersection 2 - Stations: UK0001 and UK0038
 Convergence angle = 12.92800 deg
 R.A. =  52.56653  Dec = +58.25133 deg
Intersection 3 - Stations: UK002D and UK0038
 Convergence angle = 10.11665 deg
 R.A. =  50.16196  Dec = +58.18204 deg

Best intersection: Stations UK0001 and UK0038 with Qconv = 12.93 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   1610558.44 +/- 185.38 m
 Y =  -3810802.48 +/- 116.24 m
 Z =   4980101.33 +/- 99.59 m
 Vx =    18476.14 +/- 755.40 m/s
 Vy =    25527.95 +/- 793.54 m/s
 Vz =    51166.37 +/- 421.18 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.726439e+04, -1.061319e+04, +9.084224e+03, +6.855693e+04, -4.039162e+04, +3.623939e+04
-1.061319e+04, +6.797327e+03, -5.661812e+03, -4.231889e+04, +2.543822e+04, -2.284532e+04
+9.084224e+03, -5.661812e+03, +5.256353e+03, +3.234868e+04, -2.008787e+04, +1.857884e+04
+6.855693e+04, -4.231889e+04, +3.234868e+04, +3.299376e+05, -1.865271e+05, +1.584888e+05
-4.039162e+04, +2.543822e+04, -2.008787e+04, -1.865271e+05, +1.085407e+05, -9.333535e+04
+3.623939e+04, -2.284532e+04, +1.857884e+04, +1.584888e+05, -9.333535e+04, +8.149378e+04

Timing offsets (from input data):
    UK0001: 0.000000 s
    UK002D: -0.000982 s
    UK0038: -0.000674 s

Reference point on the trajectory:
  Time: 2021-08-13 22:04:42.480732 UTC
  Lon     = +-0.823418 +/- 0.0018 deg
  Lat     = +50.468147 +/- 0.0007 deg
  Lat geo = +50.282278 +/- 0.0007 deg
  Ht      =  108869.63 +/- 188.82 m

  JD dynamic   = 2459440.420736860484 
  LST apparent = 292.9103647978 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  54.10444 +/- 1.5973 deg
  Dec       = +58.37171 +/- 0.1140 deg
  Azimuth   =  30.83555 +/- 0.6690 deg
  Elevation = +28.93588 +/- 0.6088 deg
  Vavg      =  57.26869 +/- 0.1467 km/s
  Vinit     =  60.09194 +/- 0.4217 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  53.82265 +/- 1.5973 deg
  Dec       = +58.16235 +/- 0.1140 deg
  Azimuth   =  31.11694 +/- 0.6690 deg
  Elevation = +28.86442 +/- 0.6088 deg
  Vavg      =  57.40463 +/- 0.1467 km/s
  Vinit     =  60.22788 +/- 0.4217 km/s
Radiant (geocentric, J2000):
  R.A.   =  54.36157 +/- 1.5960 deg
  Dec    = +57.84040 +/- 0.1258 deg
  Vg     =  59.05855 +/- 0.4288 km/s
  Vinf   =  60.09194 +/- 0.4217 km/s
  Zc     =  61.22375 +/- 0.6099 deg
  Zg     =  61.81179 +/- 0.6242 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  67.08353 +/- 0.9748 deg
  Bg     = +37.20424 +/- 0.3691 deg
  Vh     =  41.05438 +/- 0.4188 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  89.74798 +/- 2.2807 deg
  Bh     = +60.43939 +/- 0.5870 deg
  Vh_x   =  -0.08909 +/- 0.7655 km/s
  Vh_y   = -20.25374 +/- 0.2747 km/s
  Vh_z   = -35.71051 +/- 0.5631 km/s
Orbit:
  La Sun = 141.071919 +/- -0.0000 deg
  a      =  13.458901 +/- 508.5104 AU
  e      =   0.932142 +/- 0.0378
  i      = 113.882526 +/- 0.1115 deg
  peri   = 142.732418 +/- 2.9572 deg
  node   = 141.070185 +/- 0.0000 deg
  Pi     = 283.802603 +/- 2.9572 deg
  q      =   0.913292 +/- 0.0120 AU
  f      =  37.263464 +/- 2.9572 deg
  M      =   0.508541 +/- nan deg
  Q      =  26.004509 +/- 1017.0199 AU
  n      =   0.019961 +/- 0.0092 deg/day
  T      =  49.375899 +/- 446945763.6412 years
  Last perihelion JD = 2459414.944443 (2021-07-19 10:39:59.841365) +/- 1.3977 days
  Tj     =  -0.084822 +/- 0.2152
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +5.455803e-04, +2.331754e-04, +3.492118e-02, -1.281591e-09, +9.264091e-04, +1.629501e-05
q   , +2.331754e-04, +1.015768e-04, +1.518947e-02, -6.903898e-10, +4.035339e-04, +8.779965e-06
Tp  , +3.492118e-02, +1.518947e-02, +2.271720e+00, -1.017381e-07, +6.034497e-02, +1.293822e-03
node, -1.281591e-09, -6.903898e-10, -1.017381e-07, +1.591074e-14, -2.741768e-09, -2.024609e-10
peri, +9.264091e-04, +4.035339e-04, +6.034497e-02, -2.741768e-09, +1.603150e-03, +3.486805e-05
i   , +1.629501e-05, +8.779965e-06, +1.293822e-03, -2.024609e-10, +3.486805e-05, +2.576274e-06

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.054309
 a2 = 25.744779

Mean time residuals from time vs. length:
  Station with reference time: UK0001
  Avg. res. = 4.485e-06 s
  Stddev    = 2.12e-03 s

Begin point on the trajectory:
  Lon =    -0.835347 +/- 0.0015 deg
  Lat =    50.455389 +/- 0.0006 deg
  Ht  = 107940.64 +/- 162.81 m
End point on the trajectory:
  Lon =    -0.952892 +/- 0.0008 deg
  Lat =    50.330709 +/- 0.0007 deg
  Ht  = 98902.91 +/- 81.58 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,   0.000000,   0.000000,   107940.64,    98978.15,          0.007802,     17.10,      5.37,              66.23, 0.8375,    True,    True, {"ff_name": "FF_UK0001_20210813_220437_857_0175360.fits"}
    UK002D,   False,    -1.801980,    51.351940,  129.00,   0.000841,  37.821851,   107298.91,    99418.48,          0.014111,     38.71,     10.18,              84.53, 0.9909,    True,    True, {"ff_name": "FF_UK002D_20210813_220441_672_0171776.fits"}
    UK0038,   False,    -2.379250,    51.361350,  169.00,   0.679699,  19.051549,   105432.46,    98902.91,          0.012263,     39.09,      3.15,              79.65, 0.9677,    True,    True, {"ff_name": "FF_UK0038_20210813_220443_557_0168960.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,       1,  0.000000, 2459440.419935659505, 326.00954,  24.60144,              122.26651,  52.97746,       122.29216,       53.02054,    326.00954,     +24.60144,     325.96798,      +24.62725,  1610566.16, -3810791.81,  4980122.73,      50.468314,       -0.823096,  108881.79,  135624.57,       0.00,               25.12,   557.12,      0.00,           56099.54,     32.34,   -103.39,         164.75,  +5.88,  +5.22
  1,     UK0001,       0,  0.039732, 2459440.419936119579, 325.48720,  23.99522,              123.49221,  52.76125,       123.49089,       52.75912,    325.48720,     +23.99522,     325.48942,      +23.99394,  1609967.96, -3811618.34,  4978466.10,      50.455389,       -0.835347,  107940.64,  134910.27,    1945.61,             1920.49,    64.91,  48968.41,           56099.54,     -1.60,      5.09,           8.16,  +2.44,  +1.79
  2,     UK0001,       0,  0.079464, 2459440.419936579186, 324.92989,  23.21985,              124.91017,  52.41500,       124.91798,       52.42691,    324.92989,     +23.21985,     324.91864,      +23.22700,  1609253.75, -3812605.13,  4976488.24,      50.439951,       -0.849938,  106817.56,  134090.78,    4268.49,             4243.37,     0.22,  58463.69,           56099.54,      8.98,    -28.63,          46.16,  +3.13,  +2.49
  3,     UK0001,       0,  0.119160, 2459440.419937038794, 324.32669,  22.43101,              126.38153,  52.06905,       126.37780,       52.06363,    324.32669,     +22.43101,     324.33248,      +22.42775,  1608520.43, -3813618.35,  4974457.42,      50.424092,       -0.864911,  105665.07,  133286.56,    6653.57,             6628.44,    -0.12,  60083.51,           56099.54,     -4.10,     13.06,          21.18,  +1.81,  +1.19
  4,     UK0001,       0,  0.158860, 2459440.419937497936, 323.72550,  21.58317,              127.88488,  51.65952,       127.88689,       51.66230,    323.72550,     +21.58317,     323.72342,      +21.58485,  1607758.37, -3814671.26,  4972347.04,      50.407605,       -0.880459,  104468.11,  132491.58,    9132.10,             9106.98,    92.76,  62431.51,           57842.30,      2.11,     -6.73,          10.98,  +1.86,  +1.25
  5,     UK0001,       0,  0.198564, 2459440.419937957544, 323.14619,  20.76904,              129.31183,  51.25446,       129.31456,       51.25808,    323.14619,     +20.76904,     323.14344,      +20.77124,  1607032.94, -3815673.56,  4970338.09,      50.391902,       -0.895263,  103329.36,  131773.57,   11491.48,            11466.36,    66.26,  59424.39,           58566.40,      2.76,     -8.80,          14.43,  +1.86,  +1.26
  6,     UK0001,       0,  0.238284, 2459440.419938417617, 322.60258,  19.99095,              130.64498,  50.85091,       130.65025,       50.85765,    322.60258,     +19.99095,     322.59687,      +19.99505,  1606349.51, -3816617.84,  4968445.45,      50.377101,       -0.909215,  102257.10,  131132.19,   13714.29,            13689.16,   -97.79,  55961.79,           58545.96,      5.15,    -16.41,          27.05,  +1.47,  +0.88
  7,     UK0001,       0,  0.277960, 2459440.419938876759, 321.98947,  19.12876,              132.11538,  50.39595,       132.11282,       50.39280,    321.98947,     +19.12876,     321.99378,      +19.12683,  1605594.43, -3817661.11,  4966354.40,      50.360741,       -0.924608,  101073.12,  130464.75,   16170.10,            16144.98,   -26.19,  61896.67,           58816.40,     -2.42,      7.70,          12.76,  +1.10,  +0.52
  8,     UK0001,       0,  0.317680, 2459440.419939336367, 321.45544,  18.32186,              133.42039,  49.93971,       133.42970,       49.95078,    321.45544,     +18.32186,     321.44561,      +18.32866,  1604908.22, -3818609.22,  4964454.08,      50.345866,       -0.938607,   99997.73,  129895.14,   18401.92,            18376.80,  -181.22,  56188.86,           58767.42,      8.56,    -27.24,          45.34,  +1.49,  +0.92
  9,     UK0001,       0,  0.357380, 2459440.419939795975, 320.91586,  17.56895,              134.67398,  49.52275,       134.66678,       49.51445,    320.91586,     +17.56895,     320.92577,      +17.56382,  1604257.30, -3819508.58,  4962651.46,      50.331751,       -0.951892,   98978.15,  129387.96,   20518.99,            20493.87,  -449.79,  53326.74,           58445.79,     -6.46,     20.52,          34.29,  +3.89,  +3.33
  0,     UK002D,       0,  0.055920, 2459440.419936317950, 317.30314,   6.76086,              145.84778,  40.71651,       145.83167,       40.70084,    317.30314,      +6.76086,     317.32045,       +6.75050,  1609559.91, -3812182.13,  4977336.08,      50.446569,       -0.843661,  107298.91,  162545.27,       0.00,             3247.63,   419.28,      0.00,           56850.04,    -14.33,     54.51,          71.53,  +3.23,  +2.18
  1,     UK002D,       0,  0.096400, 2459440.419936786406, 316.97524,   6.17019,              146.52087,  40.27712,       146.53151,       40.28738,    316.97524,      +6.17019,     316.96441,       +6.17700,  1608973.51, -3812992.33,  4975712.17,      50.433892,       -0.855672,  106377.06,  162477.91,    1907.19,             5154.82,  -106.05,  47114.33,           56850.04,      9.41,    -35.88,          47.09,  +2.97,  +1.92
  2,     UK002D,       0,  0.136956, 2459440.419937255792, 316.53747,   5.48225,              147.36289,  39.77992,       147.36491,       39.78184,    316.53747,      +5.48225,     316.53593,       +5.48354,  1608265.36, -3813970.76,  4973751.06,      50.418575,       -0.870138,  105264.36,  162427.54,    4210.39,             7458.02,  -239.93,  56790.74,           56850.04,      1.78,     -6.79,           8.91,  +2.25,  +1.20
  3,     UK002D,       0,  0.177612, 2459440.419937726576, 316.02159,   4.67440,              148.33977,  39.18979,       148.32876,       39.17944,    316.02159,      +4.67440,     316.03383,       +4.66744,  1607432.74, -3815121.18,  4971445.26,      50.400557,       -0.887112,  103956.87,  162411.10,    6918.42,            10166.06,    25.00,  66608.39,           56850.04,     -9.66,     36.76,          48.27,  +3.53,  +2.48
  4,     UK002D,       0,  0.218196, 2459440.419938196428, 315.57430,   3.95495,              149.18234,  38.65421,       149.16765,       38.64055,    315.57430,      +3.95495,     315.59050,       +3.94569,  1606696.63, -3816138.24,  4969406.74,      50.384619,       -0.902133,  102801.64,  162433.77,    9312.55,            12560.18,   -19.64,  58991.94,           58254.02,    -12.87,     48.91,          64.22,  +2.35,  +1.30
  5,     UK002D,       0,  0.258852, 2459440.419938666746, 315.11015,   3.15556,              150.06523,  38.04247,       150.06851,       38.04549,    315.11015,      +3.15556,     315.10783,       +3.15762,  1605892.72, -3817248.97,  4967180.47,      50.367205,       -0.918517,  101540.78,  162499.41,   11927.18,            15174.81,   151.89,  64310.96,           59521.90,      2.86,    -10.90,          14.30,  +1.93,  +0.88
  6,     UK002D,       0,  0.299368, 2459440.419939135667, 314.69907,   2.51864,              150.80821,  37.56329,       150.79683,       37.55293,    314.69907,      +2.51864,     314.71208,       +2.51153,  1605233.19, -3818160.22,  4965354.02,      50.352912,       -0.931984,  100506.93,  162583.95,   14072.24,            17319.87,  -137.74,  52943.46,           59270.64,     -9.92,     37.70,          49.46,  +1.54,  +0.48
  7,     UK002D,       0,  0.339924, 2459440.419939605054, 314.27966,   1.84091,              151.56726,  37.04327,       151.55244,       37.02990,    314.27966,      +1.84091,     314.29636,       +1.83168,  1604538.46, -3819120.11,  4963430.08,      50.337848,       -0.946157,   99418.48,  162703.92,   16331.79,            19579.42,  -315.28,  55714.45,           58869.85,    -12.90,     49.00,          64.24,  +2.74,  +1.68
  0,     UK0038,       0,  0.121899, 2459440.419937078375, 327.96922,   4.74027,              133.96088,  34.33448,       133.94636,       34.31487,    327.96922,      +4.74027,     327.98934,       +4.72818,  1608372.36, -3813822.92,  4974047.39,      50.420890,       -0.867914,  105432.46,  183574.39,       0.00,             7110.01,   316.86,      0.00,           57218.15,     -5.92,     73.38,          82.72,  +2.91,  +1.59
  1,     UK0038,       0,  0.162271, 2459440.419937545434, 327.65877,   4.21152,              134.58181,  34.00068,       134.57839,       33.99611,    327.65877,      +4.21152,     327.66405,       +4.20869,  1607767.76, -3814658.29,  4972373.04,      50.407808,       -0.880286,  104482.86,  183370.21,    1966.42,             9076.43,  -142.75,  48707.64,           57218.15,     -1.38,     17.17,          19.37,  +2.16,  +0.84
  2,     UK0038,       0,  0.202775, 2459440.419938014355, 327.20134,   3.49060,              135.45793,  33.55603,       135.45021,       33.54584,    327.20134,      +3.49060,     327.21246,       +3.48427,  1606927.05, -3815819.86,  4970044.87,      50.389609,       -0.897419,  103163.20,  183123.85,    4700.73,            11810.74,   157.60,  67507.12,           57218.15,     -3.09,     38.38,          43.38,  +2.42,  +1.11
  3,     UK0038,       0,  0.243167, 2459440.419938481878, 326.85745,   2.93081,              136.12029,  33.20199,       136.11545,       33.19568,    326.85745,      +2.93081,     326.86486,       +2.92687,  1606281.75, -3816711.46,  4968257.81,      50.375633,       -0.910605,  102150.83,  182960.78,    6799.53,            13909.53,  -170.85,  51960.59,           57218.15,     -1.92,     23.87,          27.00,  +2.43,  +1.12
  4,     UK0038,       0,  0.283611, 2459440.419938949868, 326.48526,   2.29958,              136.84438,  32.79224,       136.85094,       32.80073,    326.48526,      +2.29958,     326.47782,       +2.30489,  1605563.09, -3817704.41,  4966267.61,      50.360062,       -0.925266,  101023.98,  182808.25,    9136.91,            16246.91,  -263.82,  57793.10,           57151.15,      2.58,    -32.20,          36.44,  +1.81,  +0.50
  5,     UK0038,       0,  0.324067, 2459440.419939417858, 326.07990,   1.64590,              137.60889,  32.37220,       137.61605,       32.38136,    326.07990,      +1.64590,     326.07191,       +1.65166,  1604809.61, -3818745.48,  4964180.98,      50.343728,       -0.940624,   99843.22,  182680.78,   11587.53,            18697.54,  -244.28,  60575.05,           57621.44,      2.80,    -34.87,          39.49,  +2.32,  +1.01
  6,     UK0038,       0,  0.364427, 2459440.419939885382, 325.75340,   1.12612,              138.21638,  32.03680,       138.22193,       32.04384,    325.75340,      +1.12612,     325.74772,       +1.13055,  1604209.26, -3819574.95,  4962518.43,      50.330709,       -0.952892,   98902.91,  182601.43,   13540.10,            20650.10,  -717.02,  48378.70,           56801.01,      2.16,    -26.88,          30.46,  +5.04,  +3.73

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.