Orbital Analysis for matched events on 20210813_005751.291_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 64.22° Bg 40.13° Vg 55.98km/s
mass 0.07647g, abs. mag -1.3
Path Details
------------
start 2.35° 53.27° 108.86km
end   2.24° 53.22° 95.58km

Orbit Details
-------------
Semimajor axis 4.42A.U., eccentricity 0.79, inclination 108.58°, Period 9.28Y, LA Sun 140.23°, 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: 2459439.540176984854
Time: 2021-08-13 00:57:51.317884 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000Z and UK002K
 Convergence angle = 22.49629 deg
 R.A. =  48.77576  Dec = +59.67024 deg
Intersection 2 - Stations: UK000Z and UK0032
 Convergence angle = 1.83613 deg
 R.A. =  27.50292  Dec = +78.76174 deg
Intersection 3 - Stations: UK002K and UK0032
 Convergence angle = 20.78266 deg
 R.A. =  48.15044  Dec = +57.91015 deg

Best intersection: Stations UK000Z and UK002K with Qconv = 22.50 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3617582.10 +/- 163.69 m
 Y =  -1423812.89 +/- 173.10 m
 Z =   5177444.52 +/- 86.37 m
 Vx =    18948.07 +/- 865.70 m/s
 Vy =    21193.71 +/- 889.12 m/s
 Vz =    49488.32 +/- 1333.37 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.629304e+04, +2.694043e+04, +1.287870e+04, +1.050379e+05, +1.051869e+05, +6.188721e+04
+2.694043e+04, +2.957752e+04, +1.371265e+04, +1.072722e+05, +1.172138e+05, +7.002664e+04
+1.287870e+04, +1.371265e+04, +7.525221e+03, +4.192483e+04, +4.399168e+04, +2.582273e+04
+1.050379e+05, +1.072722e+05, +4.192483e+04, +6.739529e+05, +6.941090e+05, +4.247065e+05
+1.051869e+05, +1.172138e+05, +4.399168e+04, +6.941090e+05, +7.678720e+05, +4.755925e+05
+6.188721e+04, +7.002664e+04, +2.582273e+04, +4.247065e+05, +4.755925e+05, +3.117431e+05

Timing offsets (from input data):
    UK000Z: -0.000460 s
    UK002K: 0.000000 s
    UK0032: -0.000121 s

Reference point on the trajectory:
  Time: 2021-08-13 00:57:51.317884 UTC
  Lon     = ++2.362838 +/- 0.0032 deg
  Lat     = +53.278961 +/- 0.0003 deg
  Lat geo = +53.097481 +/- 0.0003 deg
  Ht      =  110089.76 +/- 120.58 m

  JD dynamic   = 2459439.540978031233 
  LST apparent = 338.5163257605 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  48.20195 +/- 0.3264 deg
  Dec       = +60.12449 +/- 0.7910 deg
  Azimuth   =  50.88400 +/- 1.2519 deg
  Elevation = +52.98105 +/- 0.2815 deg
  Vavg      =  56.16418 +/- 1.0274 km/s
  Vinit     =  57.07273 +/- 1.0842 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  48.39847 +/- 0.3264 deg
  Dec       = +59.89344 +/- 0.7910 deg
  Azimuth   =  51.18032 +/- 1.2519 deg
  Elevation = +52.80478 +/- 0.2815 deg
  Vavg      =  56.29716 +/- 1.0274 km/s
  Vinit     =  57.20571 +/- 1.0842 km/s
Radiant (geocentric, J2000):
  R.A.   =  48.46029 +/- 0.3397 deg
  Dec    = +59.90959 +/- 0.7923 deg
  Vg     =  55.98368 +/- 1.1050 km/s
  Vinf   =  57.07273 +/- 1.0842 km/s
  Zc     =  37.13367 +/- 0.2790 deg
  Zg     =  37.50444 +/- 0.2695 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  64.22279 +/- 0.4833 deg
  Bg     = +40.13443 +/- 0.7214 deg
  Vh     =  39.37266 +/- 0.5913 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  89.84106 +/- 3.0679 deg
  Bh     = +66.42518 +/- 1.2683 deg
  Vh_x   =  -0.04368 +/- 0.8583 km/s
  Vh_y   = -15.74689 +/- 1.0381 km/s
  Vh_z   = -36.08657 +/- 0.2048 km/s
Orbit:
  La Sun = 140.227078 +/- -0.0000 deg
  a      =   4.415939 +/- 1.8632 AU
  e      =   0.787501 +/- 0.0489
  i      = 108.580452 +/- 1.8069 deg
  peri   = 146.336252 +/- 1.6387 deg
  node   = 140.226993 +/- 0.0001 deg
  Pi     = 286.563246 +/- 1.6386 deg
  q      =   0.938383 +/- 0.0049 AU
  f      =  33.660069 +/- 1.6388 deg
  M      =   2.597886 +/- 0.9438 deg
  Q      =   7.893495 +/- 3.7229 AU
  n      =   0.106211 +/- 0.0340 deg/day
  T      =   9.279728 +/- 7.1881 years
  Last perihelion JD = 2459415.081307 (2021-07-19 13:57:04.903357) +/- 1.3863 days
  Tj     =   0.816727 +/- 0.3148
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.398912e-03, +1.924239e-04, +6.317793e-02, -9.823073e-08, +1.246270e-03, +1.439040e-03
q   , +1.924239e-04, +2.266997e-05, +6.180376e-03, -9.100822e-09, +1.298876e-04, +1.340460e-04
Tp  , +6.317793e-02, +6.180376e-03, +1.835878e+00, -2.774167e-06, +3.743593e-02, +4.076091e-02
node, -9.823073e-08, -9.100822e-09, -2.774167e-06, +4.381843e-12, -5.606921e-08, -6.427665e-08
peri, +1.246270e-03, +1.298876e-04, +3.743593e-02, -5.606921e-08, +7.713701e-04, +8.245014e-04
i   , +1.439040e-03, +1.340460e-04, +4.076091e-02, -6.427665e-08, +8.245014e-04, +9.430818e-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: UK002K
  Avg. res. = 1.714e-06 s
  Stddev    = 1.31e-03 s

Begin point on the trajectory:
  Lon =     2.352217 +/- 0.0037 deg
  Lat =    53.273784 +/- 0.0003 deg
  Ht  = 108858.18 +/- 193.14 m
End point on the trajectory:
  Lon =     2.236310 +/- 0.0028 deg
  Lat =    53.217748 +/- 0.0003 deg
  Ht  = 95579.34 +/- 91.95 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
    UK000Z,   False,    -1.740490,    53.069201,  230.00,   0.000000,   0.000000,   108154.24,    95580.98,          0.010810,      2.74,     55.43,              40.05, 0.4141,    True,    True, {"ff_name": "FF_UK000Z_20210813_005750_792_0417536.fits"}
    UK002K,   False,    -0.382860,    53.537770,   34.00,   0.000000,   0.000000,   108099.03,    95579.34,          0.010860,     16.41,     35.64,              40.82, 0.4272,    True,    True, {"ff_name": "FF_UK002K_20210813_005748_748_0422912.fits"}
    UK0032,   False,    -0.023645,    52.984073,    6.00,   1.053088,  14.043342,   108858.18,    96065.16,          0.016752,      5.03,     54.17,              26.76, 0.2027,    True,    True, {"ff_name": "FF_UK0032_20210813_005744_954_0428800.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,     UK000Z,       0,  0.036413, 2459439.540177411400,  56.86495,  19.67955,               83.67440,  20.09072,        83.67220,       20.08939,     56.86495,     +19.67955,      56.86769,      +19.67983,  3616777.24, -1424713.14,  5175342.39,      53.270824,       +2.346102,  108154.24,  296777.32,       0.00,             2424.30,   304.97,      0.00,           53554.81,     12.66,      0.63,           8.81,  +3.73,  +1.37
  1,     UK000Z,       0,  0.076609, 2459439.540177877061,  56.92548,  19.42824,               83.79693,  19.86018,        83.82003,       19.87413,     56.92548,     +19.42824,      56.89861,      +19.42528,  3616106.01, -1425463.93,  5173589.27,      53.264032,       +2.332011,  106540.30,  295241.92,    2021.79,             4446.09,    32.67,  50298.36,           53554.81,   -132.87,     -6.55,          92.94,  +2.05,  -0.30
  2,     UK000Z,       0,  0.116789, 2459439.540178341791,  56.91773,  19.14776,               83.99160,  19.64767,        83.97985,       19.64057,     56.91773,     +19.14776,      56.93204,      +19.14925,  3615386.10, -1426269.15,  5171709.03,      53.256742,       +2.316907,  104809.56,  293602.60,    4190.20,             6614.49,   -92.11,  53967.28,           53554.81,     67.29,      3.37,          47.33,  +1.52,  -0.82
  3,     UK000Z,       0,  0.157005, 2459439.540178807452,  56.97068,  18.85836,               84.14451,  19.39177,        84.14801,       19.39389,     56.97068,     +18.85836,      56.96722,      +18.85792,  3614634.94, -1427109.34,  5169747.16,      53.249129,       +2.301152,  103003.96,  291899.98,    6452.74,             8877.03,  -124.80,  56259.72,           53554.81,    -19.95,     -0.99,          14.12,  +1.25,  -1.08
  4,     UK000Z,       0,  0.197233, 2459439.540179273114,  57.00505,  18.53330,               84.33506,  19.11908,        84.33472,       19.11887,     57.00505,     +18.53330,      57.00628,      +18.53335,  3613808.47, -1428033.76,  5167588.59,      53.240746,       +2.283830,  101017.65,  290036.66,    8942.12,            11366.42,    68.66,  61881.80,           55505.90,      1.95,      0.10,           1.39,  +1.30,  -1.01
  5,     UK000Z,       0,  0.237433, 2459439.540179738309,  57.03732,  18.25314,               84.49665,  18.88226,        84.49535,       18.88147,     57.03732,     +18.25314,      57.03984,      +18.25331,  3613103.57, -1428822.20,  5165747.55,      53.233590,       +2.269029,   99323.78,  288453.42,   11065.31,            13489.60,  -102.48,  52815.65,           55678.74,      7.33,      0.37,           5.25,  +1.60,  -0.70
  6,     UK000Z,       0,  0.277657, 2459439.540180203971,  57.07211,  17.93438,               84.68134,  18.61371,        84.67741,       18.61134,     57.07211,     +17.93438,      57.07789,      +17.93488,  3612311.54, -1429708.10,  5163678.92,      53.225543,       +2.252415,   97420.81,  286684.18,   13450.97,            15875.27,   -12.51,  59309.41,           56129.66,     22.07,      1.10,          15.90,  +1.02,  -1.27
  7,     UK000Z,       0,  0.317877, 2459439.540180669166,  57.10612,  17.62242,               84.86146,  18.35068,        84.85503,       18.34681,     57.10612,     +17.62242,      57.11499,      +17.62324,  3611545.66, -1430564.74,  5161678.63,      53.217755,       +2.236342,   95580.98,  284981.67,   15757.82,            18182.12,    -1.12,  57355.87,           56419.72,     35.91,      1.79,          26.02,  +2.31,  +0.04
  0,     UK002K,       1,  0.000000, 2459439.540176984854,  41.35342,  19.16634,               97.87181,  29.74187,        97.85453,       29.72752,     41.35342,     +19.16634,      41.37531,      +19.16447,  3617595.95, -1423797.40,  5177480.69,      53.279101,       +2.363235,  110123.07,  216519.20,       0.00,               41.71,     0.60,      0.00,           55674.72,     71.25,     32.82,          74.73,  +4.34,  +2.66
  1,     UK002K,       0,  0.040344, 2459439.540177451912,  41.32812,  18.72117,               98.21180,  29.40824,        98.20910,       29.40601,     41.32812,     +18.72117,      41.33170,      +18.72088,  3616754.28, -1424738.82,  5175282.42,      53.270591,       +2.345611,  108099.03,  214610.05,    2535.16,             2493.45,   149.79,  62838.62,           55674.72,     11.02,      5.07,          11.66,  +2.78,  +1.12
  2,     UK002K,       0,  0.080636, 2459439.540177918039,  41.30532,  18.33740,               98.50404,  29.12058,        98.51324,       29.12817,     41.30532,     +18.33740,      41.29407,      +18.33839,  3616040.10, -1425537.65,  5173417.12,      53.263365,       +2.330629,  106381.83,  212998.97,    4686.33,             4644.62,     1.39,  53389.52,           55674.72,    -37.32,    -17.15,          39.77,  +1.56,  -0.08
  3,     UK002K,       0,  0.120912, 2459439.540178384166,  41.26053,  17.96346,               98.80660,  28.85300,        98.80955,       28.85543,     41.26053,     +17.96346,      41.25732,      +17.96378,  3615350.88, -1426308.55,  5171617.04,      53.256385,       +2.316161,  104724.89,  211453.08,    6762.30,             6720.58,  -221.31,  51543.44,           55674.72,    -11.88,     -5.46,          12.75,  +1.31,  -0.32
  4,     UK002K,       0,  0.161256, 2459439.540178851224,  41.22011,  17.50762,               99.16140,  28.51774,        99.16749,       28.52275,     41.22011,     +17.50762,      41.21313,      +17.50827,  3614526.44, -1427230.70,  5169463.78,      53.248029,       +2.298884,  102743.18,  209617.94,    9245.55,             9203.84,   -40.60,  61552.03,           56362.21,    -24.38,    -11.21,          26.40,  +1.11,  -0.50
  5,     UK002K,       0,  0.201576, 2459439.540179317817,  41.15252,  17.06911,               99.52534,  28.21131,        99.51165,       28.20010,     41.15252,     +17.06911,      41.17052,      +17.06765,  3613742.34, -1428107.72,  5167415.88,      53.240075,       +2.282441,  100858.74,  207884.73,   11607.31,            11565.59,    19.99,  58575.27,           56874.81,     54.28,     25.00,          59.29,  +1.20,  -0.39
  6,     UK002K,       0,  0.241904, 2459439.540179784875,  41.12585,  16.63485,               99.84939,  27.88353,        99.84784,       27.88226,     41.12585,     +16.63485,      41.12880,      +16.63468,  3612984.33, -1428955.57,  5165436.12,      53.232379,       +2.266537,   99037.27,  206220.82,   13890.48,            13848.76,     1.53,  56615.01,           57030.00,      6.09,      2.80,           6.71,  +1.22,  -0.35
  7,     UK002K,       0,  0.282256, 2459439.540180251934,  41.06001,  16.15744,              100.23489,  27.54376,       100.21744,       27.52953,     41.06001,     +16.15744,      41.08298,      +16.15557,  3612159.63, -1429878.01,  5163282.18,      53.223999,       +2.249244,   97055.88,  204425.10,   16374.53,            16332.82,   182.58,  61559.60,           57472.51,     68.10,     31.38,          75.66,  +1.19,  -0.36
  8,     UK002K,       0,  0.322532, 2459439.540180718061,  41.04126,  15.79366,              100.50017,  27.26593,       100.49576,       27.26234,     41.04126,     +15.79366,      41.04811,      +15.79319,  3611544.98, -1430565.50,  5161676.85,      53.217748,       +2.236310,   95579.34,  203093.79,   18225.88,            18184.17,  -264.73,  45966.61,           56912.69,     17.11,      7.88,          19.13,  +1.71,  +0.17
  0,     UK0032,       0,  0.026288, 2459439.540177290328,  53.55821,  32.84446,               77.58534,  32.89825,        77.59026,       32.90155,     53.55821,     +32.84446,      53.55206,      +32.84393,  3617069.98, -1424385.71,  5176106.96,      53.273784,       +2.352217,  108858.18,  196529.80,       0.00,             1542.55,     1.12,      0.00,           57626.67,    -18.06,     -1.68,          19.03,  +2.61,  +1.14
  1,     UK0032,       0,  0.066504, 2459439.540177755989,  53.56902,  32.55044,               77.82207,  32.68163,        77.80859,       32.67258,     53.56902,     +32.55044,      53.58643,      +32.55189,  3616349.07, -1425192.06,  5174224.10,      53.266492,       +2.337097,  107124.70,  194597.15,    2171.42,             3713.97,  -122.70,  53993.93,           57626.67,     49.07,      4.61,          52.24,  +1.94,  +0.49
  2,     UK0032,       0,  0.106772, 2459439.540178222116,  53.63446,  32.20713,               78.05897,  32.39697,        78.06530,       32.40119,     53.63446,     +32.20713,      53.62690,      +32.20645,  3615515.08, -1426124.89,  5172045.90,      53.258048,       +2.319627,  105119.63,  192369.29,    4683.44,             6225.99,    91.12,  62382.66,           57626.67,    -22.77,     -2.12,          24.52,  +1.21,  -0.21
  3,     UK0032,       0,  0.147008, 2459439.540178687777,  53.66606,  31.89648,               78.29166,  32.15506,        78.29464,       32.15705,     53.66606,     +31.89648,      53.66291,      +31.89616,  3614781.58, -1426945.32,  5170130.14,      53.250616,       +2.304238,  103356.42,  190414.70,    6892.81,             8435.35,     4.10,  54910.05,           57626.67,    -10.63,     -0.99,          11.57,  +1.43,  +0.03
  4,     UK0032,       0,  0.187268, 2459439.540179153904,  53.72082,  31.56059,               78.52677,  31.88073,        78.54247,       31.89119,     53.72082,     +31.56059,      53.70181,      +31.55890,  3614001.30, -1427818.08,  5168092.22,      53.242703,       +2.287876,  101481.06,  188342.36,    9243.06,            10785.60,    56.61,  58376.84,           57663.73,    -55.46,     -5.15,          61.00,  +1.05,  -0.32
  5,     UK0032,       0,  0.227512, 2459439.540179619566,  53.75910,  31.23602,               78.76296,  31.62368,        78.77973,       31.63483,     53.75910,     +31.23602,      53.73896,      +31.23422,  3613265.79, -1428640.76,  5166171.22,      53.235237,       +2.272440,   99713.57,  186394.56,   11458.46,            13001.00,   -24.83,  55049.16,           57300.82,    -58.69,     -5.45,          65.22,  +1.17,  -0.18
  6,     UK0032,       0,  0.267764, 2459439.540180085227,  53.80748,  30.90934,               78.99199,  31.35855,        79.01784,       31.37570,     53.80748,     +30.90934,      53.77619,      +30.90657,  3612538.75, -1429453.96,  5164272.35,      53.227852,       +2.257176,   97966.68,  184475.13,   13648.34,            15190.89,  -132.24,  54404.35,           56860.84,    -89.60,     -8.29,         100.61,  +1.10,  -0.23
  7,     UK0032,       0,  0.308036, 2459439.540180551354,  53.84327,  30.54418,               79.25955,  31.07231,        79.28127,       31.08670,     53.84327,     +30.54418,      53.81738,      +30.54186,  3611747.22, -1430339.29,  5162205.06,      53.219805,       +2.240571,   96065.16,  182393.36,   16032.46,            17575.01,   -46.55,  59200.42,           56872.61,    -74.57,     -6.91,          84.69,  +1.25,  -0.06

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.