Orbital Analysis for matched events on 20210813_020052.864_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 64.21° Bg 39.03° Vg 60.22km/s
mass 0.01645g, abs. mag 0.2
Path Details
------------
start 0.87° 53.99° 109.63km
end   0.76° 53.95° 94.80km

Orbit Details
-------------
Semimajor axis -14.13A.U., eccentricity 1.07, inclination 112.87°, Period 1000000000.00Y, LA Sun 140.27°, 

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: 2459439.583945193794
Time: 2021-08-13 02:00:52.904856 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0026 and UK002K
 Convergence angle = 64.15406 deg
 R.A. =  49.21929  Dec = +58.94611 deg

Best intersection: Stations UK0026 and UK002K with Qconv = 64.15 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3793667.79 +/- 110.17 m
 Y =   -476850.60 +/- 247.21 m
 Z =   5226660.32 +/- 418.01 m
 Vx =    20629.08 +/- 853.75 m/s
 Vy =    23832.17 +/- 783.76 m/s
 Vz =    52492.15 +/- 1279.84 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.107447e+04, +2.298812e+04, +3.246337e+04, +2.648253e+04, +6.731493e+04, +7.105762e+04
+2.298812e+04, +5.059139e+04, +7.082104e+04, +5.616121e+04, +1.536506e+05, +1.659737e+05
+3.246337e+04, +7.082104e+04, +1.035980e+05, +7.458629e+04, +1.972884e+05, +2.194980e+05
+2.648253e+04, +5.616121e+04, +7.458629e+04, +7.313690e+04, +1.975189e+05, +2.146903e+05
+6.731493e+04, +1.536506e+05, +1.972884e+05, +1.975189e+05, +5.800139e+05, +6.380263e+05
+7.105762e+04, +1.659737e+05, +2.194980e+05, +2.146903e+05, +6.380263e+05, +7.444419e+05

Timing offsets (from input data):
    UK0026: -0.004340 s
    UK002K: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 02:00:52.904856 UTC
  Lon     = ++0.882457 +/- 0.0039 deg
  Lat     = +53.993026 +/- 0.0017 deg
  Lat geo = +53.812976 +/- 0.0017 deg
  Ht      =  111672.59 +/- 379.08 m

  JD dynamic   = 2459439.584746398963 
  LST apparent = 352.8356969481 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  49.12060 +/- 0.7725 deg
  Dec       = +59.01615 +/- 0.2609 deg
  Azimuth   =  57.49552 +/- 0.6028 deg
  Elevation = +59.48584 +/- 0.3595 deg
  Vavg      =  58.52453 +/- 1.2334 km/s
  Vinit     =  61.22873 +/- 1.3251 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  49.39985 +/- 0.7725 deg
  Dec       = +58.83015 +/- 0.2609 deg
  Azimuth   =  57.76956 +/- 0.6028 deg
  Elevation = +59.29636 +/- 0.3595 deg
  Vavg      =  58.64444 +/- 1.2334 km/s
  Vinit     =  61.34864 +/- 1.3251 km/s
Radiant (geocentric, J2000):
  R.A.   =  49.18156 +/- 0.7573 deg
  Dec    = +58.86776 +/- 0.2637 deg
  Vg     =  60.21510 +/- 1.3484 km/s
  Vinf   =  61.22873 +/- 1.3251 km/s
  Zc     =  30.61125 +/- 0.3603 deg
  Zg     =  30.87300 +/- 0.3536 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  64.21158 +/- 0.5279 deg
  Bg     = +39.02980 +/- 0.2334 deg
  Vh     =  42.59008 +/- 1.2617 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  84.68177 +/- 0.6546 deg
  Bh     = +62.91510 +/- 0.8990 deg
  Vh_x   =  -1.79737 +/- 0.2440 km/s
  Vh_y   = -19.30822 +/- 1.1108 km/s
  Vh_z   = -37.91935 +/- 0.8745 km/s
Orbit:
  La Sun = 140.269105 +/- -0.0000 deg
  a      = -14.126799 +/- 20.4911 AU
  e      =   1.067125 +/- 0.1117
  i      = 112.874564 +/- 0.8351 deg
  peri   = 151.139006 +/- 1.1575 deg
  node   = 140.269073 +/- 0.0001 deg
  Pi     = 291.408079 +/- 1.1575 deg
  q      =   0.948262 +/- 0.0025 AU
  f      =  28.857345 +/- 1.1575 deg
  M      =        nan +/- nan deg
  Q      = -29.201860 +/- 40.9822 AU
  n      =   0.018563 +/- 0.0324 deg/day
  T      = 1000000000.000000 +/- 471404493.6922 years
  Last perihelion JD = NaN 
  Tj     =  -0.845518 +/- 0.6430
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +6.222168e-03, +2.814514e-05, +8.502075e-02, -9.643847e-08, +1.183203e-03, +1.423519e-03
q   , +2.814514e-05, +1.117744e-06, +5.406845e-04, -3.441673e-10, +9.541329e-06, +5.131959e-06
Tp  , +8.502075e-02, +5.406845e-04, +1.188002e+00, -1.316180e-06, +1.685297e-02, +1.943695e-02
node, -9.643847e-08, -3.441673e-10, -1.316180e-06, +1.606816e-12, -1.814564e-08, -2.371899e-08
peri, +1.183203e-03, +9.541329e-06, +1.685297e-02, -1.814564e-08, +2.430992e-04, +2.680769e-04
i   , +1.423519e-03, +5.131959e-06, +1.943695e-02, -2.371899e-08, +2.680769e-04, +3.501305e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 1.602641
 a2 = 18.403050

Mean time residuals from time vs. length:
  Station with reference time: UK002K
  Avg. res. = 4.767e-06 s
  Stddev    = 2.18e-03 s

Begin point on the trajectory:
  Lon =     0.867245 +/- 0.0031 deg
  Lat =    53.987312 +/- 0.0014 deg
  Ht  = 109630.61 +/- 288.87 m
End point on the trajectory:
  Lon =     0.755308 +/- 0.0010 deg
  Lat =    53.945633 +/- 0.0010 deg
  Ht  = 94799.67 +/- 100.61 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
    UK0026,   False,    -0.023645,    52.984073,    6.00,   4.973870,  14.642551,   108998.80,    94799.67,          0.018184,     45.43,     23.15,              25.38, 1.0000,    True,    True, {"ff_name": "FF_UK0026_20210813_020046_322_0523264.fits"}
    UK002K,   False,    -0.382860,    53.537770,   34.00,   0.008364,  35.458036,   109630.61,    95456.14,          0.021618,     40.76,     30.86,              10.36, 1.0000,    True,    True, {"ff_name": "FF_UK002K_20210813_020050_216_0517376.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,     UK0026,       0,  0.050200, 2459439.583945822436, 105.63261,  67.32564,               27.45895,  40.05022,        27.46686,       40.04600,    105.63261,     +67.32564,     105.62982,      +67.31835,  3792622.07,  -478058.69,  5223999.40,      53.985543,       +0.862477,  108998.80,  167429.60,       0.00,             3103.80,   115.05,      0.00,           60177.65,      9.81,     19.21,          26.57,  +3.91,  +2.79
  1,     UK0026,       0,  0.090484, 2459439.583946288563, 106.52750,  67.23752,               27.22672,  39.74125,        27.19879,       39.75610,    106.52750,     +67.23752,     106.53955,      +67.26324,  3791829.55,  -478974.26,  5221982.79,      53.979867,       +0.847205,  106972.69,  165310.47,    2352.24,             5456.04,     0.75,  58391.43,           60177.65,    -34.17,    -67.13,          93.99,  +2.73,  +1.64
  2,     UK0026,       0,  0.130792, 2459439.583946755156, 107.53697,  67.17169,               26.92844,  39.41807,        26.90267,       39.43174,    107.53697,     +67.17169,     107.54927,      +67.19541,  3790968.43,  -479969.10,  5219791.59,      53.973692,       +0.830620,  104771.40,  163015.61,    4908.14,             8011.93,    88.63,  63409.12,           60177.65,    -31.18,    -61.23,          86.94,  +1.56,  +0.50
  3,     UK0026,       0,  0.171072, 2459439.583947221283, 108.47919,  67.11401,               26.64217,  39.12116,        26.62837,       39.12847,    108.47919,     +67.11401,     108.48668,      +67.12670,  3790186.03,  -480872.98,  5217800.72,      53.968077,       +0.815530,  102771.56,  160937.14,    7230.36,            10334.15,   -55.44,  57651.95,           60177.65,    -16.55,    -32.45,          46.68,  +1.26,  +0.23
  4,     UK0026,       0,  0.211368, 2459439.583947687875, 109.41387,  67.02754,               26.37980,  38.80737,        26.35344,       38.82130,    109.41387,     +67.02754,     109.42863,      +67.05176,  3789415.20,  -481763.49,  5215839.30,      53.962539,       +0.800655,  100801.50,  158896.09,    9518.23,            12622.03,  -234.84,  56776.68,           59352.64,    -31.25,    -61.31,          89.33,  +1.29,  +0.28
  5,     UK0026,       0,  0.251672, 2459439.583948154468, 110.45076,  66.96599,               26.05333,  38.48650,        26.05616,       38.48500,    110.45076,     +66.96599,     110.45023,      +66.96339,  3788595.28,  -482710.72,  5213752.97,      53.956643,       +0.784839,   98706.20,  156732.94,   11951.80,            15055.60,  -269.03,  60380.48,           59263.80,      3.33,      6.52,           9.64,  +1.26,  +0.28
  6,     UK0026,       0,  0.292008, 2459439.583948621061, 111.50458,  66.85262,               25.75958,  38.12522,        25.74753,       38.13157,    111.50458,     +66.85262,     111.51307,      +66.86366,  3787759.18,  -483676.64,  5211625.45,      53.950624,       +0.768708,   96569.76,  154535.61,   14433.41,            17537.21,  -257.14,  61523.43,           59474.45,    -13.99,    -27.41,          41.07,  +1.53,  +0.58
  7,     UK0026,       0,  0.332296, 2459439.583949087653, 112.39594,  66.75447,               25.50780,  37.81944,        25.48660,       37.83058,    112.39594,     +66.75447,     112.41079,      +66.77388,  3787066.39,  -484477.00,  5209862.59,      53.945633,       +0.755308,   94799.67,  152720.94,   16489.67,            19593.47,  -667.66,  51039.05,           58859.40,    -24.38,    -47.76,          72.42,  +3.87,  +2.95
  0,     UK002K,       1,  0.000000, 2459439.583945193794,  65.81254,  53.87401,               58.24007,  48.13852,        58.22499,       48.13766,     65.81254,     +53.87401,      65.82260,      +53.88219,  3793637.48,  -476885.62,  5226583.19,      53.992809,       +0.882048,  111595.08,  148775.21,       0.00,               89.97,   174.88,      0.00,           59473.83,     15.85,    -20.91,          36.38,  +5.35,  +4.49
  1,     UK002K,       0,  0.040112, 2459439.583945658058,  66.02988,  53.77870,               58.26302,  47.97945,        58.24232,       47.97825,     66.02988,     +53.77870,      66.04392,      +53.78993,  3792869.18,  -477773.21,  5224628.19,      53.987312,       +0.867245,  109630.61,  146527.44,    2280.38,             2370.35,    -0.75,  56850.24,           59473.83,     21.49,    -28.35,          50.08,  +2.72,  +1.89
  2,     UK002K,       0,  0.080240, 2459439.583946122322,  66.26034,  53.66705,               58.29960,  47.80493,        58.26149,       47.80271,     66.26034,     +53.66705,      66.28639,      +53.68775,  3792050.39,  -478719.14,  5222544.72,      53.981449,       +0.851474,  107537.25,  144133.65,    4710.61,             4800.58,   -27.50,  60562.06,           59473.83,     39.09,    -51.48,          92.51,  +1.96,  +1.17
  3,     UK002K,       0,  0.120356, 2459439.583946586587,  66.52956,  53.57664,               58.29009,  47.62154,        58.28119,       47.62103,     66.52956,     +53.57664,      66.53608,      +53.58148,  3791230.71,  -479666.08,  5220459.00,      53.975574,       +0.835682,  105441.86,  141738.68,    7143.47,             7233.44,   -50.89,  60645.60,           59473.83,      8.98,    -11.88,          21.68,  +1.47,  +0.71
  4,     UK002K,       0,  0.160484, 2459439.583947051316,  66.81290,  53.47009,               58.29305,  47.42224,        58.30269,       47.42278,     66.81290,     +53.47009,      66.80701,      +53.46483,  3790367.46,  -480663.38,  5218262.38,      53.969379,       +0.819052,  103235.28,  139218.30,    9705.69,             9795.66,    54.34,  63851.19,           60502.92,     -9.58,     12.70,          23.57,  +1.38,  +0.66
  5,     UK002K,       0,  0.200596, 2459439.583947515581,  67.07612,  53.38318,               58.27937,  47.24317,        58.32136,       47.24547,     67.07612,     +53.38318,      67.04832,      +53.36024,  3789619.39,  -481527.60,  5216358.86,      53.964006,       +0.804613,  101323.33,  137034.76,   11926.02,            12015.99,  -181.34,  55353.26,           60061.42,    -41.07,     54.71,         102.97,  +1.24,  +0.56
  6,     UK002K,       0,  0.240760, 2459439.583947980311,  67.33309,  53.23208,               58.34714,  47.03274,        58.34413,       47.03257,     67.33309,     +53.23208,      67.33617,      +53.23373,  3788753.47,  -482527.97,  5214155.48,      53.957781,       +0.787921,   99110.43,  134509.95,   14496.12,            14586.09,   -70.42,  63990.25,           60325.15,      2.91,     -3.86,           7.41,  +1.11,  +0.47
  7,     UK002K,       0,  0.280892, 2459439.583948445041,  67.62331,  53.12102,               58.34782,  46.82636,        58.36567,       46.82735,     67.62331,     +53.12102,      67.61214,      +53.11126,  3787947.71,  -483458.84,  5212105.16,      53.951982,       +0.772371,   97051.47,  132161.81,   16887.69,            16977.66,  -136.09,  59592.52,           60373.94,    -16.99,     22.58,          44.09,  +1.47,  +0.86
  8,     UK002K,       0,  0.321032, 2459439.583948909305,  67.78653,  52.97980,               58.44412,  46.66757,        58.38195,       46.66395,     67.78653,     +52.97980,      67.83127,      +53.01373,  3787323.34,  -484180.16,  5210516.41,      53.947485,       +0.760280,   95456.14,  130342.01,   18740.87,            18830.84,  -740.63,  46167.81,           59449.26,     58.91,    -77.57,         154.14,  +1.39,  +0.81

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.