Orbital Analysis for matched events on 20210813_004655.167_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 59.11° Bg 29.61° Vg 65.30km/s
mass 0.01300g, abs. mag -0.1
Path Details
------------
start 0.57° 53.06° 109.10km
end   0.44° 53.03° 99.52km

Orbit Details
-------------
Semimajor axis -11.97A.U., eccentricity 1.08, inclination 129.60°, Period 1000000000.00Y, LA Sun 140.22°, 

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: 2459439.532582954969
Time: 2021-08-13 00:46:55.167309 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000Z and UK002K
 Convergence angle = 50.97894 deg
 R.A. =  48.08823  Dec = +48.58151 deg

Best intersection: Stations UK000Z and UK002K with Qconv = 50.98 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3510695.61 +/- 133.14 m
 Y =  -1713858.58 +/- 100.04 m
 Z =   5161826.11 +/- 129.91 m
 Vx =    29430.60 +/- 1058.59 m/s
 Vy =    32128.84 +/- 803.21 m/s
 Vz =    49891.11 +/- 1034.23 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.189957e+04, +1.362075e+04, +1.637619e+04, +9.029867e+03, +2.408196e+04, +2.129909e+03
+1.362075e+04, +1.748656e+04, +1.927287e+04, +2.416125e+04, +3.590451e+04, +9.712233e+03
+1.637619e+04, +1.927287e+04, +2.270389e+04, +1.612272e+04, +3.517772e+04, +4.938312e+03
+9.029867e+03, +2.416125e+04, +1.612272e+04, +1.088860e+05, +8.132263e+04, +5.481528e+04
+2.408196e+04, +3.590451e+04, +3.517772e+04, +8.132263e+04, +8.954607e+04, +3.658338e+04
+2.129909e+03, +9.712233e+03, +4.938312e+03, +5.481528e+04, +3.658338e+04, +2.831265e+04

Timing offsets (from input data):
    UK000Z: 0.000000 s
    UK002K: -0.001252 s

Reference point on the trajectory:
  Time: 2021-08-13 00:46:55.167309 UTC
  Lon     = ++0.567158 +/- 0.0019 deg
  Lat     = +53.061860 +/- 0.0007 deg
  Lat geo = +52.879950 +/- 0.0007 deg
  Ht      =  108980.04 +/- 144.13 m

  JD dynamic   = 2459439.533383695874 
  LST apparent = 333.9792002549 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  47.50976 +/- 0.7852 deg
  Dec       = +48.86864 +/- 0.3089 deg
  Azimuth   =  64.29990 +/- 0.7249 deg
  Elevation = +45.56891 +/- 0.3189 deg
  Vavg      =  63.58288 +/- 0.8334 km/s
  Vinit     =  66.23855 +/- 1.0623 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  47.61530 +/- 0.7852 deg
  Dec       = +48.69109 +/- 0.3089 deg
  Azimuth   =  64.45171 +/- 0.7249 deg
  Elevation = +45.41068 +/- 0.3189 deg
  Vavg      =  63.76295 +/- 0.8334 km/s
  Vinit     =  66.41862 +/- 1.0623 km/s
Radiant (geocentric, J2000):
  R.A.   =  47.54892 +/- 0.8005 deg
  Dec    = +48.59862 +/- 0.3035 deg
  Vg     =  65.30238 +/- 1.0778 km/s
  Vinf   =  66.23855 +/- 1.0623 km/s
  Zc     =  44.51021 +/- 0.3204 deg
  Zg     =  44.84394 +/- 0.3311 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  59.10756 +/- 0.6601 deg
  Bg     = +29.61163 +/- 0.2044 deg
  Vh     =  42.72268 +/- 0.9006 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  67.80682 +/- 1.6513 deg
  Bh     = +49.04974 +/- 0.6062 deg
  Vh_x   = -10.57668 +/- 1.0458 km/s
  Vh_y   = -25.92619 +/- 0.5772 km/s
  Vh_z   = -32.26754 +/- 0.4541 km/s
Orbit:
  La Sun = 140.219786 +/- -0.0000 deg
  a      = -11.966817 +/- 40.9820 AU
  e      =   1.081476 +/- 0.0834
  i      = 129.597376 +/- 0.8316 deg
  peri   = 158.028731 +/- 2.7584 deg
  node   = 140.217853 +/- 0.0001 deg
  Pi     = 298.246584 +/- 2.7584 deg
  q      =   0.975007 +/- 0.0082 AU
  f      =  21.966693 +/- 2.7585 deg
  M      =        nan +/- nan deg
  Q      = -24.908640 +/- 81.9645 AU
  n      =   0.023809 +/- 0.0223 deg/day
  T      = 1000000000.000000 +/- 442216615.1943 years
  Last perihelion JD = NaN 
  Tj     =  -1.230949 +/- 0.4782
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +6.652230e-04, +5.944622e-05, +1.712204e-02, -2.030732e-08, +3.595829e-04, +2.057021e-04
q   , +5.944622e-05, +6.473552e-06, +1.722694e-03, -1.485193e-09, +3.735694e-05, +1.505642e-05
Tp  , +1.712204e-02, +1.722694e-03, +4.726523e-01, -4.679748e-07, +1.012170e-02, +4.742371e-03
node, -2.030732e-08, -1.485193e-09, -4.679748e-07, +7.149189e-13, -9.493673e-09, -7.237862e-09
peri, +3.595829e-04, +3.735694e-05, +1.012170e-02, -9.493673e-09, +2.178681e-04, +9.622100e-05
i   , +2.057021e-04, +1.505642e-05, +4.742371e-03, -7.237862e-09, +9.622100e-05, +7.327656e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.000001
 a2 = 96.756458

Mean time residuals from time vs. length:
  Station with reference time: UK000Z
  Avg. res. = 8.825e-07 s
  Stddev    = 9.39e-04 s

Begin point on the trajectory:
  Lon =     0.568738 +/- 0.0014 deg
  Lat =    53.062318 +/- 0.0004 deg
  Ht  = 109102.02 +/- 132.57 m
End point on the trajectory:
  Lon =     0.443540 +/- 0.0012 deg
  Lat =    53.026188 +/- 0.0007 deg
  Ht  = 99519.34 +/- 111.95 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,   109102.02,    99702.70,          0.024230,     59.23,     48.84,              22.81, 1.0000,    True,    True, {"ff_name": "FF_UK000Z_20210813_004645_149_0400896.fits"}
    UK002K,   False,    -0.382860,    53.537770,   34.00,   0.000125,  73.589134,   108329.30,    99519.34,          0.010230,     22.73,      3.94,              42.58, 1.0000,    True,    True, {"ff_name": "FF_UK002K_20210813_004652_864_0406528.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,  0.000000, 2459439.532582954969,  39.90686,  27.05032,               89.35758,  34.19067,        89.36051,       34.19420,     39.90686,     +27.05032,      39.90218,      +27.05129,  3510771.50, -1713775.72,  5161954.76,      53.062318,       +0.568738,  109102.02,  190322.22,       0.00,              170.81,   211.50,      0.00,           66897.83,     -9.06,    -10.94,          15.40,  +2.72,  +1.32
  1,     UK000Z,       0,  0.040124, 2459439.532583419234,  39.80055,  26.73996,               89.69473,  34.02519,        89.68367,       34.01190,     39.80055,     +26.73996,      39.81832,      +26.73630,  3509540.63, -1715119.44,  5159868.18,      53.054884,       +0.542939,  107123.99,  187758.35,    2770.28,             2599.47,   -17.60,  69042.96,           66897.83,     33.72,     40.78,          58.13,  +2.07,  +0.70
  2,     UK000Z,       0,  0.080264, 2459439.532583883964,  39.71355,  26.42588,               90.01853,  33.84483,        90.00524,       33.82893,     39.71355,     +26.42588,      39.73494,      +26.42150,  3508343.17, -1716426.69,  5157838.22,      53.047641,       +0.517829,  105200.18,  185269.70,    5465.38,             5294.57,    18.68,  67142.50,           66897.83,     39.88,     48.25,          69.69,  +2.12,  +0.78
  3,     UK000Z,       0,  0.120408, 2459439.532584348693,  39.64007,  26.11397,               90.32871,  33.65745,        90.32071,       33.64793,     39.64007,     +26.11397,      39.65318,      +26.11136,  3507194.00, -1717681.22,  5155890.14,      53.040682,       +0.493718,  103354.46,  182886.74,    8051.78,             7880.96,   -54.00,  64427.96,           66897.83,     23.62,     28.57,          41.81,  +1.66,  +0.35
  4,     UK000Z,       0,  0.160536, 2459439.532584812958,  39.50531,  25.77605,               90.70792,  33.48700,        90.67200,       33.44435,     39.50531,     +25.77605,      39.56237,      +25.76427,  3505943.09, -1719046.81,  5153769.58,      53.033097,       +0.467482,  101345.90,  180300.25,   10867.16,            10696.35,   103.36,  70160.02,           67311.27,    104.32,    126.60,         187.66,  +1.89,  +0.61
  5,     UK000Z,       0,  0.200700, 2459439.532585277688,  39.48100,  25.47388,               90.96861,  33.27629,        90.96580,       33.27297,     39.48100,     +25.47388,      39.48623,      +25.47297,  3504919.46, -1720164.29,  5152034.31,      53.026882,       +0.445976,   99702.70,  178187.30,   13171.01,            13000.20,  -253.19,  57361.14,           66006.91,      8.07,      9.76,          14.66,  +2.78,  +1.53
  0,     UK002K,       0,  0.011606, 2459439.532583105844,   3.94013,  23.64597,              129.91880,  52.15241,       129.92294,       52.16028,      3.94013,     +23.64597,       3.93350,      +23.65153,  3510290.71, -1714300.60,  5161139.71,      53.059416,       +0.558673,  108329.30,  136445.23,       0.00,              911.30,   183.21,      0.00,           65017.93,      3.36,    -19.41,          29.77,  +2.34,  +1.67
  1,     UK002K,       0,  0.051718, 2459439.532583570108,   3.40666,  23.11634,              131.03574,  51.93262,       131.03819,       51.93706,      3.40666,     +23.11634,       3.40309,      +23.11948,  3509177.14, -1715516.26,  5159251.98,      53.052686,       +0.535314,  106539.96,  134599.33,    2506.27,             3417.57,    32.51,  62481.76,           65017.93,      1.89,    -10.87,          16.90,  +1.69,  +1.04
  2,     UK002K,       0,  0.091826, 2459439.532584034372,   2.85150,  22.56980,              132.18709,  51.70047,       132.18357,       51.69435,      2.85150,     +22.56980,       2.85713,      +22.56546,  3508052.74, -1716743.75,  5157345.88,      53.045883,       +0.511724,  104733.66,  132757.75,    5036.93,             5948.23,   -93.52,  63096.23,           65017.93,     -2.58,     14.82,          23.37,  +1.25,  +0.63
  3,     UK002K,       0,  0.131970, 2459439.532584499102,   2.23851,  21.92775,              133.47822,  51.40120,       133.47908,       51.40261,      2.23851,     +21.92775,       2.23785,      +21.92875,  3506802.21, -1718108.93,  5155225.97,      53.038308,       +0.485500,  102725.31,  130737.53,    7851.46,             8762.76,    61.93,  70110.80,           65017.93,      0.59,     -3.39,           5.43,  +1.33,  +0.75
  4,     UK002K,       0,  0.172098, 2459439.532584963832,   1.66139,  21.33469,              134.67505,  51.12079,       134.67326,       51.11794,      1.66139,     +21.33469,       1.66458,      +21.33266,  3505668.99, -1719346.05,  5153304.92,      53.031433,       +0.461714,  100905.85,  128932.34,   10401.97,            11313.26,   -45.59,  63559.24,           65171.62,     -1.18,      6.79,          11.02,  +1.77,  +1.22
  5,     UK002K,       0,  0.212222, 2459439.532585428096,   1.23572,  20.85141,              135.58381,  50.86753,       135.59705,       50.88787,      1.23572,     +20.85141,       1.21892,      +20.86591,  3504805.23, -1720288.99,  5151840.67,      53.026188,       +0.443540,   99519.34,  127572.50,   12345.99,            13257.29,  -759.32,  48450.42,           62826.74,      8.36,    -48.25,          79.17,  +3.76,  +3.23

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.