Orbital Analysis for matched events on 20210813_222134.918_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 66.09° Bg 39.66° Vg 57.57km/s
mass 0.01219g, abs. mag 0.8
Path Details
------------
start -2.67° 51.50° 108.56km
end   -2.81° 51.37° 96.79km

Orbit Details
-------------
Semimajor axis 9.15A.U., eccentricity 0.90, inclination 110.04°, Period 27.66Y, LA Sun 141.08°, last Perihelion 2021-07-21

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: 2459440.431654152926
Time: 2021-08-13 22:21:34.918813 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000S and UK0020
 Convergence angle = 54.69954 deg
 R.A. =  50.93815  Dec = +60.37129 deg

Best intersection: Stations UK000S and UK0020 with Qconv = 54.70 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   1728738.54 +/- 32.83 m
 Y =  -3657973.73 +/- 27.03 m
 Z =   5053615.10 +/- 79.91 m
 Vx =    18142.32 +/- 248.30 m/s
 Vy =    22525.07 +/- 288.97 m/s
 Vz =    50998.77 +/- 382.65 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.241180e+03, +4.945918e+02, -1.261319e+03, +3.527051e+03, +4.971917e+02, -5.999246e+03
+4.945918e+02, +7.342922e+02, -1.303309e+03, +4.572395e+02, +1.301153e+03, -6.484969e+03
-1.261319e+03, -1.303309e+03, +6.006178e+03, -3.347572e+03, -2.174085e+03, +1.620133e+04
+3.527051e+03, +4.572395e+02, -3.347572e+03, +1.653945e+04, -6.093902e+02, -7.841198e+03
+4.971917e+02, +1.301153e+03, -2.174085e+03, -6.093902e+02, +5.107813e+03, -1.637486e+04
-5.999246e+03, -6.484969e+03, +1.620133e+04, -7.841198e+03, -1.637486e+04, +9.390817e+04

Timing offsets (from input data):
    UK000S: 0.000000 s
    UK0020: 0.003295 s

Reference point on the trajectory:
  Time: 2021-08-13 22:21:34.918813 UTC
  Lon     = +-2.668660 +/- 0.0005 deg
  Lat     = +51.503882 +/- 0.0004 deg
  Lat geo = +51.319402 +/- 0.0004 deg
  Ht      =  108534.48 +/- 69.81 m

  JD dynamic   = 2459440.432454893831 
  LST apparent = 295.2951640707 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  51.15106 +/- 0.2144 deg
  Dec       = +60.44132 +/- 0.2261 deg
  Azimuth   =  32.02214 +/- 0.2049 deg
  Elevation = +33.15277 +/- 0.1812 deg
  Vavg      =  58.71730 +/- 0.4397 km/s
  Vinit     =  58.62932 +/- 0.3095 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  50.89849 +/- 0.2144 deg
  Dec       = +60.21589 +/- 0.2261 deg
  Azimuth   =  32.31319 +/- 0.2049 deg
  Elevation = +33.06901 +/- 0.1812 deg
  Vavg      =  58.84887 +/- 0.4397 km/s
  Vinit     =  58.76089 +/- 0.3095 km/s
Radiant (geocentric, J2000):
  R.A.   =  51.47214 +/- 0.2152 deg
  Dec    = +59.94354 +/- 0.2322 deg
  Vg     =  57.56957 +/- 0.3151 km/s
  Vinf   =  58.62932 +/- 0.3095 km/s
  Zc     =  57.00369 +/- 0.1810 deg
  Zg     =  57.57117 +/- 0.1887 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  66.09212 +/- 0.1624 deg
  Bg     = +39.66316 +/- 0.2232 deg
  Vh     =  40.67425 +/- 0.3819 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  90.86205 +/- 0.3871 deg
  Bh     = +64.60947 +/- 0.1089 deg
  Vh_x   =   0.26239 +/- 0.1189 km/s
  Vh_y   = -17.43857 +/- 0.1204 km/s
  Vh_z   = -36.74537 +/- 0.3707 km/s
Orbit:
  La Sun = 141.083173 +/- 0.0000 deg
  a      =   9.147042 +/- 44.7206 AU
  e      =   0.898055 +/- 0.0330
  i      = 110.039791 +/- 0.1274 deg
  peri   = 146.292569 +/- 0.7604 deg
  node   = 141.081810 +/- 0.0000 deg
  Pi     = 287.374379 +/- 0.7604 deg
  q      =   0.932497 +/- 0.0023 AU
  f      =  33.703420 +/- 0.7604 deg
  M      =   0.842323 +/- nan deg
  Q      =  17.361586 +/- 89.4416 AU
  n      =   0.035627 +/- 0.0127 deg/day
  T      =  27.664424 +/- 249443807.8799 years
  Last perihelion JD = 2459416.789850 (2021-07-21 06:57:23.033427) +/- 0.5843 days
  Tj     =   0.169281 +/- 0.1869
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +7.111448e-04, +3.859565e-05, +1.402875e-02, +3.131487e-09, +2.638686e-04, -4.209964e-05
q   , +3.859565e-05, +4.337665e-06, +1.038909e-03, +2.858604e-11, +2.253599e-05, -3.859043e-07
Tp  , +1.402875e-02, +1.038909e-03, +3.111238e-01, +4.476852e-08, +6.222367e-03, -6.020579e-04
node, +3.131487e-09, +2.858604e-11, +4.476852e-08, +3.184635e-14, +6.509354e-10, -4.279815e-10
peri, +2.638686e-04, +2.253599e-05, +6.222367e-03, +6.509354e-10, +1.280043e-04, -8.756904e-06
i   , -4.209964e-05, -3.859043e-07, -6.020579e-04, -4.279815e-10, -8.756904e-06, +5.751636e-06

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 6.300017
 a2 = 7.157196

Mean time residuals from time vs. length:
  Station with reference time: UK000S
  Avg. res. = 1.623e-05 s
  Stddev    = 4.03e-03 s

Begin point on the trajectory:
  Lon =    -2.668339 +/- 0.0005 deg
  Lat =    51.504203 +/- 0.0003 deg
  Ht  = 108562.45 +/- 63.74 m
End point on the trajectory:
  Lon =    -2.805286 +/- 0.0007 deg
  Lat =    51.368583 +/- 0.0009 deg
  Ht  = 96792.05 +/- 116.91 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
    UK000S,   False,    -1.778230,    50.857470,   24.00,   7.234726,   3.908477,   108562.45,    97022.00,          0.011199,      5.75,     26.74,              55.22, 1.0000,    True,    True, {"ff_name": "FF_UK000S_20210813_222131_634_0198912.fits"}
    UK0020,   False,    -3.515726,    50.691998,   17.00,   1.827581,  12.229204,   106967.53,    96792.05,          0.032741,     55.67,     59.85,              12.20, 1.0000,    True,    True, {"ff_name": "FF_UK0020_20210813_222131_554_0190464.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,     UK000S,       0,  0.000000, 2459440.431654152926, 216.17350,  63.86877,              319.47913,  48.11820,       319.48591,       48.09767,    216.17350,     +63.86877,     216.12617,      +63.86550,  1728754.37, -3657954.08,  5053659.59,      51.504203,       -2.668339,  108562.45,  144863.94,       0.00,               51.15,   149.51,      0.00,           59114.11,     51.97,     11.16,          75.68,  +3.83,  +3.03
  1,     UK000S,       0,  0.039880, 2459440.431654614396, 216.36082,  63.14170,              318.42281,  47.92723,       318.42056,       47.93363,    216.36082,     +63.14170,     216.37518,      +63.14270,  1728067.20, -3658807.25,  5051727.92,      51.490269,       -2.682465,  107348.24,  143612.59,    2220.69,             2169.54,   -70.24,  55684.20,           59114.11,    -16.11,     -3.47,          23.66,  +2.49,  +1.70
  2,     UK000S,       0,  0.079724, 2459440.431655075401, 216.63348,  62.34514,              317.25435,  47.74047,       317.25394,       47.74154,    216.63348,     +62.34514,     216.63600,      +62.34530,  1727322.74, -3659731.56,  5049635.21,      51.475166,       -2.697750,  106033.39,  142283.34,    4626.52,             4575.37,    -0.44,  60381.21,           59114.11,     -2.69,     -0.58,           3.99,  +1.84,  +1.07
  3,     UK000S,       0,  0.119556, 2459440.431655536406, 216.90727,  61.52758,              316.06236,  47.54051,       316.06566,       47.53218,    216.90727,     +61.52758,     216.88970,      +61.52634,  1726572.61, -3660662.90,  5047526.57,      51.459939,       -2.713147,  104709.14,  140972.94,    7050.66,             6999.51,    88.39,  60859.30,           59114.11,     20.73,      4.46,          31.03,  +1.20,  +0.45
  4,     UK000S,       0,  0.159424, 2459440.431655997876, 217.10881,  60.78333,              314.99631,  47.33218,       314.99654,       47.33163,    217.10881,     +60.78333,     217.10814,      +60.78325,  1725904.46, -3661492.46,  5045648.38,      51.446369,       -2.726876,  103530.14,  139831.57,    9209.87,             9158.72,   -89.84,  54158.91,           58339.37,      1.36,      0.29,           2.05,  +0.97,  +0.24
  5,     UK000S,       0,  0.199268, 2459440.431656458881, 217.34078,  59.92942,              313.78058,  47.08667,       313.77937,       47.08943,    217.34078,     +59.92942,     217.34712,      +59.92982,  1725150.06, -3662429.10,  5043527.74,      51.431040,       -2.742352,  102199.54,  138571.45,   11647.80,            11596.65,    12.07,  61186.93,           58524.75,     -6.81,     -1.47,          10.37,  +1.06,  +0.35
  6,     UK000S,       0,  0.239104, 2459440.431656919885, 217.59117,  59.14634,              312.66089,  46.87271,       312.66903,       46.85505,    217.59117,     +59.14634,     217.55621,      +59.14386,  1724467.75, -3663276.24,  5041609.74,      51.417169,       -2.756362,  100996.63,  137459.75,   13852.78,            13801.63,  -118.51,  55351.39,           58251.10,     43.43,      9.34,          66.66,  +0.84,  +0.15
  7,     UK000S,       0,  0.278944, 2459440.431657381356, 217.80324,  58.25561,              311.41888,  46.58842,       311.42433,       46.57715,    217.80324,     +58.25561,     217.78185,      +58.25406,  1723708.15, -3664219.34,  5039474.48,      51.401718,       -2.771936,   99658.06,  136252.94,   16307.52,            16256.37,     0.44,  61615.02,           58417.31,     27.60,      5.94,          42.74,  +0.82,  +0.15
  8,     UK000S,       0,  0.318808, 2459440.431657842826, 217.97929,  57.48484,              310.35483,  46.33226,       310.35812,       46.32572,    217.97929,     +57.48484,     217.96768,      +57.48395,  1723062.05, -3665021.52,  5037658.26,      51.388569,       -2.785205,   98519.99,  135254.09,   18395.49,            18344.34,  -248.79,  52377.27,           58092.05,     15.96,      3.44,          24.90,  +1.02,  +0.36
  9,     UK000S,       0,  0.358640, 2459440.431658303831, 218.18169,  56.45190,              308.95333,  45.96293,       308.94719,       45.97455,    218.18169,     +56.45190,     218.20524,      +56.45344,  1722211.19, -3666077.93,  5035266.47,      51.371244,       -2.802622,   97022.00,  133975.25,   21145.14,            21093.99,   165.53,  69031.14,           58522.89,    -28.31,     -6.11,          44.58,  +2.11,  +1.47
  0,     UK0020,       0,  0.052070, 2459440.431654658169,  26.97954,  67.20324,               32.94803,  44.62550,        33.00288,       44.62128,     26.97954,     +67.20324,      26.94314,      +67.16660,  1727851.68, -3659074.84,  5051122.09,      51.485897,       -2.686858,  106967.53,  150990.62,       0.00,             2866.02,   -88.43,      0.00,           60213.74,    -75.67,     70.56,         141.34,  +2.67,  +1.78
  1,     UK0020,       0,  0.091950, 2459440.431655119639,  26.48351,  67.29720,               32.95275,  44.83907,        33.03056,       44.83318,     26.48351,     +67.29720,      26.43294,      +67.24529,  1727068.40, -3660047.33,  5048920.27,      51.470004,       -2.702931,  105584.33,  148515.83,    2531.26,             5397.28,   104.69,  63471.95,           60213.74,   -105.35,     97.93,         199.77,  +2.60,  +1.74
  2,     UK0020,       0,  0.131834, 2459440.431655581575,  26.07454,  67.32458,               33.01794,  44.99238,        33.04956,       44.98993,     26.07454,     +67.32458,      26.05474,      +67.30347,  1726507.15, -3660744.17,  5047342.56,      51.458610,       -2.714492,  104593.60,  146742.52,    4345.03,             7211.05,  -419.91,  45476.06,           60213.74,    -42.11,     39.32,          80.98,  +1.81,  +0.98
  3,     UK0020,       0,  0.171662, 2459440.431656042114,  25.40363,  67.41179,               33.06825,  45.26256,        33.08665,       45.26113,     25.40363,     +67.41179,      25.39278,      +67.39951,  1725562.67, -3661916.81,  5044687.60,      51.439425,       -2.733829,  102927.23,  143764.08,    7397.23,            10263.25,   297.20,  76634.50,           60213.74,    -23.89,     22.33,          46.91,  +1.53,  +0.74
  4,     UK0020,       0,  0.211546, 2459440.431656504050,  24.90449,  67.50083,               33.07178,  45.47361,        33.11397,       45.47038,     24.90449,     +67.50083,      24.87962,      +67.47272,  1724861.31, -3662787.60,  5042716.05,      51.425171,       -2.748228,  101690.42,  141553.30,    9663.77,            12529.79,   225.37,  56828.26,           60685.64,    -53.79,     50.12,         107.13,  +1.62,  +0.87
  5,     UK0020,       0,  0.251422, 2459440.431656965520,  24.43311,  67.55124,               33.11619,  45.65811,        33.13761,       45.65646,     24.43311,     +67.55124,      24.42131,      +67.53697,  1724256.33, -3663538.74,  5041015.42,      51.412869,       -2.760668,  100623.99,  139647.26,   11618.85,            14484.87,  -157.45,  49029.09,           59154.82,    -26.83,     25.05,          54.22,  +1.56,  +0.83
  6,     UK0020,       0,  0.291286, 2459440.431657426991,  23.86578,  67.63552,               33.13619,  45.88979,        33.16842,       45.88733,     23.86578,     +67.63552,      23.84824,      +67.61408,  1723526.70, -3664444.63,  5038964.40,      51.398026,       -2.775633,   99338.39,  137351.46,   13976.75,            16842.77,  -136.75,  59148.53,           58607.49,    -39.58,     36.88,          81.25,  +1.45,  +0.76
  7,     UK0020,       0,  0.331126, 2459440.431657887995,  23.25422,  67.68753,               33.20522,  46.12310,        33.20015,       46.12350,     23.25422,     +67.68753,      23.25820,      +67.69090,  1722804.74, -3665340.99,  5036934.96,      51.383331,       -2.790439,   98066.90,  135082.06,   16309.84,            19175.86,  -139.46,  58561.51,           58375.63,      6.10,     -5.70,          12.74,  +1.74,  +1.09
  8,     UK0020,       0,  0.371010, 2459440.431658349466,  22.68165,  67.81809,               33.15824,  46.37406,        33.23335,       46.36848,     22.68165,     +67.81809,      22.64206,      +67.76832,  1722080.56, -3666240.12,  5034899.25,      51.368583,       -2.805286,   96792.05,  132808.04,   18650.13,            21516.16,  -137.53,  58677.60,           58287.54,    -88.61,     82.13,         187.65,  +2.13,  +1.51

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.