Orbital Analysis for matched events on 20210813_023424.375_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 63.00° Bg 38.09° Vg 58.53km/s
mass 0.01823g, abs. mag -0.2
Path Details
------------
start -2.11° 50.57° 108.43km
end   -2.18° 50.54° 97.91km

Orbit Details
-------------
Semimajor axis 8.10A.U., eccentricity 0.88, inclination 113.28°, Period 23.07Y, LA Sun 140.29°, last Perihelion 2021-07-22

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: 2459439.607226572931
Time: 2021-08-13 02:34:24.396219 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000H and UK0038
 Convergence angle = 36.18790 deg
 R.A. =  49.34403  Dec = +57.55586 deg

Best intersection: Stations UK000H and UK0038 with Qconv = 36.19 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   4126055.67 +/- 79.86 m
 Y =   -126143.87 +/- 21.75 m
 Z =   4987073.82 +/- 52.71 m
 Vx =    21245.30 +/- 510.94 m/s
 Vy =    23607.17 +/- 438.40 m/s
 Vz =    50399.06 +/- 311.03 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+6.715045e+03, -1.766098e+03, +4.337448e+03, +3.558192e+04, -1.434822e+04, +1.589528e+04
-1.766098e+03, +5.469619e+02, -1.151473e+03, -9.108048e+03, +4.049053e+03, -4.489437e+03
+4.337448e+03, -1.151473e+03, +2.916000e+03, +2.253485e+04, -9.837267e+03, +1.004590e+04
+3.558192e+04, -9.108048e+03, +2.253485e+04, +2.870862e+05, -1.093776e+05, +1.232441e+05
-1.434822e+04, +4.049053e+03, -9.837267e+03, -1.093776e+05, +4.927726e+04, -4.782890e+04
+1.589528e+04, -4.489437e+03, +1.004590e+04, +1.232441e+05, -4.782890e+04, +5.797765e+04

Timing offsets (from input data):
    UK000H: 0.000000 s
    UK0038: -0.000556 s

Reference point on the trajectory:
  Time: 2021-08-13 02:34:24.396219 UTC
  Lon     = +-2.108530 +/- 0.0003 deg
  Lat     = +50.569953 +/- 0.0003 deg
  Lat geo = +50.384198 +/- 0.0003 deg
  Ht      =  108412.72 +/- 91.36 m

  JD dynamic   = 2459439.608027548995 
  LST apparent = 358.2488697093 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  48.01434 +/- 0.9085 deg
  Dec       = +57.78255 +/- 0.0872 deg
  Azimuth   =  56.30723 +/- 0.2671 deg
  Elevation = +60.71420 +/- 0.4750 deg
  Vavg      =  57.16387 +/- 0.3359 km/s
  Vinit     =  59.57118 +/- 0.3105 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  48.36258 +/- 0.9085 deg
  Dec       = +57.59546 +/- 0.0872 deg
  Azimuth   =  56.63276 +/- 0.2671 deg
  Elevation = +60.50414 +/- 0.4750 deg
  Vavg      =  57.28702 +/- 0.3359 km/s
  Vinit     =  59.69433 +/- 0.3105 km/s
Radiant (geocentric, J2000):
  R.A.   =  48.08838 +/- 0.9194 deg
  Dec    = +57.66789 +/- 0.0865 deg
  Vg     =  58.52852 +/- 0.3160 km/s
  Vinf   =  59.57118 +/- 0.3105 km/s
  Zc     =  29.38921 +/- 0.4756 deg
  Zg     =  29.65452 +/- 0.4827 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  63.00328 +/- 0.6098 deg
  Bg     = +38.09302 +/- 0.1424 deg
  Vh     =  40.51742 +/- 0.2671 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  82.60363 +/- 1.6251 deg
  Bh     = +63.02406 +/- 0.2121 deg
  Vh_x   =  -2.36603 +/- 0.5120 km/s
  Vh_y   = -18.22643 +/- 0.1075 km/s
  Vh_z   = -36.10901 +/- 0.2972 km/s
Orbit:
  La Sun = 140.291459 +/- 0.0000 deg
  a      =   8.104444 +/- 3.2836 AU
  e      =   0.882817 +/- 0.0228
  i      = 113.276324 +/- 0.2131 deg
  peri   = 150.030031 +/- 1.9161 deg
  node   = 140.291604 +/- 0.0000 deg
  Pi     = 290.321635 +/- 1.9161 deg
  q      =   0.949701 +/- 0.0068 AU
  f      =  29.966456 +/- 1.9162 deg
  M      =   0.915216 +/- 0.2820 deg
  Q      =  15.259186 +/- 6.5616 AU
  n      =   0.042719 +/- 0.0116 deg/day
  T      =  23.072011 +/- 18.2512 years
  Last perihelion JD = 2459418.183830 (2021-07-22 16:24:42.935858) +/- 1.3731 days
  Tj     =   0.178887 +/- 0.1355
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +5.281050e-04, +1.609407e-04, +3.242077e-02, -4.841025e-09, +7.891715e-04, +7.253957e-05
q   , +1.609407e-04, +5.236857e-05, +1.041466e-02, -1.524779e-09, +2.549277e-04, +2.284888e-05
Tp  , +3.242077e-02, +1.041466e-02, +2.076749e+00, -3.056116e-07, +5.078045e-02, +4.579481e-03
node, -4.841025e-09, -1.524779e-09, -3.056116e-07, +6.378902e-14, -7.460431e-09, -9.557412e-10
peri, +7.891715e-04, +2.549277e-04, +5.078045e-02, -7.460431e-09, +1.242266e-03, +1.117922e-04
i   , +7.253957e-05, +2.284888e-05, +4.579481e-03, -9.557412e-10, +1.117922e-04, +1.431975e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.035392
 a2 = 45.877114

Mean time residuals from time vs. length:
  Station with reference time: UK000H
  Avg. res. = 3.194e-07 s
  Stddev    = 5.65e-04 s

Begin point on the trajectory:
  Lon =    -2.108422 +/- 0.0003 deg
  Lat =    50.570000 +/- 0.0003 deg
  Ht  = 108429.52 +/- 91.32 m
End point on the trajectory:
  Lon =    -2.177489 +/- 0.0003 deg
  Lat =    50.540993 +/- 0.0003 deg
  Ht  = 97908.46 +/- 57.36 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
    UK000H,   False,    -1.778230,    50.857470,   24.00,   0.001462,  61.615302,   108429.52,    98167.17,          0.005976,     11.30,      2.01,              48.34, 1.0000,    True,    True, {"ff_name": "FF_UK000H_20210813_023417_071_0572160.fits"}
    UK0038,   False,    -2.379250,    51.361350,  169.00,   0.093386,  41.239240,   107907.47,    97908.46,          0.018561,     40.25,     19.86,              55.87, 1.0000,    True,    True, {"ff_name": "FF_UK0038_20210813_023418_857_0569856.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,     UK000H,       0,  0.000000, 2459439.607226808090, 344.30842,  33.33657,              216.23184,  69.60840,       216.22844,       69.60812,    344.30842,     +33.33657,     344.30954,      +33.33580,  4126062.54,  -126136.24,  4987090.11,      50.570000,       -2.108422,  108429.52,  115520.92,       0.00,               19.26,    -2.35,      0.00,           60046.15,     -0.43,      2.41,           4.38,  +2.83,  +2.52
  1,     UK000H,       0,  0.040756, 2459439.607227279805, 343.61220,  32.62287,              216.80136,  68.70872,       216.81562,       68.70987,    343.61220,     +32.62287,     343.60749,      +32.62622,  4125194.01,  -127101.33,  4985029.75,      50.564156,       -2.122352,  106305.51,  113925.34,    2435.33,             2416.07,   -33.42,  59753.91,           60046.15,      1.84,    -10.39,          19.10,  +1.75,  +1.47
  2,     UK000H,       0,  0.081552, 2459439.607227751985, 342.88361,  31.87512,              217.37763,  67.76364,       217.38343,       67.76411,    342.88361,     +31.87512,     342.88190,      +31.87653,  4124306.66,  -128087.33,  4982924.73,      50.558179,       -2.136587,  104135.68,  112326.46,    4923.44,             4904.18,    24.42,  60989.04,           60046.15,      0.77,     -4.33,           8.07,  +0.75,  +0.50
  3,     UK000H,       0,  0.122348, 2459439.607228224166, 342.17230,  31.12437,              217.89973,  66.81980,       217.90548,       66.82026,    342.17230,     +31.12437,     342.17070,      +31.12581,  4123447.07,  -129042.48,  4980885.57,      50.552384,       -2.150387,  102033.94,  110809.16,    7333.70,             7314.45,     4.42,  59080.94,           60046.15,      0.78,     -4.40,           8.32,  +0.49,  +0.27
  4,     UK000H,       0,  0.163164, 2459439.607228696346, 341.46846,  30.34851,              218.36648,  65.85395,       218.39792,       65.85648,    341.46846,     +30.34851,     341.45720,      +30.35660,  4122594.17,  -129990.19,  4978862.30,      50.546629,       -2.164086,   99948.76,  109335.61,    9725.19,             9705.93,   -35.55,  58591.91,           59689.97,      4.38,    -24.62,          47.18,  +0.53,  +0.34
  5,     UK000H,       0,  0.203876, 2459439.607229167596, 340.83814,  29.68058,              218.80524,  65.01089,       218.80152,       65.01060,    340.83814,     +29.68058,     340.84045,      +29.67960,  4121865.39,  -130799.99,  4977133.45,      50.541708,       -2.175821,   98167.17,  108103.11,   11768.68,            11749.42,  -417.32,  50193.68,           58234.42,     -0.53,      2.97,           5.75,  +1.24,  +1.07
  0,     UK0038,       0,  0.008865, 2459439.607226790860,   5.98559,  11.31981,              167.87658,  49.42971,       167.87031,       49.42705,      5.98559,     +11.31981,       5.99006,      +11.31772,  4125849.07,  -126373.44,  4986583.72,      50.568564,       -2.111797,  107907.47,  140984.54,       0.00,              579.29,    29.56,      0.00,           59230.07,      5.30,     10.73,          17.51,  +2.22,  +1.47
  1,     UK0038,       0,  0.049365, 2459439.607227259781,   5.60308,  10.59449,              168.58891,  48.75922,       168.55175,       48.74356,      5.60308,     +10.59449,       5.62997,      +10.58204,  4124998.49,  -127318.58,  4984565.94,      50.562839,       -2.125443,  105827.40,  139674.91,    2385.00,             2964.29,     1.92,  58888.80,           59230.07,     31.36,     63.56,         104.66,  +0.85,  +0.12
  2,     UK0038,       0,  0.089889, 2459439.607227728702,   5.24059,   9.84806,              169.25939,  48.06183,       169.22370,       48.04688,      5.24059,      +9.84806,       5.26676,       +9.83603,  4124152.25,  -128258.89,  4982558.45,      50.557139,       -2.139026,  103758.14,  138400.59,    4757.83,             5337.12,   -39.31,  58553.76,           59230.07,     30.08,     60.99,         101.35,  +0.04,  -0.67
  3,     UK0038,       0,  0.130465, 2459439.607228198089,   4.89843,   9.04382,              169.89424,  47.30153,       169.91184,       47.30886,      4.89843,      +9.04382,       4.88609,       +9.04978,  4123277.19,  -129231.24,  4980482.58,      50.551239,       -2.153071,  101618.60,  137113.82,    7211.49,             7790.78,    -2.80,  60470.73,           59230.07,    -14.85,    -30.05,          50.43,  +0.09,  -0.60
  4,     UK0038,       0,  0.170981, 2459439.607228667010,   4.51078,   8.30268,              170.56879,  46.60573,       170.55281,       46.59910,      4.51078,      +8.30268,       4.52318,       +8.29723,  4122454.95,  -130144.89,  4978532.02,      50.545689,       -2.166284,   99608.40,  135934.05,    9517.03,            10096.32,  -110.85,  56904.42,           58866.76,     13.46,     27.28,          46.16,  +0.23,  -0.44
  5,     UK0038,       0,  0.211449, 2459439.607229135465,   4.21699,   7.64753,              171.08306,  45.98314,       171.09136,       45.98656,      4.21699,      +7.64753,       4.21170,       +7.65038,  4121759.56,  -130917.59,  4976882.39,      50.540993,       -2.177489,   97908.46,  134958.90,   11466.87,            12046.16,  -571.73,  48182.37,           57239.20,     -7.00,    -14.17,          24.16,  +1.70,  +1.05

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.