Orbital Analysis for matched events on 20210810_004601.257_UK

Summary for Event
-----------------
shower ID 547 KAP
Lg 50.87° Bg 17.72° Vg 57.72km/s
mass 0.00318g, abs. mag 1.2
Path Details
------------
start -3.64° 50.90° 111.72km
end   -3.77° 50.88° 105.10km

Orbit Details
-------------
Semimajor axis 1.13A.U., eccentricity 0.14, inclination 145.42°, Period 1.21Y, LA Sun 137.34°, last Perihelion 2021-06-25

Full details below
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Detailed report below graphs

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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: 2459436.531959000975
Time: 2021-08-10 00:46:01.257684 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000T and UK0024
 Convergence angle = 37.24792 deg
 R.A. =  43.67495  Dec = +34.61048 deg

Best intersection: Stations UK000T and UK0024 with Qconv = 37.25 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3423163.64 +/- 50.61 m
 Y =  -2258438.10 +/- 57.17 m
 Z =   5013372.28 +/- 55.62 m
 Vx =    35231.72 +/- 392.58 m/s
 Vy =    32450.03 +/- 666.52 m/s
 Vz =    34057.32 +/- 422.67 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.747284e+03, -1.927056e+03, +2.545141e+03, +1.685176e+04, -1.849328e+04, +1.629469e+04
-1.927056e+03, +3.485672e+03, -2.490018e+03, -1.850496e+04, +2.269430e+04, -2.180733e+04
+2.545141e+03, -2.490018e+03, +3.323050e+03, +1.487069e+04, -1.970281e+04, +2.015828e+04
+1.685176e+04, -1.850496e+04, +1.487069e+04, +1.581060e+05, -1.739086e+05, +1.480905e+05
-1.849328e+04, +2.269430e+04, -1.970281e+04, -1.739086e+05, +2.074909e+05, -1.890100e+05
+1.629469e+04, -2.180733e+04, +2.015828e+04, +1.480905e+05, -1.890100e+05, +1.817135e+05

Timing offsets (from input data):
    UK000T: 0.000000 s
    UK0024: 0.000160 s

Reference point on the trajectory:
  Time: 2021-08-10 00:46:01.257684 UTC
  Lon     = +-3.644839 +/- 0.0005 deg
  Lat     = +50.901318 +/- 0.0002 deg
  Lat geo = +50.716087 +/- 0.0002 deg
  Ht      =  111722.09 +/- 82.56 m

  JD dynamic   = 2459436.532759741880 
  LST apparent = 326.5850989740 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  42.64650 +/- 0.6912 deg
  Dec       = +35.41393 +/- 0.3647 deg
  Azimuth   =  74.92194 +/- 0.2206 deg
  Elevation = +34.99601 +/- 0.6494 deg
  Vavg      =  57.08521 +/- 0.1423 km/s
  Vinit     =  58.77227 +/- 0.1988 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  42.73215 +/- 0.6912 deg
  Dec       = +35.25059 +/- 0.3647 deg
  Azimuth   =  75.01397 +/- 0.2206 deg
  Elevation = +34.83517 +/- 0.6494 deg
  Vavg      =  57.32204 +/- 0.1423 km/s
  Vinit     =  59.00910 +/- 0.1988 km/s
Radiant (geocentric, J2000):
  R.A.   =  42.80829 +/- 0.6971 deg
  Dec    = +34.96646 +/- 0.3734 deg
  Vg     =  57.71571 +/- 0.2025 km/s
  Vinf   =  58.77227 +/- 0.1988 km/s
  Zc     =  55.05237 +/- 0.6498 deg
  Zg     =  55.59403 +/- 0.6613 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  50.86607 +/- 0.4718 deg
  Bg     = +17.71679 +/- 0.5168 deg
  Vh     =  31.10539 +/- 0.3084 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  54.26808 +/- 1.0158 deg
  Bh     = +34.38035 +/- 0.8624 deg
  Vh_x   = -14.99199 +/- 0.3876 km/s
  Vh_y   = -20.83905 +/- 0.2404 km/s
  Vh_z   = -17.56472 +/- 0.5523 km/s
Orbit:
  La Sun = 137.339799 +/- 0.0000 deg
  a      =   1.133485 +/- 0.0252 AU
  e      =   0.144743 +/- 0.0059
  i      = 145.423445 +/- 0.8038 deg
  peri   = 130.852975 +/- 11.3384 deg
  node   = 137.335384 +/- 0.0002 deg
  Pi     = 268.188360 +/- 11.3385 deg
  q      =   0.969420 +/- 0.0252 AU
  f      =  49.140631 +/- 11.3382 deg
  M      =  37.457772 +/- 9.5957 deg
  Q      =   1.297549 +/- 0.0264 AU
  n      =   0.816735 +/- 0.0301 deg/day
  T      =   1.206769 +/- 0.0394 years
  Last perihelion JD = 2459390.669875 (2021-06-25 04:04:37.238837) +/- 8.9493 days
  Tj     =   3.830965 +/- 0.1129
Shower association:
  IAU No.  =  547
  IAU code =  KAP

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +3.639759e-05, -1.024276e-04, -2.713505e-02, -8.327778e-09, -6.594123e-04, +3.800431e-05
q   , -1.024276e-04, +6.731898e-04, +2.341837e-01, +7.598217e-08, +5.233769e-03, -3.571179e-04
Tp  , -2.713505e-02, +2.341837e-01, +8.569219e+01, +2.729655e-05, +1.887895e+00, -1.289279e-01
node, -8.327778e-09, +7.598217e-08, +2.729655e-05, +9.493814e-12, +6.053710e-07, -4.463122e-08
peri, -6.594123e-04, +5.233769e-03, +1.887895e+00, +6.053710e-07, +4.176053e-02, -2.855161e-03
i   , +3.800431e-05, -3.571179e-04, -1.289279e-01, -4.463122e-08, -2.855161e-03, +2.099535e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = -0.029779
 a2 = 46.236219

Mean time residuals from time vs. length:
  Station with reference time: UK000T
  Avg. res. = 9.821e-06 s
  Stddev    = 3.13e-03 s

Begin point on the trajectory:
  Lon =    -3.644967 +/- 0.0003 deg
  Lat =    50.901297 +/- 0.0002 deg
  Ht  = 111715.44 +/- 81.73 m
End point on the trajectory:
  Lon =    -3.773481 +/- 0.0003 deg
  Lat =    50.879469 +/- 0.0002 deg
  Ht  = 105100.18 +/- 66.92 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
    UK000T,   False,    -3.557111,    51.483925,   37.50,   0.000000,   0.000000,   111715.44,   105100.18,          0.020877,     37.80,     27.90,              70.58, 1.0000,    True,    True, {"ff_name": "FF_UK000T_20210810_004556_259_0388352.fits"}
    UK0024,   False,    -2.949770,    50.877440,   82.00,   0.000000,   0.000000,   110090.69,   106040.36,          0.013890,     17.51,     23.58,              79.04, 1.0000,    True,    True, {"ff_name": "FF_UK0024_20210810_004558_929_0397056.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,     UK000T,       0,  0.000000, 2459436.531959000975, 323.71951,  20.78321,              185.40047,  59.21260,       185.44675,       59.24653,    323.71951,     +20.78321,     323.69626,      +20.81856,  3423156.68, -2258444.50,  5013365.56,      50.901297,       -3.644967,  111715.44,  129558.89,       0.00,               11.60,    93.16,      0.00,           57538.85,     55.54,    -75.28,         148.94,  +5.00,  +4.44
  1,     UK000T,       0,  0.040792, 2459436.531959473155, 322.82624,  20.30279,              186.95115,  58.67354,       186.97128,       58.68783,    322.82624,     +20.30279,     322.81626,      +20.31787,  3421775.63, -2259716.52,  5012030.54,      50.896956,       -3.670599,  110394.36,  128766.84,    2303.83,             2315.43,    -0.46,  56477.39,           57538.85,     23.64,    -32.03,          63.76,  +3.23,  +2.68
  2,     UK000T,       0,  0.081672, 2459436.531959946267, 321.85593,  19.76754,              188.59080,  58.05872,       188.58587,       58.05533,    321.85593,     +19.76754,     321.85842,      +19.76391,  3420280.25, -2261093.83,  5010585.01,      50.892247,       -3.698346,  108964.53,  127950.78,    4798.36,             4809.96,    91.47,  61020.96,           57538.85,     -5.67,      7.68,          15.39,  +1.97,  +1.43
  3,     UK000T,       0,  0.122464, 2459436.531960418448, 320.99555,  19.28421,              190.00609,  57.49156,       189.97988,       57.47403,    320.99555,     +19.28421,     321.00850,      +19.26518,  3418961.10, -2262308.83,  5009309.83,      50.888087,       -3.722849,  107703.72,  127267.55,    6998.92,             7010.52,  -105.41,  53945.81,           57538.85,    -29.69,     40.17,          80.96,  +2.03,  +1.51
  4,     UK000T,       0,  0.163420, 2459436.531960892491, 320.03010,  18.68992,              191.54106,  56.78938,       191.53341,       56.78440,    320.03010,     +18.68992,     320.03422,      +18.68443,  3417454.69, -2263696.30,  5007853.63,      50.883327,       -3.750812,  106264.54,  126529.86,    9511.86,             9523.46,     0.45,  61357.11,           58062.05,     -8.54,     11.56,          23.44,  +2.52,  +2.01
  5,     UK000T,       0,  0.204204, 2459436.531961364672, 319.24362,  18.20174,              192.75754,  56.20280,       192.76322,       56.20642,    319.24362,     +18.20174,     319.24148,      +18.20579,  3416235.46, -2264819.27,  5006675.05,      50.879469,       -3.773481,  105100.18,  125966.87,   11545.73,            11557.33,  -362.64,  49869.28,           57042.83,      6.28,     -8.50,          17.31,  +4.77,  +4.27
  0,     UK0024,       0,  0.050999, 2459436.531959719490, 289.63234,  45.50835,              272.62645,  64.62703,       272.58856,       64.63115,    289.63234,     +45.50835,     289.64776,      +45.49555,  3421458.09, -2260008.99,  5011723.59,      50.895957,       -3.676543,  110090.69,  121520.59,       0.00,             2845.13,   -70.64,      0.00,           58455.97,    -28.52,    -21.18,          60.30,  +1.81,  +1.39
  1,     UK0024,       0,  0.091911, 2459436.531960193068, 288.40444,  44.77011,              272.00520,  63.52186,       271.96350,       63.52638,    288.40444,     +44.77011,     288.42230,      +44.75568,  3419996.29, -2261355.37,  5010310.51,      50.891352,       -3.703673,  108693.09,  121086.09,    2438.53,             5283.66,   -36.61,  59604.16,           58455.97,    -32.46,    -24.11,          68.88,  +1.72,  +1.30
  2,     UK0024,       0,  0.132931, 2459436.531960667577, 287.10099,  43.90950,              271.30321,  62.29406,       271.32132,       62.29211,    287.10099,     +43.90950,     287.09331,      +43.91593,  3418377.87, -2262846.01,  5008746.04,      50.886245,       -3.733698,  107146.45,  120660.55,    5138.31,             7983.45,   252.34,  65816.41,           58455.97,     14.61,     10.85,          31.11,  +2.27,  +1.86
  3,     UK0024,       0,  0.173675, 2459436.531961139292, 286.15145,  43.30689,              270.90541,  61.39930,       270.89096,       61.40086,    286.15145,     +43.30689,     286.15856,      +43.30167,  3417219.99, -2263912.47,  5007626.76,      50.882585,       -3.755232,  106040.36,  120394.19,    7069.85,             9914.98,  -210.74,  47406.54,           58455.97,    -11.97,     -8.89,          25.54,  +4.74,  +4.34

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.