Orbital Analysis for matched events on 20210813_230750.221_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 61.55° Bg 39.24° Vg 60.32km/s
mass 0.07487g, abs. mag -1.7
Path Details
------------
start 0.43° 53.29° 110.41km
end   0.28° 53.20° 97.82km

Orbit Details
-------------
Semimajor axis -20.10A.U., eccentricity 1.05, inclination 113.44°, Period 1000000000.00Y, LA Sun 141.11°, 

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: 2459440.463775706477
Time: 2021-08-13 23:07:50.370144 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000C and UK002K
 Convergence angle = 21.12851 deg
 R.A. =  46.75651  Dec = +58.60219 deg

Best intersection: Stations UK000C and UK002K with Qconv = 21.13 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2497675.28 +/- 225.81 m
 Y =  -2977651.64 +/- 61.15 m
 Z =   5178715.47 +/- 156.55 m
 Vx =    22499.68 +/- 1184.91 m/s
 Vy =    22563.34 +/- 1050.64 m/s
 Vz =    52399.64 +/- 925.55 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.662869e+04, -7.142975e+03, +1.674525e+04, +9.963249e+04, -3.017546e+04, +6.804737e+04
-7.142975e+03, +2.930332e+03, -4.654319e+03, -2.418367e+04, +1.393192e+04, -1.117251e+04
+1.674525e+04, -4.654319e+03, +1.162358e+04, +6.841094e+04, -2.093668e+04, +4.763665e+04
+9.963249e+04, -2.418367e+04, +6.841094e+04, +5.321045e+05, -1.270723e+05, +4.349971e+05
-3.017546e+04, +1.393192e+04, -2.093668e+04, -1.270723e+05, +7.664283e+04, -6.921520e+04
+6.804737e+04, -1.117251e+04, +4.763665e+04, +4.349971e+05, -6.921520e+04, +3.980359e+05

Timing offsets (from input data):
    UK000C: -0.003907 s
    UK002K: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 23:07:50.370144 UTC
  Lon     = ++0.430296 +/- 0.0021 deg
  Lat     = +53.294190 +/- 0.0006 deg
  Lat geo = +53.112747 +/- 0.0006 deg
  Ht      =  110387.29 +/- 232.84 m

  JD dynamic   = 2459440.464578173123 
  LST apparent = 309.9901623082 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  45.08095 +/- 1.9094 deg
  Dec       = +58.69607 +/- 0.1269 deg
  Azimuth   =  43.37983 +/- 0.8917 deg
  Elevation = +41.10547 +/- 0.7319 deg
  Vavg      =  57.54317 +/- 0.6251 km/s
  Vinit     =  61.32750 +/- 1.0008 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  45.03613 +/- 1.9094 deg
  Dec       = +58.47127 +/- 0.1269 deg
  Azimuth   =  43.63415 +/- 0.8917 deg
  Elevation = +40.98591 +/- 0.7319 deg
  Vavg      =  57.69032 +/- 0.6251 km/s
  Vinit     =  61.47465 +/- 1.0008 km/s
Radiant (geocentric, J2000):
  R.A.   =  45.32206 +/- 1.9124 deg
  Dec    = +58.34457 +/- 0.1197 deg
  Vg     =  60.31537 +/- 1.0185 km/s
  Vinf   =  61.32750 +/- 1.0008 km/s
  Zc     =  49.02653 +/- 0.7338 deg
  Zg     =  49.46131 +/- 0.7446 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  61.54725 +/- 1.2349 deg
  Bg     = +39.23900 +/- 0.3096 deg
  Vh     =  42.37365 +/- 0.8942 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  77.32107 +/- 3.1048 deg
  Bh     = +64.21044 +/- 0.8432 deg
  Vh_x   =  -4.04634 +/- 0.9538 km/s
  Vh_y   = -17.98584 +/- 0.8388 km/s
  Vh_z   = -38.15315 +/- 0.7182 km/s
Orbit:
  La Sun = 141.114025 +/- 0.0000 deg
  a      = -20.098871 +/- 250.3893 AU
  e      =   1.048587 +/- 0.0790
  i      = 113.437660 +/- 0.6973 deg
  peri   = 158.367682 +/- 3.4611 deg
  node   = 141.112808 +/- 0.0001 deg
  Pi     = 299.480490 +/- 3.4611 deg
  q      =   0.976549 +/- 0.0117 AU
  f      =  21.628275 +/- 3.4611 deg
  M      =        nan +/- nan deg
  Q      = -41.174292 +/- 500.7737 AU
  n      =   0.010938 +/- 0.0291 deg/day
  T      = 1000000000.000000 +/- 498887627.8765 years
  Last perihelion JD = NaN 
  Tj     =  -0.752148 +/- 0.4542
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +3.472648e-03, +5.160005e-04, +1.301029e-01, -3.117851e-08, +2.913797e-03, +4.139787e-04
q   , +5.160005e-04, +9.080051e-05, +2.165909e-02, -4.244636e-09, +4.956265e-04, +5.636136e-05
Tp  , +1.301029e-01, +2.165909e-02, +5.259114e+00, -1.098263e-06, +1.195306e-01, +1.458283e-02
node, -3.117851e-08, -4.244636e-09, -1.098263e-06, +3.288436e-13, -2.428077e-08, -4.364542e-09
peri, +2.913797e-03, +4.956265e-04, +1.195306e-01, -2.428077e-08, +2.724158e-03, +3.224027e-04
i   , +4.139787e-04, +5.636136e-05, +1.458283e-02, -4.364542e-09, +3.224027e-04, +5.792809e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 21.647638
 a2 = 10.566126

Mean time residuals from time vs. length:
  Station with reference time: UK002K
  Avg. res. = 5.408e-07 s
  Stddev    = 7.35e-04 s

Begin point on the trajectory:
  Lon =     0.430552 +/- 0.0020 deg
  Lat =    53.294352 +/- 0.0006 deg
  Ht  = 110409.35 +/- 226.20 m
End point on the trajectory:
  Lon =     0.282946 +/- 0.0013 deg
  Lat =    53.201331 +/- 0.0006 deg
  Ht  = 97818.14 +/- 168.22 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
    UK000C,   False,    -0.727590,    51.263100,   57.00,   0.056612,  38.814583,   108214.77,   100920.72,          0.009804,     44.13,      1.71,              24.01, 1.0000,    True,    True, {"ff_name": "FF_UK000C_20210813_230747_757_0270080.fits"}
    UK002K,   False,    -0.382860,    53.537770,   34.00,   4.083509,  14.845268,   110409.35,    97818.14,          0.029903,     58.41,     18.93,              48.28, 1.0000,    True,    True, {"ff_name": "FF_UK002K_20210813_230744_365_0261376.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,     UK000C,       0,  0.055411, 2459440.463777079247,  94.70972,  58.52851,               18.58828,  23.25615,        18.58043,       23.26352,     94.70972,     +58.52851,      94.71696,      +58.53808,  2496462.72, -2978867.64,  5175891.52,      53.278195,       +0.405208,  108214.77,  262487.55,       0.00,             3305.09,    30.64,      0.00,           62385.58,     -1.79,    -47.20,          37.11,  +2.82,  +0.72
  1,     UK000C,       0,  0.095499, 2459440.463777543511,  95.11439,  58.44787,               18.40876,  23.10121,        18.40298,       23.10664,     95.11439,     +58.44787,      95.11993,      +58.45491,  2495584.03, -2979748.81,  5173845.14,      53.266594,       +0.386769,  106641.04,  260319.98,    2395.04,             5700.13,   -32.82,  59744.52,           62385.58,     -1.32,    -34.53,          27.38,  +1.92,  -0.16
  2,     UK000C,       0,  0.135567, 2459440.463778007310,  95.53528,  58.38378,               18.21288,  22.95907,        18.22442,       22.94823,     95.53528,     +58.38378,      95.52440,      +58.36976,  2494712.48, -2980622.82,  5171815.39,      53.255079,       +0.368480,  105080.57,  258174.06,    4770.62,             8075.71,  -114.51,  59288.65,           62385.58,      2.68,     68.34,          54.64,  +1.96,  -0.10
  3,     UK000C,       0,  0.175691, 2459440.463778471574,  95.99508,  58.25842,               18.01990,  22.75316,        18.01308,       22.75954,     95.99508,     +58.25842,      96.00210,      +58.26667,  2493694.62, -2981643.57,  5169444.88,      53.241620,       +0.347150,  103258.75,  255673.72,    7545.02,            10850.11,   199.18,  69145.68,           62385.58,     -1.53,    -39.94,          32.24,  +1.55,  -0.49
  4,     UK000C,       0,  0.215747, 2459440.463778935373,  96.34494,  58.20269,               17.85621,  22.63387,        17.86388,       22.62668,     96.34494,     +58.20269,      96.33793,      +58.19342,  2492989.97, -2982350.21,  5167803.81,      53.232296,       +0.332332,  101997.89,  253945.16,    9465.69,            12770.79,  -336.68,  47949.71,           60074.20,      1.75,     44.70,          36.33,  +2.57,  +0.55
  5,     UK000C,       0,  0.255819, 2459440.463779399171,  96.62709,  58.12920,               17.73486,  22.51142,        17.73462,       22.51165,     96.62709,     +58.12920,      96.62804,      +58.12949,  2492387.85, -2982954.04,  5166401.53,      53.224324,       +0.319647,  100920.72,  252469.90,   11106.89,            14411.99, -1152.99,  40956.38,           56683.55,     -0.05,     -1.40,           1.15,  +5.05,  +3.04
  0,     UK002K,       0,  0.000000, 2459440.463777432218, 341.47700,  34.99223,              116.27409,  60.77804,       116.28057,       60.79585,    341.47700,     +34.99223,     341.45992,      +35.00370,  2497687.59, -2977639.30,  5178744.13,      53.294352,       +0.430552,  110409.35,  126113.79,       0.00,               33.55,   157.33,      0.00,           60004.05,     12.28,    -37.87,          65.12,  +2.43,  +1.93
  1,     UK002K,       0,  0.040168, 2459440.463777896948, 340.82719,  34.31478,              118.00021,  60.60282,       118.01506,       60.63834,    340.82719,     +34.31478,     340.79321,      +34.33759,  2496752.98, -2978576.55,  5176567.52,      53.282025,       +0.410948,  108734.75,  124392.74,    2547.46,             2513.91,   174.29,  63420.15,           60004.05,     24.25,    -74.90,         130.55,  +1.17,  +0.70
  2,     UK002K,       0,  0.080296, 2459440.463778361678, 340.21779,  33.71275,              119.56779,  60.45190,       119.57906,       60.47608,    340.21779,     +33.71275,     340.19483,      +33.72825,  2495923.89, -2979407.99,  5174636.63,      53.271082,       +0.393540,  107249.66,  122889.66,    4807.34,             4773.79,   -26.78,  56316.80,           60004.05,     16.41,    -50.63,          89.33,  +0.63,  +0.18
  3,     UK002K,       0,  0.120440, 2459440.463778826408, 339.53521,  33.04136,              121.31102,  60.27147,       121.31149,       60.27238,    339.53521,     +33.04136,     339.53483,      +33.04194,  2495018.12, -2980316.32,  5172527.20,      53.259118,       +0.374539,  105627.76,  121275.11,    7276.18,             7242.63,   -19.88,  61499.53,           60004.05,      0.61,     -1.89,           3.38,  +0.46,  +0.04
  4,     UK002K,       0,  0.160612, 2459440.463779291138, 338.85771,  32.32545,              123.08939,  60.03809,       123.08873,       60.03693,    338.85771,     +32.32545,     338.85951,      +32.32471,  2494101.03, -2981236.00,  5170391.38,      53.246995,       +0.355303,  103986.09,  119670.36,    9775.90,             9742.35,    16.20,  62225.48,           60475.29,     -0.78,      2.40,           4.35,  +0.36,  -0.03
  5,     UK002K,       0,  0.200784, 2459440.463779756334, 338.23310,  31.63387,              124.75126,  59.78342,       124.75616,       59.79128,    338.23310,     +31.63387,     338.22627,      +31.63889,  2493250.26, -2982089.19,  5168409.99,      53.235741,       +0.337447,  102463.60,  118209.29,   12094.87,            12061.32,  -128.48,  57726.02,           60216.90,      5.25,    -16.17,          29.66,  +0.28,  -0.08
  6,     UK002K,       0,  0.240988, 2459440.463780221529, 337.56735,  30.86284,              126.54152,  59.46869,       126.56054,       59.49679,    337.56735,     +30.86284,     337.54079,      +30.88082,  2492337.80, -2983004.22,  5166284.98,      53.223661,       +0.318310,  100831.25,  116673.79,   14581.95,            14548.40,  -107.02,  61861.43,           60301.08,     18.68,    -57.56,         106.97,  +0.60,  +0.27
  7,     UK002K,       0,  0.281180, 2459440.463780686725, 336.96794,  30.15735,              128.14592,  59.16194,       128.17879,       59.20731,    336.96794,     +30.15735,     336.92437,      +30.18641,  2491525.78, -2983818.54,  5164393.85,      53.212904,       +0.301262,   99379.00,  115334.90,   16795.28,            16761.73,  -358.55,  55069.08,           59899.74,     30.04,    -92.66,         174.20,  +1.48,  +1.17
  8,     UK002K,       0,  0.321376, 2459440.463781151921, 336.30076,  29.38869,              129.89151,  58.81910,       129.92745,       58.86546,    336.30076,     +29.38869,     336.25607,      +29.41846,  2490652.76, -2984694.03,  5162360.67,      53.201331,       +0.282946,   97818.14,  113926.43,   19174.88,            19141.32,  -444.08,  59199.71,           59665.82,     30.64,    -94.47,         179.81,  +3.11,  +2.83

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.