Orbital Analysis for matched events on 20210813_222645.133_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 65.07° Bg 39.17° Vg 58.31km/s
mass 0.03269g, abs. mag -1.1
Path Details
------------
start 2.19° 51.49° 109.53km
end   2.08° 51.39° 100.11km

Orbit Details
-------------
Semimajor axis 12.15A.U., eccentricity 0.92, inclination 111.44°, Period 42.35Y, LA Sun 141.09°, last Perihelion 2021-07-22

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Input measurement type: Right Ascension for meas1, Declination for meas2, epoch of date

Uncertainties type:
 Purely geometric uncertainties

Reference JD: 2459440.435244604014
Time: 2021-08-13 22:26:45.133787 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002C and UK002K
 Convergence angle = 28.43033 deg
 R.A. =  48.32745  Dec = +58.37644 deg

Best intersection: Stations UK002C and UK002K with Qconv = 28.43 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2112069.45 +/- 374.15 m
 Y =  -3453076.46 +/- 134.24 m
 Z =   5053375.09 +/- 154.67 m
 Vx =    19273.10 +/- 2441.25 m/s
 Vy =    22962.45 +/- 874.28 m/s
 Vz =    51232.47 +/- 2335.77 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+7.804984e+04, +2.176355e+04, +2.794042e+04, +3.541506e+05, +7.689865e+04, +9.390686e+04
+2.176355e+04, +8.797718e+03, +8.955620e+03, +7.287235e+04, +2.476628e+04, +1.858573e+04
+2.794042e+04, +8.955620e+03, +1.169435e+04, +1.063984e+05, +2.511560e+04, +2.929878e+04
+3.541506e+05, +7.287235e+04, +1.063984e+05, +2.087793e+06, +3.817163e+05, +5.440059e+05
+7.689865e+04, +2.476628e+04, +2.511560e+04, +3.817163e+05, +1.066516e+05, +9.168370e+04
+9.390686e+04, +1.858573e+04, +2.929878e+04, +5.440059e+05, +9.168370e+04, +1.451451e+05

Timing offsets (from input data):
    UK002C: 0.000000 s
    UK002K: -2.031433 s

Reference point on the trajectory:
  Time: 2021-08-13 22:26:45.133787 UTC
  Lon     = ++2.192058 +/- 0.0055 deg
  Lat     = +51.489518 +/- 0.0005 deg
  Lat geo = +51.305045 +/- 0.0005 deg
  Ht      =  109526.72 +/- 173.30 m

  JD dynamic   = 2459440.436045344919 
  LST apparent = 301.4519832395 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  49.99222 +/- 2.5179 deg
  Dec       = +59.66589 +/- 1.4513 deg
  Azimuth   =  35.83451 +/- 2.3848 deg
  Elevation = +35.12592 +/- 0.2148 deg
  Vavg      =  58.82004 +/- 0.9709 km/s
  Vinit     =  59.35902 +/- 1.7822 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  49.81450 +/- 2.5179 deg
  Dec       = +59.43319 +/- 1.4513 deg
  Azimuth   =  36.11591 +/- 2.3848 deg
  Elevation = +35.02986 +/- 0.2148 deg
  Vavg      =  58.96194 +/- 0.9709 km/s
  Vinit     =  59.50092 +/- 1.7822 km/s
Radiant (geocentric, J2000):
  R.A.   =  50.31091 +/- 2.5614 deg
  Dec    = +59.22080 +/- 1.4308 deg
  Vg     =  58.31269 +/- 1.8121 km/s
  Vinf   =  59.35902 +/- 1.7822 km/s
  Zc     =  55.02370 +/- 0.2141 deg
  Zg     =  55.55439 +/- 0.2152 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  65.06854 +/- 2.2374 deg
  Bg     = +39.17053 +/- 0.9014 deg
  Vh     =  40.96778 +/- 1.0013 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  87.33106 +/- 6.9109 deg
  Bh     = +64.03433 +/- 1.4446 deg
  Vh_x   =  -0.83524 +/- 2.5481 km/s
  Vh_y   = -17.91757 +/- 0.9493 km/s
  Vh_z   = -36.83235 +/- 0.4445 km/s
Orbit:
  La Sun = 141.086622 +/- -0.0000 deg
  a      =  12.149152 +/- 37.6028 AU
  e      =   0.922435 +/- 0.0922
  i      = 111.442553 +/- 2.7395 deg
  peri   = 148.703297 +/- 5.6297 deg
  node   = 141.085311 +/- 0.0002 deg
  Pi     = 289.788608 +/- 5.6295 deg
  q      =   0.942348 +/- 0.0197 AU
  f      =  31.292687 +/- 5.6298 deg
  M      =   0.512010 +/- nan deg
  Q      =  23.355956 +/- 75.2097 AU
  n      =   0.023275 +/- 0.0249 deg/day
  T      =  42.346700 +/- 471404375.9305 years
  Last perihelion JD = 2459418.437519 (2021-07-22 22:30:01.638253) +/- 2.3703 days
  Tj     =  -0.003005 +/- 0.5635
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.422040e-03, +5.428632e-04, +9.272759e-02, -7.205477e-08, +2.368546e-03, +9.527942e-04
q   , +5.428632e-04, +2.192479e-04, +3.677971e-02, -2.840261e-08, +9.448916e-04, +3.765906e-04
Tp  , +9.272759e-02, +3.677971e-02, +6.206558e+00, -4.793413e-06, +1.591522e-01, +6.350102e-02
node, -7.205477e-08, -2.840261e-08, -4.793413e-06, +3.942480e-12, -1.228791e-07, -5.217751e-08
peri, +2.368546e-03, +9.448916e-04, +1.591522e-01, -1.228791e-07, +4.083496e-03, +1.628299e-03
i   , +9.527942e-04, +3.765906e-04, +6.350102e-02, -5.217751e-08, +1.628299e-03, +6.906499e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = -0.145142
 a2 = 26.161031

Mean time residuals from time vs. length:
  Station with reference time: UK002C
  Avg. res. = 3.242e-05 s
  Stddev    = 5.69e-03 s

Begin point on the trajectory:
  Lon =     2.192058 +/- 0.0053 deg
  Lat =    51.489518 +/- 0.0002 deg
  Ht  = 109526.72 +/- 159.23 m
End point on the trajectory:
  Lon =     2.079853 +/- 0.0059 deg
  Lat =    51.393282 +/- 0.0002 deg
  Ht  = 100108.55 +/- 170.57 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
    UK002C,   False,    -1.801980,    51.351940,  130.00,   7.223114,   8.276783,   109526.72,   100108.55,          0.008891,     37.89,     26.84,              45.65, 1.0000,    True,    True, {"ff_name": "FF_UK002C_20210813_222645_752_0204800.fits"}
    UK002K,   False,    -0.382860,    53.537770,   34.00,   0.000000,   0.000000,   107861.39,   101019.62,          0.024247,    130.39,     15.02,              89.61, 1.0000,    True,    True, {"ff_name": "FF_UK002K_20210813_222644_867_0199936.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,     UK002C,       0,  0.000000, 2459440.435244604014,  18.12861,  18.41787,               85.28632,  20.04810,        85.28632,       20.04810,     18.12861,     +18.41787,      18.12861,      +18.41786,  2112069.45, -3453076.46,  5053375.09,      51.489518,       +2.192058,  109526.72,  301143.66,       0.00,                0.00,   203.15,      0.00,           57031.96,      0.00,      0.00,           0.00,  +3.62,  +1.23
  1,     UK002C,       0,  0.040164, 2459440.435245068744,  18.03624,  18.13382,               85.55491,  19.89112,        85.56592,       19.91075,     18.03624,     +18.13382,      18.01465,      +18.14187,  2111381.90, -3453895.63,  5051547.40,      51.477108,       +2.177538,  108308.52,  299697.49,    2117.60,             2117.60,   -63.35,  52723.85,           57031.96,    -67.11,    -94.72,          79.90,  +2.21,  -0.17
  2,     UK002C,       0,  0.080312, 2459440.435245533474,  17.87072,  17.82363,               85.89732,  19.75976,        85.89169,       19.74975,     17.87072,     +17.82363,      17.88214,      +17.81953,  2110587.62, -3454841.96,  5049436.02,      51.462763,       +2.160795,  106901.81,  298038.63,    4563.89,             4563.89,    -0.20,  60931.79,           57031.96,     34.01,     48.09,          40.76,  +2.38,  +0.01
  3,     UK002C,       0,  0.120480, 2459440.435245998669,  17.75953,  17.51880,               86.19413,  19.59840,        86.19462,       19.59927,     17.75953,     +17.51880,      17.75907,      +17.51916,  2109855.40, -3455714.34,  5047489.62,      51.449532,       +2.145349,  105605.54,  296518.26,    6819.03,             6819.03,  -129.39,  56142.81,           57031.96,     -2.94,     -4.16,           3.55,  +1.98,  -0.38
  4,     UK002C,       0,  0.160656, 2459440.435246463399,  17.62522,  17.19039,               86.52467,  19.43339,        86.52510,       19.43415,     17.62522,     +17.19039,      17.62505,      +17.19070,  2109063.52, -3456657.80,  5045384.61,      51.435214,       +2.128661,  104204.21,  294885.58,    9257.94,             9257.94,   -75.29,  60705.58,           57808.04,     -2.55,     -3.60,           3.09,  +1.95,  -0.40
  5,     UK002C,       0,  0.200832, 2459440.435246928595,  17.48671,  16.86087,               86.85882,  19.26993,        86.85729,       19.26722,     17.48671,     +16.86087,      17.49054,      +16.85977,  2108274.63, -3457597.70,  5043287.56,      51.420941,       +2.112039,  102808.79,  293270.25,   11687.63,            11687.63,   -30.41,  60476.02,           58410.99,      9.08,     12.83,          11.05,  +1.89,  -0.45
  6,     UK002C,       0,  0.241012, 2459440.435247393325,  17.35340,  16.52536,               87.19275,  19.09843,        87.19242,       19.09786,     17.35340,     +16.52536,      17.35503,      +16.52513,  2107485.82, -3458537.52,  5041190.69,      51.406662,       +2.095422,  101414.08,  291666.44,   14117.10,            14117.10,    14.01,  60464.66,           58846.41,      1.89,      2.67,           2.32,  +2.09,  -0.23
  7,     UK002C,       0,  0.281180, 2459440.435247858521,  17.22611,  16.20834,               87.50892,  18.93698,        87.50897,       18.93707,     17.22611,     +16.20834,      17.22719,      +16.20837,  2106747.13, -3459417.60,  5039227.11,      51.393282,       +2.079853,  100108.55,  290174.34,   16392.15,            16392.15,   -95.27,  56638.51,           58843.80,     -0.29,     -0.41,           0.36,  +2.84,  +0.53
  0,     UK002K,       0,  0.060311, 2459440.435245394241, 335.20028, -10.32878,              141.93110,  19.07810,       141.93110,       19.07810,    335.20028,     -10.32878,     335.20056,      -10.32878,  2111129.46, -3454196.38,  5050876.38,      51.472550,       +2.172153,  107861.39,  309683.83,       0.00,             2895.06,  -481.80,      0.00,           63046.89,     -0.00,     -0.02,           0.01,  +2.70,  +0.25
  1,     UK002K,       0,  0.100499, 2459440.435245859437, 334.90764, -10.82944,              142.40969,  18.71979,       142.40614,       18.71565,    334.90764,     -10.82944,     334.91283,      -10.83204,  2110117.54, -3455402.01,  5048186.45,      51.454269,       +2.150868,  106069.56,  309769.13,    3116.61,             6011.67,   249.29,  77550.76,           63046.89,      3.32,     28.64,          19.20,  +1.73,  -0.73
  2,     UK002K,       0,  0.140659, 2459440.435246324167, 334.69439, -11.22563,              142.76877,  18.42837,       142.77351,       18.43388,    334.69439,     -11.22563,     334.68868,      -11.22215,  2109332.44, -3456337.41,  5046099.46,      51.440077,       +2.134321,  104680.04,  309855.53,    5534.64,             8429.70,   283.47,  60209.89,           63046.89,     -4.44,    -38.23,          25.62,  +1.29,  -1.17
  3,     UK002K,       0,  0.180783, 2459440.435246788431, 334.49278, -11.56042,              143.09141,  18.18896,       143.09142,       18.18898,    334.49278,     -11.56042,     334.49355,      -11.56040,  2108651.10, -3457149.17,  5044288.29,      51.427753,       +2.119941,  103474.63,  309945.01,    7633.10,            10528.15,     0.20,  52299.29,           63046.89,     -0.01,     -0.11,           0.08,  +1.24,  -1.22
  4,     UK002K,       0,  0.220951, 2459440.435247253627, 334.27697, -11.97681,              143.45741,  17.87767,       143.47162,       17.89411,    334.27697,     -11.97681,     334.25895,      -11.96637,  2107832.34, -3458124.66,  5042111.85,      51.412936,       +2.102698,  102026.70,  310072.63,   10154.77,            13049.83,   137.55,  62778.30,           61824.39,    -13.32,   -114.47,          76.66,  +3.98,  +1.52
  5,     UK002K,       0,  0.260999, 2459440.435247716960, 334.04500, -12.22173,              143.77236,  17.73100,       143.73579,       17.68880,    334.04500,     -12.22173,     334.09491,      -12.24859,  2107262.67, -3458803.38,  5040597.52,      51.402621,       +2.090652,  101019.62,  310171.65,   11909.30,            14804.36,  -485.14,  43810.57,           58909.00,     33.85,    294.32,         197.02,  +3.98,  +1.52

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.