Orbital Analysis for matched events on 20210813_015510.782_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 61.86° Bg 35.27° Vg 58.24km/s
mass 0.10085g, abs. mag -2.3
Path Details
------------
start -1.73° 54.52° 111.89km
end   -1.89° 54.47° 94.22km

Orbit Details
-------------
Semimajor axis 3.71A.U., eccentricity 0.74, inclination 117.07°, Period 7.14Y, LA Sun 140.27°, last Perihelion 2021-07-20

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: 2459439.579985909630
Time: 2021-08-13 01:55:10.782592 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0026 and UK002Z
 Convergence angle = 9.95110 deg
 R.A. =  48.37166  Dec = +54.48070 deg

Best intersection: Stations UK0026 and UK002Z with Qconv = 9.95 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3703605.43 +/- 143.62 m
 Y =   -733609.63 +/- 235.05 m
 Z =   5261553.14 +/- 445.20 m
 Vx =    22752.04 +/- 1330.60 m/s
 Vy =    25386.65 +/- 1797.65 m/s
 Vz =    48511.60 +/- 1793.04 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+9.739696e+03, +1.307067e+04, -2.445027e+04, +2.774294e+04, +3.784128e+04, -6.934588e+04
+1.307067e+04, +2.048421e+04, -3.602140e+04, +4.127454e+04, +6.573577e+04, -1.111865e+05
-2.445027e+04, -3.602140e+04, +7.141634e+04, -8.969454e+04, -1.261950e+05, +2.217437e+05
+2.774294e+04, +4.127454e+04, -8.969454e+04, +1.931568e+05, +2.558129e+05, -4.292805e+05
+3.784128e+04, +6.573577e+04, -1.261950e+05, +2.558129e+05, +3.899611e+05, -6.193141e+05
-6.934588e+04, -1.111865e+05, +2.217437e+05, -4.292805e+05, -6.193141e+05, +1.012976e+06

Timing offsets (from input data):
    UK0026: -0.000457 s
    UK002Z: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 01:55:10.782592 UTC
  Lon     = +-1.727936 +/- 0.0039 deg
  Lat     = +54.516648 +/- 0.0029 deg
  Lat geo = +54.337695 +/- 0.0030 deg
  Ht      =  111970.87 +/- 310.28 m

  JD dynamic   = 2459439.580786650535 
  LST apparent = 348.7958912931 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  48.13265 +/- 0.5328 deg
  Dec       = +54.90347 +/- 1.9291 deg
  Azimuth   =  64.47482 +/- 3.3321 deg
  Elevation = +56.76613 +/- 0.8558 deg
  Vavg      =  58.82889 +/- 0.8936 km/s
  Vinit     =  59.29175 +/- 0.9044 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  48.36701 +/- 0.5328 deg
  Dec       = +54.71643 +/- 1.9291 deg
  Azimuth   =  64.68242 +/- 3.3321 deg
  Elevation = +56.56560 +/- 0.8558 deg
  Vavg      =  58.96554 +/- 0.8936 km/s
  Vinit     =  59.42840 +/- 0.9044 km/s
Radiant (geocentric, J2000):
  R.A.   =  48.21206 +/- 0.5355 deg
  Dec    = +54.69812 +/- 1.9482 deg
  Vg     =  58.24444 +/- 0.9199 km/s
  Vinf   =  59.29175 +/- 0.9044 km/s
  Zc     =  33.31133 +/- 0.8471 deg
  Zg     =  33.61681 +/- 0.8630 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  61.85822 +/- 0.6119 deg
  Bg     = +35.26788 +/- 1.9088 deg
  Vh     =  38.88176 +/- 1.7393 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  78.54546 +/- 1.9178 deg
  Bh     = +59.87697 +/- 1.7541 deg
  Vh_x   =  -3.87512 +/- 0.6770 km/s
  Vh_y   = -19.12449 +/- 0.2696 km/s
  Vh_z   = -33.63077 +/- 2.1280 km/s
Orbit:
  La Sun = 140.265302 +/- -0.0000 deg
  a      =   3.706803 +/- 32.6608 AU
  e      =   0.744785 +/- 0.1573
  i      = 117.065258 +/- 2.0015 deg
  peri   = 147.632181 +/- 2.4388 deg
  node   = 140.264860 +/- 0.0001 deg
  Pi     = 287.897041 +/- 2.4389 deg
  q      =   0.946031 +/- 0.0054 AU
  f      =  32.363986 +/- 2.4387 deg
  M      =   3.309183 +/- nan deg
  Q      =   6.467575 +/- 65.3217 AU
  n      =   0.138104 +/- 0.0500 deg/day
  T      =   7.136741 +/- 446947576.1983 years
  Last perihelion JD = 2459415.619173 (2021-07-20 02:51:36.585833) +/- 1.4454 days
  Tj     =   0.891481 +/- 0.8369
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +6.297243e-03, +2.341896e-04, +1.159470e-01, +1.241601e-07, +2.044298e-03, -1.707316e-03
q   , +2.341896e-04, +1.116132e-05, +4.691385e-03, +4.639235e-09, +8.644899e-05, -6.383536e-05
Tp  , +1.159470e-01, +4.691385e-03, +2.198678e+00, +2.290714e-06, +3.932810e-02, -3.149321e-02
node, +1.241601e-07, +4.639235e-09, +2.290714e-06, +2.466823e-12, +4.041851e-08, -3.391396e-08
peri, +2.044298e-03, +8.644899e-05, +3.932810e-02, +4.041851e-08, +7.090560e-04, -5.557829e-04
i   , -1.707316e-03, -6.383536e-05, -3.149321e-02, -3.391396e-08, -5.557829e-04, +4.662841e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.000000
 a2 = 0.000000

Mean time residuals from time vs. length:
  Station with reference time: UK002Z
  Avg. res. = 1.268e-06 s
  Stddev    = 1.13e-03 s

Begin point on the trajectory:
  Lon =    -1.728652 +/- 0.0038 deg
  Lat =    54.516449 +/- 0.0030 deg
  Ht  = 111891.12 +/- 319.30 m
End point on the trajectory:
  Lon =    -1.889060 +/- 0.0031 deg
  Lat =    54.472158 +/- 0.0022 deg
  Ht  = 94222.79 +/- 196.43 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
    UK0026,   False,    -0.023645,    52.984073,    6.00,   3.630590,   0.000000,   108729.84,    98654.72,          0.011263,     17.39,     42.12,              70.62, 1.0000,    True,   False, {"ff_name": "FF_UK0026_20210813_015508_134_0514816.fits"}
    UK002Z,   False,    -0.382830,    53.537790,   34.00,   0.000000,   0.000000,   111891.12,    94222.79,          0.022042,     15.89,     66.02,              65.51, 1.0000,    True,    True, {"ff_name": "FF_UK002Z_20210813_015503_686_0508672.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,     UK0026,       0,  0.071142, 2459439.579986737110, 227.06494,  54.07251,              326.70775,  26.86746,       326.71366,       26.86378,    227.06494,     +54.07251,     227.05428,      +54.07244,  3702118.45,  -735268.79,  5258382.63,      54.508561,       -1.757327,  108729.84,  233234.80,       0.00,             3875.06,  -107.46,      0.00,           59373.55,     24.18,      9.99,          23.13,  +1.49,  -0.35
  1,     UK0026,       0,  0.111418, 2459439.579987203237, 227.09778,  53.45876,              326.30391,  26.37075,       326.32009,       26.36069,    227.09778,     +53.45876,     227.06862,      +53.45857,  3701111.10,  -736392.79,  5256234.76,      54.503074,       -1.777213,  106534.58,  232399.88,    2625.16,             6500.22,   129.67,  65179.19,           59373.55,     66.13,     27.30,          63.49,  +0.84,  -0.99
  2,     UK0026,       0,  0.151666, 2459439.579987668898, 227.10645,  52.92677,              325.96726,  25.93289,       325.98161,       25.92398,    227.10645,     +52.92677,     227.08107,      +52.92660,  3700244.31,  -737359.95,  5254386.61,      54.498347,       -1.794355,  104645.89,  231703.74,    4884.00,             8759.07,     2.14,  56123.19,           59373.55,     58.62,     24.20,          56.46,  +0.46,  -1.36
  3,     UK0026,       0,  0.191938, 2459439.579988135025, 227.07731,  52.37413,              325.64148,  25.46432,       325.63285,       25.46967,    227.07731,     +52.37413,     227.09359,      +52.37423,  3699349.58,  -738358.29,  5252478.88,      54.493462,       -1.812050,  102696.53,  231006.05,    7215.67,            11090.73,   -53.99,  57897.97,           59373.55,    -35.21,    -14.55,          34.02,  +0.29,  -1.53
  4,     UK0026,       0,  0.232206, 2459439.579988601152, 227.09645,  51.79196,              325.27317,  24.98677,       325.26814,       24.98988,    227.09645,     +51.79196,     227.10634,      +51.79201,  3698412.08,  -739404.34,  5250479.97,      54.488338,       -1.830589,  100654.27,  230297.92,    9658.78,            13533.84,     1.55,  60671.14,           59377.17,    -20.49,     -8.46,          19.86,  -0.05,  -1.86
  5,     UK0026,       0,  0.272474, 2459439.579989067279, 227.10702,  51.21837,              324.91757,  24.51268,       324.91160,       24.51637,    227.10702,     +51.21837,     227.11863,      +51.21844,  3697494.08,  -740428.65,  5248522.61,      54.483315,       -1.848753,   98654.72,  229627.80,   12051.10,            15926.16,     6.31,  59409.97,           59382.89,    -24.31,    -10.04,          23.63,  -0.03,  -1.84
  0,     UK002Z,       0,  0.000000, 2459439.579985909630, 244.78097,  59.34334,              321.57804,  37.70379,       321.54854,       37.72070,    244.78097,     +59.34334,     244.83655,      +59.33809,  3703568.84,  -733650.45,  5261475.14,      54.516449,       -1.728652,  111891.12,  180276.42,       0.00,               95.34,   330.95,      0.00,           56479.17,    -88.17,    -21.24,         103.77,  +2.04,  +0.76
  1,     UK002Z,       0,  0.040560, 2459439.579986379016, 244.59638,  58.71119,              321.08632,  37.19757,       321.07639,       37.20324,    244.59638,     +58.71119,     244.61500,      +58.70944,  3702725.53,  -734591.41,  5259677.05,      54.511864,       -1.745318,  110052.97,  179363.58,    2197.66,             2293.00,   123.74,  54182.89,           56479.17,    -29.64,     -7.13,          35.06,  +0.68,  -0.59
  2,     UK002Z,       0,  0.081144, 2459439.579986848868, 244.38321,  58.05798,              320.59893,  36.66149,       320.59352,       36.66457,    244.38321,     +58.05798,     244.39344,      +58.05704,  3701859.64,  -735557.56,  5257830.81,      54.507152,       -1.762432,  108165.82,  178449.58,    4454.16,             4549.50,   -26.05,  55600.85,           56479.17,    -16.10,     -3.87,          19.14,  +0.25,  -1.01
  3,     UK002Z,       0,  0.121784, 2459439.579987319186, 244.10401,  57.35044,              320.10584,  36.05720,       320.07470,       36.07485,    244.10401,     +57.35044,     244.16065,      +57.34515,  3700924.92,  -736600.53,  5255837.79,      54.502059,       -1.780900,  106128.89,  177489.53,    6890.06,             6985.40,     0.23,  59938.43,           56479.17,    -92.59,    -22.30,         110.68,  -0.05,  -1.30
  4,     UK002Z,       0,  0.162416, 2459439.579987789504, 243.90604,  56.63727,              319.58187,  35.47453,       319.56470,       35.48423,    243.90604,     +56.63727,     243.93723,      +56.63439,  3700002.09,  -737630.22,  5253870.16,      54.497025,       -1.799142,  104118.14,  176569.77,    9294.94,             9390.28,    -4.03,  59186.85,           57338.17,    -51.02,    -12.27,          61.30,  -0.37,  -1.60
  5,     UK002Z,       0,  0.203080, 2459439.579988260288, 243.65770,  55.89819,              319.07216,  34.84875,       319.04103,       34.86627,    243.65770,     +55.89819,     243.71303,      +55.89306,  3699049.96,  -738692.60,  5251840.05,      54.491825,       -1.817965,  102043.82,  175650.23,   11776.18,            11871.52,    66.17,  61018.11,           58109.92,    -92.32,    -22.23,         111.51,  -0.54,  -1.76
  6,     UK002Z,       0,  0.243704, 2459439.579988730140, 243.44790,  55.19950,              318.58953,  34.26200,       318.55441,       34.28170,    243.44790,     +55.19950,     243.50955,      +55.19378,  3698161.44,  -739684.00,  5249945.56,      54.486967,       -1.835548,  100108.32,  174820.06,   14091.66,            14187.00,   -27.02,  56997.85,           58266.12,   -104.04,    -25.05,         126.26,  -0.50,  -1.71
  7,     UK002Z,       0,  0.284372, 2459439.579989200924, 243.31667,  54.44165,              318.02895,  33.65878,       318.04006,       33.65257,    243.31667,     +54.44165,     243.29894,      +54.44343,  3697217.40,  -740737.37,  5247932.67,      54.481799,       -1.854227,   98052.12,  173967.22,   16551.84,            16647.18,    21.88,  60494.24,           58517.10,     32.90,      7.90,          40.12,  +0.29,  -0.91
  8,     UK002Z,       0,  0.325044, 2459439.579989671707, 243.06466,  53.69667,              317.55191,  33.01224,       317.53391,       33.02226,    243.06466,     +53.69667,     243.09623,      +53.69382,  3696283.75,  -741779.13,  5245941.97,      54.476683,       -1.872708,   96018.83,  173154.24,   18984.92,            19080.26,    43.45,  59822.00,           58721.28,    -53.23,    -12.80,          65.21,  -0.25,  -1.44
  9,     UK002Z,       0,  0.365640, 2459439.579990141559, 242.92887,  53.02441,              317.08341,  32.46161,       317.08859,       32.45873,    242.92887,     +53.02441,     242.92180,      +53.02522,  3695458.96,  -742699.43,  5244183.34,      54.472158,       -1.889060,   94222.79,  172462.27,   21134.34,            21229.68,  -214.14,  52946.57,           58510.46,     15.32,      3.68,          18.85,  +0.13,  -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.