Orbital Analysis for matched events on 20210813_002621.141_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 65.16° Bg 40.01° Vg 57.96km/s
mass 0.01608g, abs. mag -0.6
Path Details
------------
start 0.74° 50.65° 106.88km
end   0.64° 50.59° 96.77km

Orbit Details
-------------
Semimajor axis 15.71A.U., eccentricity 0.94, inclination 109.90°, Period 62.28Y, LA Sun 140.21°, last Perihelion 2021-07-21

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: 2459439.518300250638
Time: 2021-08-13 00:26:21.182049 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002C and UK002N
 Convergence angle = 17.50732 deg
 R.A. =  46.96767  Dec = +58.82311 deg

Best intersection: Stations UK002C and UK002N with Qconv = 17.51 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3531922.75 +/- 292.39 m
 Y =  -2121670.49 +/- 59.79 m
 Z =   4993428.43 +/- 69.77 m
 Vx =    18964.02 +/- 1268.02 m/s
 Vy =    22265.31 +/- 376.19 m/s
 Vz =    51253.26 +/- 992.16 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+9.415884e+04, +1.774250e+04, +2.119510e+04, +4.038711e+05, +6.030261e+04, +5.037007e+04
+1.774250e+04, +3.929545e+03, +4.133692e+03, +7.948451e+04, +1.549715e+04, +1.101838e+04
+2.119510e+04, +4.133692e+03, +5.356169e+03, +9.219178e+04, +1.358390e+04, +1.084228e+04
+4.038711e+05, +7.948451e+04, +9.219178e+04, +1.795633e+06, +2.981039e+05, +2.440887e+05
+6.030261e+04, +1.549715e+04, +1.358390e+04, +2.981039e+05, +7.796667e+04, +5.525595e+04
+5.037007e+04, +1.101838e+04, +1.084228e+04, +2.440887e+05, +5.525595e+04, +5.060666e+04

Timing offsets (from input data):
    UK002C: -0.000032 s
    UK002N: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 00:26:21.182049 UTC
  Lon     = ++0.749872 +/- 0.0028 deg
  Lat     = +50.658839 +/- 0.0012 deg
  Lat geo = +50.473195 +/- 0.0012 deg
  Ht      =  108382.29 +/- 192.53 m

  JD dynamic   = 2459439.519101459067 
  LST apparent = 329.0062316472 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  49.57798 +/- 1.5576 deg
  Dec       = +60.28945 +/- 0.7626 deg
  Azimuth   =  45.06534 +/- 1.4833 deg
  Elevation = +46.31802 +/- 0.4111 deg
  Vavg      =  56.56820 +/- 0.7395 km/s
  Vinit     =  59.01080 +/- 0.6842 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  49.67343 +/- 1.5576 deg
  Dec       = +60.04010 +/- 0.7626 deg
  Azimuth   =  45.36211 +/- 1.4833 deg
  Elevation = +46.16866 +/- 0.4111 deg
  Vavg      =  56.71567 +/- 0.7395 km/s
  Vinit     =  59.15828 +/- 0.6842 km/s
Radiant (geocentric, J2000):
  R.A.   =  49.89546 +/- 1.5872 deg
  Dec    = +60.03537 +/- 0.7579 deg
  Vg     =  57.95805 +/- 0.6966 km/s
  Vinf   =  59.01080 +/- 0.6842 km/s
  Zc     =  43.81326 +/- 0.4144 deg
  Zg     =  44.22800 +/- 0.4271 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  65.16129 +/- 1.3171 deg
  Bg     = +40.00871 +/- 0.4451 deg
  Vh     =  41.16580 +/- 0.2700 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  89.77108 +/- 4.1041 deg
  Bh     = +64.84570 +/- 0.4651 deg
  Vh_x   =  -0.06991 +/- 1.2760 km/s
  Vh_y   = -17.49769 +/- 0.3238 km/s
  Vh_z   = -37.26190 +/- 0.1295 km/s
Orbit:
  La Sun = 140.206072 +/- 0.0000 deg
  a      =  15.711231 +/- 7.6006 AU
  e      =   0.940384 +/- 0.0230
  i      = 109.900568 +/- 1.3388 deg
  peri   = 147.562714 +/- 2.9365 deg
  node   = 140.205656 +/- 0.0001 deg
  Pi     = 287.768369 +/- 2.9364 deg
  q      =   0.936634 +/- 0.0118 AU
  f      =  32.433534 +/- 2.9365 deg
  M      =   0.357451 +/- 0.2516 deg
  Q      =  30.485827 +/- 15.1922 AU
  n      =   0.015827 +/- 0.0100 deg/day
  T      =  62.275316 +/- 54.3730 years
  Last perihelion JD = 2459416.933675 (2021-07-21 10:24:29.489662) +/- 1.9628 days
  Tj     =  -0.071059 +/- 0.1589
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +5.704439e-04, +2.463667e-04, +4.327914e-02, -3.744667e-08, +1.104475e-03, +5.311256e-04
q   , +2.463667e-04, +1.529822e-04, +2.527847e-02, -2.077375e-08, +6.626992e-04, +2.949810e-04
Tp  , +4.327914e-02, +2.527847e-02, +4.218952e+00, -3.502255e-06, +1.101435e-01, +4.970622e-02
node, -3.744667e-08, -2.077375e-08, -3.502255e-06, +2.983407e-12, -9.108695e-08, -4.229488e-08
peri, +1.104475e-03, +6.626992e-04, +1.101435e-01, -9.108695e-08, +2.880733e-03, +1.292918e-03
i   , +5.311256e-04, +2.949810e-04, +4.970622e-02, -4.229488e-08, +1.292918e-03, +5.996716e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.035628
 a2 = 34.358731

Mean time residuals from time vs. length:
  Station with reference time: UK002N
  Avg. res. = 4.841e-07 s
  Stddev    = 6.96e-04 s

Begin point on the trajectory:
  Lon =     0.735736 +/- 0.0024 deg
  Lat =    50.649871 +/- 0.0010 deg
  Ht  = 106878.90 +/- 165.19 m
End point on the trajectory:
  Lon =     0.639579 +/- 0.0009 deg
  Lat =    50.589383 +/- 0.0004 deg
  Ht  = 96771.55 +/- 51.71 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,   0.000000,   0.000000,   103769.46,    97316.43,          0.010713,     27.68,     30.58,              53.80, 1.0000,    True,    True, {"ff_name": "FF_UK002C_20210813_002611_497_0379904.fits"}
    UK002N,   False,    -0.727590,    51.263100,   57.00,   0.024129,  35.184259,   106878.90,    96771.55,          0.008419,     20.12,     11.98,              52.95, 1.0000,    True,    True, {"ff_name": "FF_UK002N_20210813_002620_377_0388352.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,  0.110257, 2459439.518301526550,  21.89345,   7.72286,              113.51584,  27.13086,       113.50029,       27.11355,     21.89345,      +7.72286,      21.91540,       +7.71675,  3529872.28, -2124077.92,  4987886.71,      50.631300,       +0.706193,  103769.46,  220861.89,       0.00,             6380.50,     0.52,      0.00,           58924.67,     63.32,     57.33,          79.77,  +5.51,  +3.79
  1,     UK002C,       0,  0.150513, 2459439.518301992211,  21.75921,   7.21507,              113.96633,  26.79270,       113.96057,       26.78633,     21.75921,      +7.21507,      21.76778,       +7.21281,  3529097.84, -2124987.17,  4985793.67,      50.620884,       +0.689636,  102028.01,  219532.22,    2409.83,             8790.34,    34.82,  59862.65,           58924.67,     23.28,     21.07,          29.50,  +2.26,  +0.55
  2,     UK002C,       0,  0.190765, 2459439.518302458338,  21.62539,   6.71657,              114.40807,  26.46073,       114.41042,       26.46331,     21.62539,      +6.71657,      21.62296,       +6.71749,  3528345.67, -2125870.27,  4983760.82,      50.610760,       +0.673548,  100337.02,  218258.32,    4750.37,            11130.87,     0.05,  58147.12,           58924.67,     -9.41,     -8.51,          11.99,  +1.95,  +0.26
  3,     UK002C,       0,  0.231013, 2459439.518302924000,  21.47366,   6.20879,              114.86967,  26.13010,       114.86970,       26.13013,     21.47366,      +6.20879,      21.47459,       +6.20880,  3527582.25, -2126766.60,  4981697.54,      50.600478,       +0.657221,   98621.12,  216983.80,    7125.94,            13506.44,     0.55,  59023.32,           58924.67,     -0.12,     -0.11,           0.15,  +3.51,  +1.83
  4,     UK002C,       0,  0.271201, 2459439.518303389195,  21.35714,   5.81857,              115.22272,  25.87513,       115.22120,       25.87347,     21.35714,      +5.81857,      21.36035,       +5.81798,  3527001.67, -2127448.24,  4980128.43,      50.592652,       +0.644763,   97316.43,  216024.79,    8932.54,            15313.05,  -564.37,  44953.83,           56118.89,      6.01,      5.44,           7.74,  +5.38,  +3.71
  0,     UK002N,       1,  0.000000, 2459439.518300250638,   9.14981,  14.52725,              122.36612,  40.42741,       122.35602,       40.41583,      9.14981,     +14.52725,       9.16299,      +14.52175,  3531916.62, -2121677.69,  4993411.87,      50.658757,       +0.749911,  108368.51,  165181.70,       0.00,               19.06,   145.46,      0.00,           58379.83,     20.48,     34.42,          50.02,  +5.63,  +4.54
  1,     UK002N,       0,  0.040376, 2459439.518300718162,   8.91580,  13.98752,              122.99997,  40.09757,       122.99571,       40.09275,      8.91580,     +13.98752,       8.92147,      +13.98523,  3531254.61, -2122454.95,  4991622.67,      50.649871,       +0.735736,  106878.90,  163981.53,    2060.01,             2079.07,  -177.15,  51020.62,           58379.83,      8.51,     14.31,          20.94,  +3.02,  +1.95
  2,     UK002N,       0,  0.080840, 2459439.518301186152,   8.63243,  13.32981,              123.76352,  39.69110,       123.76613,       39.69402,      8.63243,     +13.32981,       8.62942,      +13.33121,  3530460.94, -2123386.77,  4989477.67,      50.639211,       +0.718773,  105093.45,  162567.10,    4529.68,             4548.74,   -95.30,  61033.75,           58379.83,     -5.15,     -8.65,          12.78,  +1.74,  +0.68
  3,     UK002N,       0,  0.121316, 2459439.518301654607,   8.34068,  12.64730,              124.54542,  39.26401,       124.55555,       39.27520,      8.34068,     +12.64730,       8.32830,      +12.65266,  3529652.15, -2124336.36,  4987291.79,      50.628340,       +0.701489,  103274.43,  161152.20,    7046.40,             7065.47,    32.91,  62178.21,           58379.83,    -19.67,    -33.03,          49.21,  +1.20,  +0.16
  4,     UK002N,       0,  0.161752, 2459439.518302122597,   8.04285,  12.01589,              125.29150,  38.87951,       125.28915,       38.87693,      8.04285,     +12.01589,       8.04649,      +12.01465,  3528904.61, -2125214.04,  4985271.43,      50.618284,       +0.685499,  101593.55,  159868.12,    9372.56,             9391.62,   -27.10,  57526.78,           58677.66,      4.50,      7.57,          11.37,  +1.08,  +0.06
  5,     UK002N,       0,  0.202216, 2459439.518302591052,   7.74592,  11.35047,              126.05223,  38.46170,       126.04683,       38.45586,      7.74592,     +11.35047,       7.75354,      +11.34766,  3528135.97, -2126116.47,  4983194.08,      50.607937,       +0.669062,   99865.65,  158572.94,   11764.33,            11783.39,   -23.14,  59108.67,           58824.34,     10.20,     17.15,          25.96,  +1.01,  +0.01
  6,     UK002N,       0,  0.242684, 2459439.518303059507,   7.47843,  10.69505,              126.76739,  38.03382,       126.77505,       38.04200,      7.47843,     +10.69505,       7.46992,      +10.69901,  3527400.51, -2126979.97,  4981206.37,      50.598029,       +0.653325,   98212.69,  157357.53,   14052.90,            14071.96,  -122.62,  56552.55,           58633.18,    -14.27,    -23.99,          36.59,  +1.24,  +0.26
  7,     UK002N,       0,  0.283084, 2459439.518303527031,   7.22768,  10.12121,              127.40534,  37.66455,       127.41281,       37.67246,      7.22768,     +10.12121,       7.21961,      +10.12506,  3526759.16, -2127732.97,  4979473.02,      50.589383,       +0.639579,   96771.55,  156316.49,   16048.59,            16067.66,  -510.96,  49398.40,           57785.02,    -13.79,    -23.17,          35.58,  +2.60,  +1.63

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.