Orbital Analysis for matched events on 20210810_214135.511_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 60.41° Bg 39.82° Vg 61.76km/s
mass 0.01159g, abs. mag 0.3
Path Details
------------
start -1.12° 51.90° 112.16km
end   -1.28° 51.75° 99.56km

Orbit Details
-------------
Semimajor axis -4.52A.U., eccentricity 1.21, inclination 113.21°, Period 1000000000.00Y, LA Sun 138.18°, 

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: 2459437.403883237857
Time: 2021-08-10 21:41:35.551461 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0027 and UK9989
 Convergence angle = 87.75583 deg
 R.A. =  44.29987  Dec = +58.73959 deg

Best intersection: Stations UK0027 and UK9989 with Qconv = 87.76 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =    962024.61 +/- 446.63 m
 Y =  -3895225.46 +/- 30.21 m
 Z =   5086197.31 +/- 610.44 m
 Vx =    23547.08 +/- 1473.99 m/s
 Vy =    22068.25 +/- 1637.62 m/s
 Vz =    53808.05 +/- 2007.92 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+9.511458e+04, +1.658602e+03, +1.317473e+05, +2.715483e+05, -6.539373e+03, +3.819755e+05
+1.658602e+03, +8.272506e+02, +2.007236e+03, +4.864948e+03, +7.857545e+02, +4.467569e+03
+1.317473e+05, +2.007236e+03, +1.826737e+05, +3.763044e+05, -9.403842e+03, +5.304125e+05
+2.715483e+05, +4.864948e+03, +3.763044e+05, +7.972072e+05, -1.174567e+04, +1.136570e+06
-6.539373e+03, +7.857545e+02, -9.403842e+03, -1.174567e+04, +5.893887e+03, -1.198941e+04
+3.819755e+05, +4.467569e+03, +5.304125e+05, +1.136570e+06, -1.198941e+04, +1.642245e+06

Timing offsets (from input data):
    UK0027: 0.000000 s
    UK9989: 0.000169 s

Reference point on the trajectory:
  Time: 2021-08-10 21:41:35.551461 UTC
  Lon     = +-1.109197 +/- 0.0062 deg
  Lat     = +51.915452 +/- 0.0025 deg
  Lat geo = +51.731729 +/- 0.0026 deg
  Ht      =  113268.34 +/- 551.96 m

  JD dynamic   = 2459437.404684438370 
  LST apparent = 283.8730212700 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  43.14314 +/- 1.8653 deg
  Dec       = +59.04641 +/- 0.2018 deg
  Azimuth   =  31.68414 +/- 0.7668 deg
  Elevation = +31.32480 +/- 0.7395 deg
  Vavg      =  61.17948 +/- 0.9570 km/s
  Vinit     =  62.74376 +/- 2.2077 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  42.89117 +/- 1.8653 deg
  Dec       = +58.84671 +/- 0.2018 deg
  Azimuth   =  31.94952 +/- 0.7668 deg
  Elevation = +31.25172 +/- 0.7395 deg
  Vavg      =  61.31130 +/- 0.9570 km/s
  Vinit     =  62.87557 +/- 2.2077 km/s
Radiant (geocentric, J2000):
  R.A.   =  43.35292 +/- 1.9007 deg
  Dec    = +58.55997 +/- 0.2485 deg
  Vg     =  61.75536 +/- 2.2480 km/s
  Vinf   =  62.74376 +/- 2.2077 km/s
  Zc     =  58.83159 +/- 0.7408 deg
  Zg     =  59.34453 +/- 0.7955 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  60.40871 +/- 1.0981 deg
  Bg     = +39.81919 +/- 0.5784 deg
  Vh     =  44.12341 +/- 2.0889 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  78.08504 +/- 4.2771 deg
  Bh     = +63.67354 +/- 0.1617 deg
  Vh_x   =  -4.04002 +/- 1.4069 km/s
  Vh_y   = -19.14649 +/- 0.8285 km/s
  Vh_z   = -39.54700 +/- 1.8620 km/s
Orbit:
  La Sun = 138.176418 +/- nan deg
  a      =  -4.516622 +/- 17.8908 AU
  e      =   1.214411 +/- 0.1758
  i      = 113.214507 +/- 1.1303 deg
  peri   = 156.735298 +/- 7.2673 deg
  node   = 138.174561 +/- 0.0001 deg
  Pi     = 294.909860 +/- 7.2672 deg
  q      =   0.968412 +/- 0.0245 AU
  f      =  23.260492 +/- 7.2673 deg
  M      =        nan +/- nan deg
  Q      = -10.001656 +/- 35.7894 AU
  n      =   0.102680 +/- 0.0832 deg/day
  T      = 1000000000.000000 +/- 498887636.2040 years
  Last perihelion JD = NaN 
  Tj     =  -1.658303 +/- 1.0423
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.072058e-02, +1.944721e-03, +4.392598e-01, -1.034869e-07, +9.863672e-03, +1.343733e-03
q   , +1.944721e-03, +3.753580e-04, +8.355995e-02, -1.923744e-08, +1.887526e-03, +2.501112e-04
Tp  , +4.392598e-01, +8.355995e-02, +1.866490e+01, -4.319650e-06, +4.210348e-01, +5.614455e-02
node, -1.034869e-07, -1.923744e-08, -4.319650e-06, +1.022968e-12, -9.723629e-08, -1.328679e-08
peri, +9.863672e-03, +1.887526e-03, +4.210348e-01, -9.723629e-08, +9.502920e-03, +1.263978e-03
i   , +1.343733e-03, +2.501112e-04, +5.614455e-02, -1.328679e-08, +1.263978e-03, +1.725803e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.114059
 a2 = 18.506579

Mean time residuals from time vs. length:
  Station with reference time: UK0027
  Avg. res. = 3.212e-06 s
  Stddev    = 1.79e-03 s

Begin point on the trajectory:
  Lon =    -1.122916 +/- 0.0055 deg
  Lat =    51.901702 +/- 0.0023 deg
  Ht  = 112155.23 +/- 494.36 m
End point on the trajectory:
  Lon =    -1.279951 +/- 0.0016 deg
  Lat =    51.745275 +/- 0.0005 deg
  Ht  = 99563.15 +/- 154.23 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
    UK0027,   False,    -2.374601,    51.371449,   48.00,   0.000000,   0.000000,   112155.23,    99563.15,          0.011036,     25.13,     11.74,              25.45, 1.0000,    True,    True, {"ff_name": "FF_UK0027_20210810_214133_678_0122368.fits"}
    UK9989,   False,    -1.019700,    50.938801,  158.00,   0.027576,  22.287711,   103753.35,   100591.26,          0.030735,     35.99,     65.71,              31.13, 1.0000,   False,   False, {"ff_name": "FF_UK9989_20210810_214137_840_0000000.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,     UK0027,       1,  0.000000, 2459437.403883237857, 359.03877,  54.28818,               54.82534,  46.03894,        54.84408,       46.01784,    359.03877,     +54.28818,     359.05818,      +54.26656,   962063.97, -3895188.57,  5086287.27,      51.916125,       -1.108359,  113322.88,  156163.63,       0.00,              104.89,   707.32,      0.00,           58616.93,    -28.61,     61.19,          89.22,  +5.01,  +4.04
  1,     UK0027,       0,  0.039740, 2459437.403883697465, 358.54316,  54.10595,               55.25809,  46.20415,        55.26234,       46.19932,    358.54316,     +54.10595,     358.54676,      +54.10104,   961220.91, -3895978.68,  5084360.76,      51.901702,       -1.122916,  112155.23,  154111.27,    2246.43,             2141.54,   250.53,  56528.26,           58616.93,     -6.43,     13.78,          20.36,  +1.98,  +1.04
  2,     UK0027,       0,  0.079452, 2459437.403884157073, 358.00545,  53.91922,               55.71575,  46.39048,        55.71427,       46.39218,    358.00545,     +53.91922,     358.00274,      +53.92093,   960340.73, -3896803.59,  5082349.43,      51.886637,       -1.138102,  110936.77,  151974.85,    4591.77,             4486.88,   104.19,  59058.71,           58616.93,      2.23,     -4.77,           7.15,  +1.24,  +0.33
  3,     UK0027,       0,  0.119156, 2459437.403884616680, 357.44991,  53.71887,               56.20023,  46.58131,        56.19091,       46.59213,    357.44991,     +53.71887,     357.43823,      +53.72969,   959444.93, -3897643.13,  5080302.41,      51.871296,       -1.153551,  109697.31,  149807.21,    6978.73,             6873.84,    -0.02,  60118.89,           58616.93,     13.89,    -29.81,          45.28,  +1.11,  +0.23
  4,     UK0027,       0,  0.158824, 2459437.403885075822, 356.83895,  53.50310,               56.72991,  46.79560,        56.71838,       46.80913,    356.83895,     +53.50310,     356.82465,      +53.51651,   958490.54, -3898537.57,  5078121.53,      51.854943,       -1.169994,  108377.48,  147505.88,    9521.79,             9416.90,    54.11,  64108.48,           59878.75,     17.04,    -36.55,          56.40,  +1.13,  +0.29
  5,     UK0027,       0,  0.198500, 2459437.403885534965, 356.23661,  53.33082,               57.20278,  47.02841,        57.21748,       47.01102,    356.23661,     +53.33082,     356.25366,      +53.31371,   957620.22, -3899353.23,  5076132.74,      51.840023,       -1.184999,  107174.52,  145413.83,   11840.86,            11735.96,  -116.24,  58450.13,           60035.64,    -21.59,     46.13,          72.25,  +1.14,  +0.33
  6,     UK0027,       0,  0.238156, 2459437.403885994107, 355.61418,  53.08922,               57.77621,  47.24089,        57.78161,       47.23442,    355.61418,     +53.08922,     355.62040,      +53.08292,   956673.68, -3900240.33,  5073969.77,      51.823788,       -1.201298,  105866.89,  143147.26,   14363.02,            14258.13,   -82.25,  63601.05,           60473.26,     -7.87,     16.84,          26.78,  +0.89,  +0.11
  7,     UK0027,       0,  0.277784, 2459437.403886452783, 354.94256,  52.81701,               58.41375,  47.46734,        58.40647,       47.47621,    354.94256,     +52.81701,     354.93333,      +52.82555,   955668.10, -3901182.75,  5071671.90,      51.806530,       -1.218598,  104478.48,  140749.49,   17042.48,            16937.59,   110.81,  67615.47,           61249.79,     10.54,    -22.58,          36.52,  +0.50,  -0.24
  8,     UK0027,       0,  0.317428, 2459437.403886911459, 354.30686,  52.56908,               59.00832,  47.68880,        58.99873,       47.70065,    354.30686,     +52.56908,     354.29471,      +52.58038,   954753.06, -3902040.33,  5069580.91,      51.790818,       -1.234350,  103215.74,  138576.11,   19480.72,            19375.83,    61.63,  61503.22,           61629.27,     13.81,    -29.57,          48.57,  +0.45,  -0.26
  9,     UK0027,       0,  0.357080, 2459437.403887370601, 353.69474,  52.33394,               59.57963,  47.90598,        59.57325,       47.91395,    353.69474,     +52.33394,     353.68671,      +52.34147,   953898.69, -3902841.04,  5067628.57,      51.776140,       -1.249064,  102037.33,  136554.62,   21757.27,            21652.38,  -149.73,  57413.31,           61592.79,      9.12,    -19.52,          32.54,  +0.35,  -0.33
 10,     UK0027,       0,  0.396704, 2459437.403887829278, 353.03184,  52.07378,               60.20955,  48.14100,        60.20737,       48.14376,    353.03184,     +52.07378,     353.02930,      +52.07637,   952992.13, -3903690.67,  5065556.96,      51.760557,       -1.264663,  100787.55,  134419.15,   24172.92,            24068.02,  -220.25,  60964.18,           61544.35,      3.11,     -6.64,          11.25,  +0.42,  -0.22
 11,     UK0027,       0,  0.436320, 2459437.403888287488, 352.36435,  51.81130,               60.84883,  48.37990,        60.85442,       48.37269,    352.36435,     +51.81130,     352.37227,      +51.80462,   952103.52, -3904523.47,  5063526.38,      51.745275,       -1.279951,   99563.15,  132335.39,   26540.70,            26435.81,  -338.12,  59768.36,           61448.19,     -7.94,     16.95,          29.18,  +1.23,  +0.62
  0,     UK9989,       0,  0.301862, 2459437.403886964545, 157.80851,  82.68657,              351.44613,  46.28870,       351.45862,       46.32650,    157.80851,     +82.68657,     157.98210,      +82.71846,   955142.70, -3901675.16,  5070471.29,      51.797509,       -1.227732,  103753.35,  142202.15,       0.00,            18337.58,     0.02,      0.00,           63317.31,    -84.40,    -46.25,         139.60,  +1.70,  +0.94
  1,     UK9989,       0,  0.321862, 2459437.403887195978, 159.66802,  82.54042,              351.05761,  46.36950,       351.06345,       46.38752,    159.66802,     +82.54042,     159.75264,      +82.55527,   954690.95, -3902098.54,  5069438.97,      51.789751,       -1.235510,  103130.05,  141213.35,    1203.76,            19541.33,   -51.10,  60187.75,           63317.31,    -39.92,    -21.85,          66.47,  +1.72,  +0.97
  2,     UK9989,       0,  0.341862, 2459437.403887427412, 161.50134,  82.37581,              350.64994,  46.44675,       350.65086,       46.44965,    161.50134,     +82.37581,     161.51532,      +82.37814,   954226.84, -3902533.50,  5068378.44,      51.781778,       -1.243497,  102489.87,  140201.07,    2440.41,            20777.99,   -69.32,  61832.69,           63317.31,     -6.36,     -3.48,          10.67,  +1.26,  +0.53
  3,     UK9989,       0,  0.361862, 2459437.403887658846, 163.15819,  82.13222,              350.17126,  46.46788,       350.18653,       46.51771,    163.15819,     +82.13222,     163.39825,      +82.17124,   953713.25, -3903014.84,  5067204.81,      51.772953,       -1.252325,  101781.64,  139085.04,    3808.94,            22146.52,    44.34,  68426.36,           63317.31,   -108.40,    -59.47,         183.36,  +1.19,  +0.47
  4,     UK9989,       0,  0.381862, 2459437.403887890279, 164.67100,  82.03302,              349.87238,  46.57258,       349.86940,       46.56276,    164.67100,     +82.03302,     164.62359,      +82.02548,   953369.09, -3903337.38,  5066418.36,      51.767037,       -1.258268,  101307.14,  138339.97,    4725.99,            23063.57,  -293.48,  45852.80,           60285.83,     21.26,     11.62,          36.13,  +1.25,  +0.55
  5,     UK9989,       0,  0.401862, 2459437.403888122179, 166.56882,  81.82141,              349.39475,  46.66293,       349.38507,       46.63014,    166.56882,     +81.82141,     166.40885,      +81.79697,   952849.70, -3903824.15,  5065231.49,      51.758108,       -1.267193,  100591.26,  137219.23,    6109.95,            24447.53,  -164.40,  69198.04,           60692.86,     70.35,     38.37,         120.45,  +1.61,  +0.92

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.