Orbital Analysis for matched events on 20210813_011556.518_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 65.13° Bg 39.13° Vg 56.03km/s
mass 0.00618g, abs. mag 0.9
Path Details
------------
start 1.30° 53.25° 111.36km
end   1.20° 53.21° 99.80km

Orbit Details
-------------
Semimajor axis 3.96A.U., eccentricity 0.77, inclination 109.62°, Period 7.87Y, LA Sun 140.24°, last Perihelion 2021-07-17

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: 2459439.552737481426
Time: 2021-08-13 01:15:56.518395 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002K and UK0032
 Convergence angle = 10.88610 deg
 R.A. =  55.09875  Dec = +62.93095 deg

Best intersection: Stations UK002K and UK0032 with Qconv = 10.89 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3700166.42 +/- 526.75 m
 Y =  -1202958.45 +/- 461.03 m
 Z =   5176624.47 +/- 767.67 m
 Vx =    18610.36 +/- 2170.46 m/s
 Vy =    22331.45 +/- 1555.17 m/s
 Vz =    49164.14 +/- 3104.24 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+3.734309e+05, +3.202459e+05, +5.135679e+05, +6.975103e+05, +4.162063e+05, +3.042802e+05
+3.202459e+05, +2.756321e+05, +4.434898e+05, +6.067942e+05, +3.661976e+05, +2.765928e+05
+5.135679e+05, +4.434898e+05, +7.195348e+05, +1.009964e+06, +6.163524e+05, +5.035533e+05
+6.975103e+05, +6.067942e+05, +1.009964e+06, +2.411049e+06, +1.677372e+06, +2.037515e+06
+4.162063e+05, +3.661976e+05, +6.163524e+05, +1.677372e+06, +1.250184e+06, +1.693250e+06
+3.042802e+05, +2.765928e+05, +5.035533e+05, +2.037515e+06, +1.693250e+06, +2.780666e+06

Timing offsets (from input data):
    UK002K: 0.007503 s
    UK0032: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 01:15:56.518395 UTC
  Lon     = ++1.302639 +/- 0.0089 deg
  Lat     = +53.252611 +/- 0.0016 deg
  Lat geo = +53.071115 +/- 0.0016 deg
  Ht      =  111291.99 +/- 828.14 m

  JD dynamic   = 2459439.553538222332 
  LST apparent = 341.9901753860 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  50.19319 +/- 1.4687 deg
  Dec       = +59.40521 +/- 1.2458 deg
  Azimuth   =  52.42776 +/- 2.3626 deg
  Elevation = +53.39856 +/- 0.2584 deg
  Vavg      =  57.29026 +/- 3.4416 km/s
  Vinit     =  57.11525 +/- 2.8994 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  50.39897 +/- 1.4687 deg
  Dec       = +59.17810 +/- 1.2458 deg
  Azimuth   =  52.71691 +/- 2.3626 deg
  Elevation = +53.21753 +/- 0.2584 deg
  Vavg      =  57.42489 +/- 3.4416 km/s
  Vinit     =  57.24987 +/- 2.8994 km/s
Radiant (geocentric, J2000):
  R.A.   =  50.42775 +/- 1.5660 deg
  Dec    = +59.19580 +/- 1.2379 deg
  Vg     =  56.02723 +/- 2.9595 km/s
  Vinf   =  57.11525 +/- 2.8994 km/s
  Zc     =  36.71236 +/- 0.2634 deg
  Zg     =  37.07799 +/- 0.3015 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  65.13088 +/- 1.4643 deg
  Bg     = +39.12734 +/- 0.9325 deg
  Vh     =  39.07433 +/- 2.0022 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  90.98672 +/- 8.6139 deg
  Bh     = +64.80234 +/- 1.7186 deg
  Vh_x   =   0.28648 +/- 2.0242 km/s
  Vh_y   = -16.63313 +/- 2.1613 km/s
  Vh_z   = -35.35619 +/- 1.3755 km/s
Orbit:
  La Sun = 140.239138 +/- -0.0000 deg
  a      =   3.955089 +/- 23.6085 AU
  e      =   0.766648 +/- 0.1497
  i      = 109.619006 +/- 3.8558 deg
  peri   = 142.617825 +/- 8.3732 deg
  node   = 140.239073 +/- 0.0003 deg
  Pi     = 282.856898 +/- 8.3730 deg
  q      =   0.922927 +/- 0.0286 AU
  f      =  37.378508 +/- 8.3733 deg
  M      =   3.377935 +/- nan deg
  Q      =   6.987252 +/- 47.2203 AU
  n      =   0.125305 +/- 0.1311 deg/day
  T      =   7.865658 +/- 253395486.0395 years
  Last perihelion JD = 2459412.595914 (2021-07-17 02:18:06.966759) +/- 6.3032 days
  Tj     =   0.939966 +/- 0.9914
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.568014e-02, +2.251592e-03, +5.776990e-01, -3.434182e-07, +1.243676e-02, +5.216868e-03
q   , +2.251592e-03, +4.568946e-04, +1.028993e-01, -7.067462e-08, +2.333676e-03, +1.078883e-03
Tp  , +5.776990e-01, +1.028993e-01, +2.433494e+01, -1.575344e-05, +5.413606e-01, +2.402810e-01
node, -3.434182e-07, -7.067462e-08, -1.575344e-05, +1.128433e-11, -3.581806e-07, -1.718157e-07
peri, +1.243676e-02, +2.333676e-03, +5.413606e-01, -3.581806e-07, +1.213675e-02, +5.466309e-03
i   , +5.216868e-03, +1.078883e-03, +2.402810e-01, -1.718157e-07, +5.466309e-03, +2.617271e-03

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 102.236423
 a2 = 0.000001

Mean time residuals from time vs. length:
  Station with reference time: UK0032
  Avg. res. = 2.877e-06 s
  Stddev    = 1.70e-03 s

Begin point on the trajectory:
  Lon =     1.303259 +/- 0.0089 deg
  Lat =    53.252896 +/- 0.0015 deg
  Ht  = 111363.46 +/- 835.28 m
End point on the trajectory:
  Lon =     1.201880 +/- 0.0052 deg
  Lat =    53.206495 +/- 0.0008 deg
  Ht  = 99797.62 +/- 481.09 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
    UK002K,   False,    -0.382860,    53.537770,   34.00,   0.000000,   0.000000,   109017.04,   100174.18,          0.006551,     11.87,     13.39,              37.71, 1.0000,    True,    True, {"ff_name": "FF_UK002K_20210813_011555_002_0450048.fits"}
    UK0032,   False,    -0.023645,    52.984073,    6.00, 239.900166,   0.000000,   111363.46,    99797.62,          0.034638,     38.12,     76.35,              13.83, 1.0000,    True,    True, {"ff_name": "FF_UK0032_20210813_011551_223_0455936.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,     UK002K,       0,  0.027954, 2459439.552737731487,  31.83123,  25.14040,              105.79520,  42.56218,       105.79483,       42.56180,     31.83123,     +25.14040,      31.83183,      +25.14028,  3699243.00, -1204066.51,  5174185.01,      53.243507,       +1.282824,  109017.04,  159552.05,       0.00,             2833.99,   364.31,      0.00,           56390.41,      0.99,      0.88,           1.71,  +3.15,  +2.14
  1,     UK002K,       0,  0.068186, 2459439.552738197148,  31.69842,  24.76185,              106.24519,  42.34407,       106.23585,       42.33439,     31.69842,     +24.76185,      31.71129,      +24.75866,  3698643.36, -1204786.05,  5172600.89,      53.237589,       +1.269844,  107539.98,  158070.19,    1840.31,             4674.29,   -93.24,  45742.36,           56390.41,     24.54,     21.76,          42.80,  +2.37,  +1.38
  2,     UK002K,       0,  0.108522, 2459439.552738663740,  31.54219,  24.23472,              106.84015,  42.02203,       106.83632,       42.01810,     31.54219,     +24.23472,      31.54774,      +24.23343,  3697836.90, -1205753.76,  5170470.42,      53.229625,       +1.252442,  105553.76,  156092.18,    4315.34,             7149.33,    77.99,  61360.33,           56390.41,      9.88,      8.76,          17.44,  +1.97,  +1.00
  3,     UK002K,       0,  0.148850, 2459439.552739130799,  31.37337,  23.70600,              107.44364,  41.70370,       107.43603,       41.69596,     31.37337,     +23.70600,      31.38407,      +23.70345,  3697043.50, -1206705.78,  5168374.47,      53.221783,       +1.235315,  103600.05,  154160.26,    6750.26,             9584.25,   209.56,  60377.90,           56390.41,     19.33,     17.14,          34.57,  +1.77,  +0.83
  4,     UK002K,       0,  0.189122, 2459439.552739596926,  31.25373,  23.28313,              107.90800,  41.43880,       107.90798,       41.43877,     31.25373,     +23.28313,      31.25452,      +23.28313,  3696427.82, -1207444.57,  5166747.97,      53.215692,       +1.221983,  102084.13,  152669.30,    8639.80,            11473.79,  -201.04,  46919.46,           55062.09,      0.06,      0.06,           0.11,  +2.32,  +1.40
  5,     UK002K,       0,  0.229462, 2459439.552740063518,  31.08821,  22.74131,              108.51026,  41.10430,       108.50991,       41.10395,     31.08821,     +22.74131,      31.08960,      +22.74120,  3695651.99, -1208375.53,  5164698.41,      53.208011,       +1.205225,  100174.18,  150805.51,   11020.82,            13854.81,  -124.05,  59023.93,           55249.04,      0.86,      0.76,           1.57,  +4.42,  +3.53
  0,     UK0032,       0,  0.000000, 2459439.552737481426,  45.95157,  47.18634,               70.81824,  49.18137,        70.85849,       49.24275,     45.95157,     +47.18634,      45.85481,      +47.19794,  3700195.43, -1202923.64,  5176701.11,      53.252896,       +1.303259,  111363.46,  146083.95,       0.00,               89.03,  -784.03,      0.00,           66001.98,   -152.43,    -75.81,         240.37,  +4.87,  +4.05
  1,     UK0032,       0,  0.040084, 2459439.552737945225,  45.81517,  46.97355,               71.16822,  49.14221,        71.17778,       49.15681,     45.81517,     +46.97355,      45.79242,      +46.97635,  3699333.15, -1203958.33,  5174423.16,      53.244396,       +1.284673,  109239.11,  143494.23,    2646.35,             2557.32,  -605.15,  66020.11,           66001.98,    -35.54,    -17.87,          57.18,  +2.26,  +1.48
  2,     UK0032,       0,  0.080204, 2459439.552738409489,  45.70972,  46.72740,               71.54258,  49.06658,        71.53719,       49.05841,     45.70972,     +46.72740,      45.72283,      +46.72582,  3698395.44, -1205083.54,  5171945.95,      53.235142,       +1.264470,  106929.35,  140681.19,    5524.19,             5435.16,   -18.77,  71730.86,           66001.98,     19.51,      9.86,          32.05,  +2.45,  +1.71
  3,     UK0032,       0,  0.120332, 2459439.552738874219,  45.68800,  46.51204,               71.82844,  48.95956,        71.83887,       48.97518,     45.68800,     +46.51204,      45.66409,      +46.51503,  3697632.52, -1205998.99,  5169930.51,      53.227606,       +1.247998,  105050.47,  138393.33,    7865.57,             7776.55,    30.69,  58347.83,           66001.98,    -36.81,    -18.52,          61.42,  +1.80,  +1.09
  4,     UK0032,       0,  0.160452, 2459439.552739338484,  45.64316,  46.29850,               72.12441,  48.86621,        72.14103,       48.89083,     45.64316,     +46.29850,      45.60544,      +46.30319,  3696890.27, -1206889.66,  5167969.65,      53.220267,       +1.231964,  103222.73,  136169.14,   10143.56,            10054.53,    17.22,  56779.34,           63582.39,    -57.20,    -28.74,          96.97,  +2.28,  +1.61
  5,     UK0032,       0,  0.200584, 2459439.552739803214,  45.61443,  46.07864,               72.41789,  48.75951,        72.44827,       48.80398,     45.61443,     +46.07864,      45.54601,      +46.08705,  3696157.04, -1207769.49,  5166032.65,      53.213012,       +1.216119,  101417.50,  133973.88,   12393.82,            12304.80,   -24.67,  56071.53,           61817.78,   -101.97,    -51.06,         175.57,  +2.73,  +2.09
  6,     UK0032,       0,  0.240668, 2459439.552740267012,  45.51077,  45.88470,               72.72242,  48.70990,        72.73154,       48.72322,     45.51077,     +45.88470,      45.49110,      +45.88724,  3695499.02, -1208559.09,  5164294.29,      53.206495,       +1.201880,   99797.62,  132004.75,   14413.31,            14324.29,  -294.59,  50381.45,           59963.56,    -30.07,    -15.16,          52.61,  +4.32,  +3.72

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.