Orbital Analysis for matched events on 20210813_013133.449_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 59.00° Bg 38.86° Vg 58.58km/s
mass 0.01333g, abs. mag -0.3
Path Details
------------
start -3.86° 51.78° 112.06km
end   -4.03° 51.71° 90.93km

Orbit Details
-------------
Semimajor axis 8.01A.U., eccentricity 0.88, inclination 113.11°, Period 22.69Y, LA Sun 140.25°, last Perihelion 2021-07-29

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: 2459439.563581596594
Time: 2021-08-13 01:31:33.449946 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0024 and UK002H
 Convergence angle = 86.33314 deg
 R.A. =  42.48266  Dec = +57.31704 deg

Best intersection: Stations UK0024 and UK002H with Qconv = 86.33 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3798576.68 +/- 133.35 m
 Y =  -1326763.71 +/- 121.13 m
 Z =   5075730.82 +/- 44.22 m
 Vx =    23852.58 +/- 444.20 m/s
 Vy =    21461.18 +/- 378.22 m/s
 Vz =    50247.57 +/- 118.40 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.959437e+04, -1.646454e+04, -2.985814e+03, +5.784952e+04, -5.210467e+04, -1.316607e+04
-1.646454e+04, +1.638169e+04, +3.844559e+03, -4.994156e+04, +5.003806e+04, +9.500363e+03
-2.985814e+03, +3.844559e+03, +2.151324e+03, -9.927934e+03, +1.034239e+04, +1.704873e+03
+5.784952e+04, -4.994156e+04, -9.927934e+03, +1.788510e+05, -1.601058e+05, -4.179924e+04
-5.210467e+04, +5.003806e+04, +1.034239e+04, -1.601058e+05, +1.605239e+05, +3.109208e+04
-1.316607e+04, +9.500363e+03, +1.704873e+03, -4.179924e+04, +3.109208e+04, +1.219199e+04

Timing offsets (from input data):
    UK0024: -0.000104 s
    UK002H: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 01:31:33.449946 UTC
  Lon     = +-3.855351 +/- 0.0011 deg
  Lat     = +51.779521 +/- 0.0013 deg
  Lat geo = +51.595553 +/- 0.0013 deg
  Ht      =  112044.53 +/- 88.14 m

  JD dynamic   = 2459439.564382337499 
  LST apparent = 340.7467554013 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  41.97907 +/- 0.9691 deg
  Dec       = +57.43919 +/- 0.1268 deg
  Azimuth   =  56.02145 +/- 0.4300 deg
  Elevation = +55.32552 +/- 0.4725 deg
  Vavg      =  58.06425 +/- 0.0302 km/s
  Vinit     =  59.61834 +/- 0.0564 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  42.22921 +/- 0.9691 deg
  Dec       = +57.23110 +/- 0.1268 deg
  Azimuth   =  56.29648 +/- 0.4300 deg
  Elevation = +55.13336 +/- 0.4725 deg
  Vavg      =  58.20323 +/- 0.0302 km/s
  Vinit     =  59.75732 +/- 0.0564 km/s
Radiant (geocentric, J2000):
  R.A.   =  42.13525 +/- 0.9728 deg
  Dec    = +57.25489 +/- 0.1262 deg
  Vg     =  58.57704 +/- 0.0574 km/s
  Vinf   =  59.61834 +/- 0.0564 km/s
  Zc     =  34.77759 +/- 0.4735 deg
  Zg     =  35.09374 +/- 0.4775 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  58.99697 +/- 0.6577 deg
  Bg     = +38.85510 +/- 0.1665 deg
  Vh     =  40.50203 +/- 0.0735 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  73.15034 +/- 1.5559 deg
  Bh     = +65.13962 +/- 0.3969 deg
  Vh_x   =  -4.93559 +/- 0.3957 km/s
  Vh_y   = -16.29639 +/- 0.3757 km/s
  Vh_z   = -36.74890 +/- 0.1085 km/s
Orbit:
  La Sun = 140.249551 +/- 0.0000 deg
  a      =   8.014482 +/- 0.4896 AU
  e      =   0.877194 +/- 0.0070
  i      = 113.113884 +/- 0.1648 deg
  peri   = 159.839729 +/- 1.5564 deg
  node   = 140.249229 +/- 0.0000 deg
  Pi     = 300.088958 +/- 1.5564 deg
  q      =   0.984223 +/- 0.0051 AU
  f      =  20.156533 +/- 1.5564 deg
  M      =   0.645575 +/- 0.0438 deg
  Q      =  15.044740 +/- 0.9827 AU
  n      =   0.043440 +/- 0.0034 deg/day
  T      =  22.688918 +/- 2.1485 years
  Last perihelion JD = 2459424.703118 (2021-07-29 04:52:29.418148) +/- 1.0452 days
  Tj     =   0.181561 +/- 0.0344
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +5.307519e-05, -2.907881e-05, -5.739938e-03, +2.205042e-10, -1.523675e-04, -3.096797e-06
q   , -2.907881e-05, +2.870836e-05, +5.915531e-03, +6.263933e-10, +1.537970e-04, -8.814430e-06
Tp  , -5.739938e-03, +5.915531e-03, +1.224244e+00, +1.382215e-07, +3.178140e-02, -1.944959e-03
node, +2.205042e-10, +6.263933e-10, +1.382215e-07, +4.564831e-14, +3.480081e-09, -6.420882e-10
peri, -1.523675e-04, +1.537970e-04, +3.178140e-02, +3.480081e-09, +8.255359e-04, -4.897008e-05
i   , -3.096797e-06, -8.814430e-06, -1.944959e-03, -6.420882e-10, -4.897008e-05, +9.031634e-06

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.000000
 a2 = 49.407375

Mean time residuals from time vs. length:
  Station with reference time: UK002H
  Avg. res. = 6.200e-06 s
  Stddev    = 2.49e-03 s

Begin point on the trajectory:
  Lon =    -3.855214 +/- 0.0010 deg
  Lat =    51.779578 +/- 0.0013 deg
  Ht  = 112061.23 +/- 85.59 m
End point on the trajectory:
  Lon =    -4.030135 +/- 0.0004 deg
  Lat =    51.706987 +/- 0.0005 deg
  Ht  = 90925.25 +/- 40.89 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
    UK0024,   False,    -2.949770,    50.877440,   82.00,   0.000129,  35.070890,   100273.32,    90925.25,          0.043022,     17.03,    112.26,              55.01, 1.0000,    True,    True, {"ff_name": "FF_UK0024_20210813_013129_660_0475136.fits"}
    UK002H,   False,    -2.412630,    53.386080,   20.00,   2.125120,   6.831797,   112061.23,    92078.26,          0.010527,     42.32,      8.77,              93.00, 1.0000,    True,    True, {"ff_name": "FF_UK002H_20210813_013129_348_0461568.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,     UK0024,       0,  0.233586, 2459439.563584383111, 240.89812,  62.66981,              324.27016,  39.43029,       324.28411,       39.42071,    240.89812,     +62.66981,     240.86738,      +62.67274,  3792847.79, -1331918.24,  5063662.40,      51.739196,       -3.952640,  100273.32,  156018.51,       0.00,            14319.09,   161.66,      0.00,           58820.51,     38.80,      5.93,          51.89,  +1.74,  +0.77
  1,     UK0024,       0,  0.274210, 2459439.563584853429, 240.53244,  61.97593,              323.68700,  38.87728,       323.67342,       38.88655,    240.53244,     +61.97593,     240.56193,      +61.97314,  3791951.72, -1332724.47,  5061774.75,      51.732868,       -3.967886,   98433.03,  154882.43,    2239.68,            16558.77,   -20.59,  55131.98,           58820.51,    -37.56,     -5.76,          50.60,  +0.56,  -0.39
  2,     UK0024,       0,  0.314906, 2459439.563585324213, 240.23758,  61.18789,              322.99865,  38.28470,       322.99983,       38.28390,    240.23758,     +61.18789,     240.23542,      +61.18813,  3790961.94, -1333615.02,  5059689.68,      51.725872,       -3.984713,   96400.57,  153655.33,    4713.59,            19032.68,    27.09,  60789.95,           58820.51,      3.25,      0.50,           4.42,  -0.50,  -1.43
  3,     UK0024,       0,  0.355598, 2459439.563585795462, 240.00440,  60.39436,              322.29822,  37.70336,       322.33704,       37.67719,    240.00440,     +60.39436,     239.92470,      +60.40199,  3789987.15, -1334492.08,  5057636.21,      51.718975,       -4.001294,   94399.17,  152476.67,    7150.02,            21469.11,    37.53,  59874.97,           58820.51,    106.15,     16.16,         145.26,  -0.99,  -1.91
  4,     UK0024,       0,  0.396238, 2459439.563586265780, 239.75584,  59.66980,              321.68674,  37.15145,       321.73795,       37.11711,    239.75584,     +59.66980,     239.65269,      +59.67968,  3789105.61, -1335285.24,  5055779.16,      51.712733,       -4.016309,   92589.46,  151437.31,    9353.39,            23672.48,  -181.99,  54216.75,           58071.61,    139.40,     21.18,         192.05,  -0.84,  -1.74
  5,     UK0024,       0,  0.436834, 2459439.563586735632, 239.55953,  58.99154,              321.11178,  36.64288,       321.18736,       36.59244,    239.55953,     +58.99154,     239.40975,      +59.00588,  3788294.86, -1336014.71,  5054071.24,      51.706987,       -4.030135,   90925.25,  150504.15,   11379.83,            25698.91,  -575.82,  49917.15,           56694.87,    204.91,     31.03,         284.03,  +0.41,  -0.48
  0,     UK002H,       0,  0.000000, 2459439.563581596594, 316.44425,  -5.04870,              209.24913,  27.67722,       209.25147,       27.67779,    316.44425,      -5.04870,     316.44142,       -5.04754,  3798584.81, -1326756.40,  5075747.94,      51.779578,       -3.855214,  112061.23,  234084.55,       0.00,               20.32,  -211.08,      0.00,           61995.46,      1.79,     -8.62,           7.76,  +3.24,  +1.39
  1,     UK002H,       0,  0.040508, 2459439.563582065515, 316.06476,  -5.62855,              209.46405,  27.01197,       209.46098,       27.01122,    316.06476,      -5.62855,     316.06633,       -5.63008,  3797454.66, -1327773.25,  5073367.16,      51.771641,       -3.874364,  109738.32,  234198.14,    2824.77,             2804.46,   158.04,  69733.72,           61995.46,     -2.35,     11.35,          10.21,  +2.54,  +0.69
  2,     UK002H,       0,  0.080904, 2459439.563582533039, 315.77697,  -6.08178,              209.62028,  26.49438,       209.62210,       26.49482,    315.77697,      -6.08178,     315.77487,       -6.08087,  3796578.87, -1328561.23,  5071522.24,      51.765484,       -3.889245,  107938.50,  234310.74,    5013.76,             4993.44,   -61.32,  54188.12,           61995.46,      1.40,     -6.77,           6.09,  +2.21,  +0.36
  3,     UK002H,       0,  0.121372, 2459439.563583001029, 315.43154,  -6.62139,              209.80668,  25.87707,       209.81198,       25.87837,    315.43154,      -6.62139,     315.42684,       -6.61873,  3795532.36, -1329502.82,  5069317.68,      51.758120,       -3.907000,  105788.13,  234471.16,    7629.45,             7609.13,   141.74,  64636.05,           61995.46,      4.10,    -19.81,          17.79,  +1.07,  -0.78
  4,     UK002H,       0,  0.161776, 2459439.563583469018, 315.13798,  -7.08372,              209.96162,  25.34870,       209.97302,       25.35149,    315.13798,      -7.08372,     315.12859,       -7.07797,  3794637.17, -1330308.26,  5067431.88,      51.751815,       -3.922218,  103948.93,  234632.26,    9866.94,             9846.62,   -29.59,  55377.86,           60677.53,      8.87,    -42.81,          38.43,  +0.80,  -1.05
  5,     UK002H,       0,  0.202208, 2459439.563583937008, 314.80420,  -7.57832,              210.14569,  24.77736,       210.14656,       24.77757,    314.80420,      -7.57832,     314.80334,       -7.57788,  3793660.82, -1331186.73,  5065375.10,      51.744932,       -3.938804,  101943.25,  234831.79,   12307.29,            12286.97,     0.27,  60356.95,           60254.93,      0.68,     -3.27,           2.93,  +0.63,  -1.22
  6,     UK002H,       0,  0.242636, 2459439.563584404532, 314.51191,  -8.07116,              210.28486,  24.21996,       210.31171,       24.22652,    314.51191,      -8.07116,     314.49037,       -8.05746,  3792722.04, -1332031.38,  5063397.50,      51.738308,       -3.954763,  100015.05,  235047.66,   14653.70,            14633.39,   -63.57,  58039.37,           59866.65,     21.08,   -101.85,          91.27,  +0.28,  -1.58
  7,     UK002H,       0,  0.283060, 2459439.563584872521, 314.17783,  -8.56036,              210.46618,  23.65328,       210.48081,       23.65685,    314.17783,      -8.56036,     314.16621,       -8.55286,  3791749.92, -1332906.04,  5061349.64,      51.731442,       -3.971288,   98018.62,  235295.58,   17083.47,            17063.15,   -43.81,  60107.02,           59724.86,     11.55,    -55.76,          49.92,  +0.31,  -1.55
  8,     UK002H,       0,  0.323492, 2459439.563585340511, 313.84318,  -9.05527,              210.64365,  23.08077,       210.64980,       23.08227,    313.84318,      -9.05527,     313.83854,       -9.05210,  3790767.55, -1333789.92,  5059280.18,      51.724497,       -3.987991,   96001.43,  235571.37,   19538.87,            19518.55,     1.10,  60729.02,           59725.62,      4.88,    -23.55,          21.06,  +0.12,  -1.74
  9,     UK002H,       0,  0.363908, 2459439.563585808501, 313.51351,  -9.53607,              210.81825,  22.52300,       210.81326,       22.52178,    313.51351,      -9.53607,     313.51808,       -9.53865,  3789807.25, -1334653.94,  5057257.24,      51.717702,       -4.004328,   94029.84,  235865.57,   21939.07,            21918.76,    -8.23,  59387.59,           59707.58,     -3.98,     19.19,          17.14,  +0.31,  -1.55
 10,     UK002H,       0,  0.404320, 2459439.563586276025, 313.18884, -10.01167,              210.98710,  21.97151,       210.97340,       21.96817,    313.18884,     -10.01167,     313.20072,      -10.01880,  3788856.57, -1335509.31,  5055254.54,      51.710968,       -4.020507,   92078.26,  236180.64,   24315.25,            24294.94,   -41.35,  58798.88,           59656.45,    -11.01,     53.01,          47.28,  +0.56,  -1.31

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.