Orbital Analysis for matched events on 20210813_224557.738_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 69.51° Bg 36.51° Vg 59.99km/s
mass 0.00370g, abs. mag 1.0
Path Details
------------
start -1.31° 49.65° 108.99km
end   -1.41° 49.56° 101.55km

Orbit Details
-------------
Semimajor axis -71.51A.U., eccentricity 1.01, inclination 114.60°, Period 1000000000.00Y, LA Sun 141.10°, 

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: 2459440.448584937956
Time: 2021-08-13 22:45:57.738639 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002D and UK0038
 Convergence angle = 8.31684 deg
 R.A. =  58.29249  Dec = +57.85507 deg

Best intersection: Stations UK002D and UK0038 with Qconv = 8.32 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2277296.13 +/- 253.05 m
 Y =  -3538800.77 +/- 280.56 m
 Z =   4920736.70 +/- 78.11 m
 Vx =    17068.88 +/- 1686.83 m/s
 Vy =    27259.53 +/- 1506.34 m/s
 Vz =    51844.21 +/- 460.53 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+5.601245e+04, -6.181652e+04, -1.579458e+04, +1.975007e+05, -2.008115e+05, -2.345966e+04
-6.181652e+04, +6.897472e+04, +1.766519e+04, -2.172890e+05, +2.234945e+05, +2.512527e+04
-1.579458e+04, +1.766519e+04, +4.940832e+03, -5.599212e+04, +5.630588e+04, +7.282131e+03
+1.975007e+05, -2.172890e+05, -5.599212e+04, +1.028761e+06, -1.049761e+06, -1.665760e+05
-2.008115e+05, +2.234945e+05, +5.630588e+04, -1.049761e+06, +1.096273e+06, +1.623247e+05
-2.345966e+04, +2.512527e+04, +7.282131e+03, -1.665760e+05, +1.623247e+05, +3.399720e+04

Timing offsets (from input data):
    UK000H: 0.000000 s
    UK002D: 0.000000 s
    UK0038: 0.000433 s

Reference point on the trajectory:
  Time: 2021-08-13 22:45:57.738639 UTC
  Lon     = +-1.313422 +/- 0.0009 deg
  Lat     = +49.649638 +/- 0.0029 deg
  Lat geo = +49.462840 +/- 0.0029 deg
  Ht      =  108977.17 +/- 184.40 m

  JD dynamic   = 2459440.449385678861 
  LST apparent = 302.7621722128 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  57.94678 +/- 3.6690 deg
  Dec       = +58.18582 +/- 0.1962 deg
  Azimuth   =  33.48549 +/- 1.4713 deg
  Elevation = +30.15625 +/- 1.4722 deg
  Vavg      =  60.42623 +/- 0.4770 km/s
  Vinit     =  61.01025 +/- 0.4131 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  57.71614 +/- 3.6690 deg
  Dec       = +57.96453 +/- 0.1962 deg
  Azimuth   =  33.76257 +/- 1.4713 deg
  Elevation = +30.07628 +/- 1.4722 deg
  Vavg      =  60.57322 +/- 0.4770 km/s
  Vinit     =  61.15724 +/- 0.4131 km/s
Radiant (geocentric, J2000):
  R.A.   =  58.21587 +/- 3.6422 deg
  Dec    = +57.71251 +/- 0.2087 deg
  Vg     =  59.99275 +/- 0.4202 km/s
  Vinf   =  61.01025 +/- 0.4131 km/s
  Zc     =  59.99960 +/- 1.4750 deg
  Zg     =  60.55591 +/- 1.4841 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  69.50816 +/- 2.2669 deg
  Bg     = +36.51438 +/- 0.7323 deg
  Vh     =  41.99745 +/- 0.4153 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  93.46427 +/- 4.0788 deg
  Bh     = +58.21063 +/- 1.9463 deg
  Vh_x   =   1.33688 +/- 1.4159 km/s
  Vh_y   = -22.08375 +/- 1.4568 km/s
  Vh_z   = -35.69743 +/- 0.3642 km/s
Orbit:
  La Sun = 141.099434 +/- 0.0000 deg
  a      = -71.511905 +/- 40.5031 AU
  e      =   1.012393 +/- 0.0360
  i      = 114.603861 +/- 0.5524 deg
  peri   = 138.684087 +/- 4.8784 deg
  node   = 141.097895 +/- 0.0000 deg
  Pi     = 279.781982 +/- 4.8784 deg
  q      =   0.886223 +/- 0.0263 AU
  f      =  41.311839 +/- 4.8783 deg
  M      =        nan +/- nan deg
  Q      = -143.910034 +/- 81.0026 AU
  n      =   0.001630 +/- 0.0063 deg/day
  T      = 1000000000.000000 +/- 377739599.7306 years
  Last perihelion JD = NaN 
  Tj     =  -0.560223 +/- 0.2103
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +4.280077e-04, -3.428839e-04, -3.923259e-02, -8.863593e-09, -1.221943e-03, +1.150042e-04
q   , -3.428839e-04, +3.161185e-04, +3.667147e-02, +8.984969e-09, +1.132345e-03, -1.165609e-04
Tp  , -3.923259e-02, +3.667147e-02, +4.329489e+00, +1.041997e-06, +1.327613e-01, -1.352426e-02
node, -8.863593e-09, +8.984969e-09, +1.041997e-06, +3.016676e-13, +3.211448e-08, -3.910880e-09
peri, -1.221943e-03, +1.132345e-03, +1.327613e-01, +3.211448e-08, +4.082487e-03, -4.167440e-04
i   , +1.150042e-04, -1.165609e-04, -1.352426e-02, -3.910880e-09, -4.167440e-04, +5.070241e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.053115
 a2 = 35.170664

Mean time residuals from time vs. length:
  Station with reference time: UK002D
  Avg. res. = 2.263e-05 s
  Stddev    = 4.76e-03 s

Begin point on the trajectory:
  Lon =    -1.313263 +/- 0.0009 deg
  Lat =    49.649795 +/- 0.0029 deg
  Ht  = 108989.52 +/- 188.14 m
End point on the trajectory:
  Lon =    -1.410574 +/- 0.0007 deg
  Lat =    49.555058 +/- 0.0025 deg
  Ht  = 101547.65 +/- 141.95 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
    UK000H,    True,    -1.778230,    50.857470,   24.00, 3158.898426,   0.777956,   106952.37,   103428.00,          0.054958,       nan,       nan,              96.73, 0.0000,    True,    True, {"ff_name": "FF_UK000H_20210813_224548_672_0236288.fits"}
    UK002D,   False,    -1.801980,    51.351940,  129.00,   0.021359,  38.507295,   108989.52,   101547.65,          0.010003,     38.84,      6.28,             105.07, 1.0000,    True,    True, {"ff_name": "FF_UK002D_20210813_224551_418_0233472.fits"}
    UK0038,   False,    -2.379250,    51.361350,  169.00,  35.397705,   0.000000,   108670.91,   102635.55,          0.012826,     52.56,      0.79,              99.64, 1.0000,    True,    True, {"ff_name": "FF_UK0038_20210813_224553_262_0230656.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,     UK000H,       1,  0.116594, 2459440.448586287443, 312.80974,  -2.07213,              166.92217,  36.31382,       166.99943,       36.36471,    312.80974,      -2.07213,     312.74133,       -2.03063,  2276168.07, -3540602.32,  4917310.38,      49.623923,       -1.340093,  106952.37,  177677.86,       0.00,             4032.09, -3339.89,      0.00,           58136.20,     53.10,   -243.59,         289.42,  +1.64,  +0.39
  1,     UK000H,       1,  0.157178, 2459440.448586757295, 312.44491,  -2.62070,              167.46373,  35.82170,       167.51619,       35.85609,    312.44491,      -2.62070,     312.39869,       -2.59246,  2275589.60, -3541526.15,  4915553.36,      49.610728,       -1.353685,  105914.76,  178035.37,    2067.66,             6099.75, -3748.27,  50947.71,           58136.20,     36.27,   -166.01,         196.87,  +1.41,  +0.16
  2,     UK000H,       1,  0.197898, 2459440.448587228544, 312.00211,  -3.30009,              168.11373,  35.20753,       168.14263,       35.22637,    312.00211,      -3.30009,     311.97703,       -3.28449,  2274873.61, -3542669.62,  4913378.63,      49.594388,       -1.370465,  104631.15,  178510.70,    4626.88,             8658.98, -3673.39,  62849.24,           58136.20,     20.13,    -91.92,         108.73,  +1.42,  +0.16
  3,     UK000H,       1,  0.238570, 2459440.448587699328, 311.61747,  -3.95129,              168.67906,  34.61045,       168.71858,       34.63610,    311.61747,      -3.95129,     311.58293,       -3.92988,  2274202.12, -3543742.01,  4911339.07,      49.579055,       -1.386208,  103428.00,  178988.61,    7027.03,            11059.13, -3754.65,  59012.37,           58136.20,     27.66,   -126.39,         149.10,  +1.31,  +0.05
  0,     UK002D,       0,  0.000000, 2459440.448584937956, 311.69853,  -9.69777,              169.42558,  28.40757,       169.43418,       28.41361,    311.69853,      -9.69777,     311.69020,       -9.69266,  2277303.01, -3538789.78,  4920757.60,      49.649795,       -1.313263,  108989.52,  222566.14,       0.00,               24.59,  -233.98,      0.00,           62179.58,      6.00,    -37.12,          34.85,  +2.89,  +1.15
  1,     UK002D,       0,  0.040516, 2459440.448585406877, 311.31252, -10.31098,              169.93282,  27.84152,       169.94536,       27.85029,    311.31252,     -10.31098,     311.30050,      -10.30350,  2276482.94, -3540099.47,  4918266.73,      49.631103,       -1.332468,  107517.38,  223427.71,    2931.25,             2906.66,   176.20,  72348.03,           62179.58,      8.79,    -54.43,          50.90,  +2.55,  +0.80
  2,     UK002D,       0,  0.080872, 2459440.448585873935, 311.02519, -10.73584,              170.30212,  27.45000,       170.30417,       27.45143,    311.02519,     -10.73584,     311.02353,      -10.73461,  2275899.90, -3541030.60,  4916495.84,      49.617807,       -1.346167,  106471.34,  224061.14,    5015.23,             4990.64,  -201.95,  51639.81,           62179.58,      1.45,     -8.94,           8.34,  +2.22,  +0.47
  3,     UK002D,       0,  0.121332, 2459440.448586342391, 310.67420, -11.28560,              170.75206,  26.93933,       170.75625,       26.94225,    310.67420,     -11.28560,     310.67061,      -11.28308,  2275152.76, -3542223.81,  4914226.51,      49.600760,       -1.363670,  105131.60,  224899.10,    7685.79,             7661.20,     0.13,  66004.87,           62179.58,      2.97,    -18.34,          17.04,  +1.93,  +0.17
  4,     UK002D,       0,  0.161752, 2459440.448586809915, 310.34352, -11.78483,              171.16890,  26.47506,       171.16749,       26.47408,    310.34352,     -11.78483,     310.34557,      -11.78568,  2274462.61, -3543326.00,  4912130.29,      49.585004,       -1.379846,  103894.78,  225698.43,   10152.61,            10128.02,     0.92,  61029.87,           61981.39,     -1.00,      6.20,           5.74,  +2.06,  +0.29
  5,     UK002D,       0,  0.202164, 2459440.448587277904, 310.03524, -12.27843,              171.55628,  26.01265,       171.56401,       26.01800,    310.03524,     -12.27843,     310.02849,      -12.27375,  2273787.13, -3544404.75,  4910078.63,      49.569576,       -1.395678,  102684.91,  226504.13,   12567.01,            12542.42,   -50.23,  59744.48,           61605.37,      5.54,    -34.23,          31.57,  +2.23,  +0.45
  6,     UK002D,       0,  0.242552, 2459440.448587745428, 309.74511, -12.73850,              171.91653,  25.58057,       171.93177,       25.59110,    309.74511,     -12.73850,     309.73112,      -12.72925,  2273151.86, -3545419.31,  4908149.06,      49.555058,       -1.410574,  101547.65,  227282.70,   14837.72,            14813.13,  -243.60,  56222.40,           60894.92,     10.96,    -67.78,          62.31,  +4.70,  +2.92
  0,     UK0038,       0,  0.005751, 2459440.448584998958, 321.48107,  -9.53403,              158.04926,  26.74733,       158.04896,       26.74705,    321.48107,      -9.53403,     321.48142,       -9.53424,  2277125.58, -3539073.16,  4920218.66,      49.645751,       -1.317404,  108670.91,  233625.01,       0.00,              609.64,     0.19,      0.00,           60472.57,     -0.02,      1.57,           1.39,  +2.96,  +1.12
  1,     UK0038,       0,  0.046031, 2459440.448585465085, 321.17135,  -9.96944,              158.49522,  26.39566,       158.47729,       26.37914,    321.17135,      -9.96944,     321.19130,       -9.98177,  2276508.02, -3540059.42,  4918342.91,      49.631675,       -1.331907,  107562.38,  234071.06,    2207.38,             2817.02,  -249.92,  54800.91,           60472.57,     -1.43,     94.13,          82.96,  +2.60,  +0.75
  2,     UK0038,       0,  0.086419, 2459440.448585932609, 320.81454, -10.54811,              159.02409,  25.91320,       159.01855,       25.90811,    320.81454,     -10.54811,     320.82102,      -10.55193,  2275717.15, -3541322.45,  4915940.78,      49.613638,       -1.350428,  106143.58,  234672.56,    5034.21,             5643.84,   112.83,  69991.75,           60472.57,     -0.44,     29.17,          25.64,  +2.36,  +0.51
  3,     UK0038,       0,  0.126715, 2459440.448586399201, 320.54684, -10.98917,              159.41890,  25.54280,       159.42665,       25.54988,    320.54684,     -10.98917,     320.53881,      -10.98383,  2275114.96, -3542284.17,  4914111.72,      49.599897,       -1.364567,  105063.85,  235151.52,    7186.64,             7796.28,  -193.21,  53415.61,           60472.57,      0.60,    -40.85,          35.84,  +2.25,  +0.39
  4,     UK0038,       0,  0.167103, 2459440.448586866260, 320.12930, -11.58363,              160.00578,  25.05340,       159.99533,       25.04388,    320.12930,     -11.58363,     320.14155,      -11.59086,  2274263.58, -3543643.86,  4911525.75,      49.580459,       -1.384482,  103538.23,  235862.23,   10229.81,            10839.44,   385.88,  75348.27,           63064.52,     -0.84,     55.27,          48.34,  +2.54,  +0.68
  5,     UK0038,       0,  0.207351, 2459440.448587332387, 319.91440, -11.95432,              160.32067,  24.73703,       160.32940,       24.74496,    319.91440,     -11.95432,     319.90560,      -11.94828,  2273759.57, -3544448.78,  4909994.90,      49.568946,       -1.396337,  102635.55,  236299.00,   12031.31,            12640.95,  -268.16,  44760.04,           61195.60,      0.68,    -46.26,          40.38,  +3.48,  +1.61

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.