Orbital Analysis for matched events on 20210816_232345.917_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 68.47° Bg 36.24° Vg 60.32km/s
mass 0.01972g, abs. mag 0.2
Path Details
------------
start -0.98° 53.58° 108.02km
end   -1.14° 53.48° 95.26km

Orbit Details
-------------
Semimajor axis 31.88A.U., eccentricity 0.97, inclination 116.40°, Period 180.00Y, LA Sun 144.01°, last Perihelion 2021-07-24

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: 2459443.474837007001
Time: 2021-08-16 23:23:45.917405 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002Z and UK003G
 Convergence angle = 86.87041 deg
 R.A. =  56.72547  Dec = +57.53244 deg

Best intersection: Stations UK002Z and UK003G with Qconv = 86.87 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2753605.85 +/- 16.69 m
 Y =  -2703281.33 +/- 63.38 m
 Z =   5196308.00 +/- 94.80 m
 Vx =    18066.03 +/- 220.95 m/s
 Vy =    27447.04 +/- 203.32 m/s
 Vz =    51789.11 +/- 297.13 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.876274e+02, -3.736630e+02, -5.990346e+02, +9.711019e+02, -4.270816e+02, -1.145703e+03
-3.736630e+02, +4.257845e+03, +5.611284e+03, -8.291466e+03, +1.846545e+03, -2.967700e+02
-5.990346e+02, +5.611284e+03, +9.153054e+03, -1.301748e+04, +5.968749e+02, +9.497699e+02
+9.711019e+02, -8.291466e+03, -1.301748e+04, +2.706471e+04, +1.127848e+04, +1.866474e+04
-4.270816e+02, +1.846545e+03, +5.968749e+02, +1.127848e+04, +2.971465e+04, +3.750512e+04
-1.145703e+03, -2.967700e+02, +9.497699e+02, +1.866474e+04, +3.750512e+04, +6.407271e+04

Timing offsets (from input data):
    UK002Z: -0.000949 s
    UK003G: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-16 23:23:45.917405 UTC
  Lon     = +-0.980790 +/- 0.0006 deg
  Lat     = +53.583469 +/- 0.0008 deg
  Lat geo = +53.402508 +/- 0.0008 deg
  Ht      =  108001.82 +/- 51.07 m

  JD dynamic   = 2459443.475637747906 
  LST apparent = 315.5283783057 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  56.64653 +/- 0.2297 deg
  Dec       = +57.60573 +/- 0.0855 deg
  Azimuth   =  41.97231 +/- 0.1577 deg
  Elevation = +38.18215 +/- 0.0821 deg
  Vavg      =  59.46186 +/- 0.1253 km/s
  Vinit     =  61.33378 +/- 0.2941 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  56.55270 +/- 0.2297 deg
  Dec       = +57.38843 +/- 0.0855 deg
  Azimuth   =  42.21996 +/- 0.1577 deg
  Elevation = +38.07348 +/- 0.0821 deg
  Vavg      =  59.61025 +/- 0.1253 km/s
  Vinit     =  61.48217 +/- 0.2941 km/s
Radiant (geocentric, J2000):
  R.A.   =  56.85106 +/- 0.2290 deg
  Dec    = +57.22761 +/- 0.0852 deg
  Vg     =  60.32136 +/- 0.2991 km/s
  Vinf   =  61.33378 +/- 0.2941 km/s
  Zc     =  51.95249 +/- 0.0822 deg
  Zg     =  52.41712 +/- 0.0820 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  68.46955 +/- 0.1625 deg
  Bg     = +36.24148 +/- 0.0732 deg
  Vh     =  41.52767 +/- 0.2653 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  87.72598 +/- 0.4221 deg
  Bh     = +59.17532 +/- 0.1937 deg
  Vh_x   =  -0.84434 +/- 0.1585 km/s
  Vh_y   = -21.26255 +/- 0.2423 km/s
  Vh_z   = -35.66144 +/- 0.1744 km/s
Orbit:
  La Sun = 144.007120 +/- -0.0000 deg
  a      =  31.879212 +/- 49.3375 AU
  e      =   0.970847 +/- 0.0228
  i      = 116.395813 +/- 0.2391 deg
  peri   = 146.439942 +/- 0.5568 deg
  node   = 144.005783 +/- 0.0000 deg
  Pi     = 290.445725 +/- 0.5568 deg
  q      =   0.929367 +/- 0.0020 AU
  f      =  33.555966 +/- 0.5568 deg
  M      =   0.126095 +/- 0.1976 deg
  Q      =  62.829057 +/- 98.6752 AU
  n      =   0.005476 +/- 0.0081 deg/day
  T      = 179.995648 +/- 785.2118 years
  Last perihelion JD = 2459420.447768 (2021-07-24 22:44:47.157570) +/- 0.4609 days
  Tj     =  -0.364235 +/- 0.1355
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +5.621677e-04, +2.687904e-05, +1.036538e-02, -6.644149e-09, +1.903866e-04, +8.398809e-05
q   , +2.687904e-05, +4.505437e-06, +8.830055e-04, -4.923657e-10, +2.064169e-05, +6.208755e-06
Tp  , +1.036538e-02, +8.830055e-04, +2.377527e-01, -1.435994e-07, +4.898959e-03, +1.813407e-03
node, -6.644149e-09, -4.923657e-10, -1.435994e-07, +1.208457e-13, -2.877332e-09, -1.526537e-09
peri, +1.903866e-04, +2.064169e-05, +4.898959e-03, -2.877332e-09, +1.058292e-04, +3.631777e-05
i   , +8.398809e-05, +6.208755e-06, +1.813407e-03, -1.526537e-09, +3.631777e-05, +1.928349e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.060764
 a2 = 26.177510

Mean time residuals from time vs. length:
  Station with reference time: UK003G
  Avg. res. = 2.648e-06 s
  Stddev    = 1.63e-03 s

Begin point on the trajectory:
  Lon =    -0.980510 +/- 0.0004 deg
  Lat =    53.583654 +/- 0.0007 deg
  Ht  = 108024.03 +/- 35.82 m
End point on the trajectory:
  Lon =    -1.143303 +/- 0.0002 deg
  Lat =    53.476555 +/- 0.0001 deg
  Ht  = 95259.31 +/- 18.01 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
    UK002Z,   False,    -0.382830,    53.537790,   34.00,   0.257160,  21.706029,   104167.26,    95259.31,          0.016167,     12.68,     28.64,              64.92, 1.0000,   False,    True, {"ff_name": "FF_UK002Z_20210816_232346_554_0295936.fits"}
    UK003G,   False,    -1.802002,    51.351948,  130.00,   0.000000,   0.000000,   108024.03,    96158.42,          0.008137,     35.60,     13.24,              28.42, 1.0000,    True,    True, {"ff_name": "FF_UK003G_20210816_232342_455_0300544.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,     UK002Z,       0,  0.104683, 2459443.474838225637, 280.32616,  48.66223,              272.27849,  67.25255,       272.28303,       67.25105,    280.32616,     +48.66223,     280.32340,      +48.66316,  2751777.93, -2706058.42,  5191067.98,      53.551397,       -1.029661,  104167.26,  112760.51,       0.00,             6205.74,    -1.07,      0.00,           61236.37,      4.16,     -1.84,           8.32,  -0.53,  -0.79
  1,     UK002Z,       0,  0.145447, 2459443.474838697352, 279.56668,  47.57886,              270.41827,  66.30752,       270.35621,       66.32751,    279.56668,     +47.57886,     279.61088,      +47.56636,  2751038.13, -2707182.38,  5188947.21,      53.538401,       -1.049428,  102616.33,  111839.59,    2511.62,             8717.37,    10.34,  61613.79,           61236.37,    -57.03,     25.25,         115.03,  -0.64,  -0.88
  2,     UK002Z,       0,  0.186187, 2459443.474839169066, 278.90575,  46.48028,              268.61624,  65.37685,       268.57964,       65.38838,    278.90575,     +46.48028,     278.93216,      +46.47296,  2750315.03, -2708280.96,  5186874.33,      53.525689,       -1.068750,  101100.98,  110987.37,    4966.54,            11172.28,   -33.48,  60258.05,           61236.37,    -33.85,     14.99,          68.80,  -0.65,  -0.88
  3,     UK002Z,       0,  0.226971, 2459443.474839641247, 278.25160,  45.32162,              266.84545,  64.38444,       266.84985,       64.38309,    278.25160,     +45.32162,     278.24948,      +45.32249,  2749568.27, -2709415.47,  5184733.64,      53.512551,       -1.088696,   99536.66,  110157.90,    7501.75,            13707.49,     0.29,  62161.92,           61236.37,      4.10,     -1.82,           8.41,  -0.70,  -0.91
  4,     UK002Z,       0,  0.267755, 2459443.474840112962, 277.59211,  44.20834,              265.31812,  63.38108,       265.28990,       63.38965,    277.59211,     +44.20834,     277.61304,      +44.20272,  2748854.20, -2710500.34,  5182686.64,      53.499980,       -1.107774,   98041.35,  109414.27,    9926.01,            16131.76,   -76.88,  59441.52,           60937.19,    -26.66,     11.81,          54.97,  -0.79,  -0.99
  5,     UK002Z,       0,  0.308531, 2459443.474840585142, 277.00632,  43.06101,              263.79609,  62.37372,       263.81725,       62.36740,    277.00632,     +43.06101,     276.99272,      +43.06523,  2748140.48, -2711584.67,  5180640.65,      53.487406,       -1.126840,   96547.33,  108720.21,   12349.08,            18554.82,  -154.76,  59423.88,           60635.51,     20.25,     -8.98,          42.02,  -0.58,  -0.76
  6,     UK002Z,       0,  0.349231, 2459443.474841055926, 276.47783,  42.06711,              262.59880,  61.46717,       262.61295,       61.46299,    276.47783,     +42.06711,     276.46928,      +42.06993,  2747524.97, -2712519.79,  5178876.19,      53.476555,       -1.143303,   95259.31,  108162.59,   14438.73,            20644.47,  -561.40,  51342.69,           59533.96,     13.71,     -6.08,          28.61,  +0.74,  +0.57
  7,     UK002Z,       1,  0.389883, 2459443.474841526709, 275.96430,  41.19183,              261.66315,  60.62555,       261.59484,       60.64558,    275.96430,     +41.19183,     276.01450,      +41.17816,  2746980.02, -2713347.71,  5177314.01,      53.466942,       -1.157897,   94119.27,  107701.12,   16288.81,            22494.56, -1204.65,  45510.35,           57909.76,    -67.09,     29.67,         140.50,  +6.04,  +5.88
  0,     UK003G,       0,  0.000000, 2459443.474837007001, 112.15779,  58.77684,               12.34913,  21.64667,        12.34471,       21.65214,    112.15779,     +58.77684,     112.16273,      +58.78319,  2753616.43, -2703265.25,  5196338.33,      53.583654,       -0.980510,  108024.03,  278419.18,       0.00,               35.93,   249.73,      0.00,           59750.08,    -11.58,    -31.16,          24.63,  +1.57,  -0.65
  1,     UK003G,       0,  0.040112, 2459443.474837471265, 112.60780,  58.69307,               12.12927,  21.50609,        12.13066,       21.50437,    112.60780,     +58.69307,     112.60639,      +58.69108,  2752882.26, -2704380.66,  5194233.71,      53.570780,       -1.000132,  106483.46,  276227.71,    2492.51,             2456.58,   210.16,  62138.68,           59750.08,      3.62,      9.72,           7.74,  +0.96,  -1.25
  2,     UK003G,       0,  0.080236, 2459443.474837935530, 113.02916,  58.59895,               11.92651,  21.36012,        11.92502,       21.36196,    113.02916,     +58.59895,     113.03121,      +58.60107,  2752186.78, -2705437.28,  5192239.99,      53.558576,       -1.018726,  105024.61,  274156.45,    4853.66,             4817.73,   110.35,  58846.38,           59750.08,     -3.85,    -10.34,           8.30,  +0.62,  -1.57
  3,     UK003G,       0,  0.120352, 2459443.474838399794, 113.45825,  58.50952,               11.71714,  21.21852,        11.71768,       21.21785,    113.45825,     +58.50952,     113.45813,      +58.50875,  2751494.73, -2706488.68,  5190256.14,      53.546423,       -1.037226,  103573.49,  272100.21,    7203.13,             7167.20,    -0.64,  58567.01,           59750.08,      1.38,      3.72,           3.01,  +0.57,  -1.60
  4,     UK003G,       0,  0.160480, 2459443.474838864524, 113.89034,  58.40648,               11.50845,  21.06418,        11.50447,       21.06907,    113.89034,     +58.40648,     113.89567,      +58.41211,  2750792.30, -2707555.85,  5188242.52,      53.534080,       -1.056000,  102101.11,  270018.13,    9587.87,             9551.94,   -77.11,  59428.22,           59537.27,    -10.09,    -27.11,          22.10,  +0.55,  -1.61
  5,     UK003G,       0,  0.200620, 2459443.474839328788, 114.35510,  58.29149,               11.28354,  20.89506,        11.27363,       20.90722,    114.35510,     +58.29149,     114.36770,      +58.30546,  2750041.69, -2708696.23,  5186090.77,      53.520881,       -1.076047,  100528.32,  267799.09,   12136.18,            12100.25,     9.27,  63485.65,           60040.82,    -24.88,    -66.95,          55.01,  +0.35,  -1.79
  6,     UK003G,       0,  0.240756, 2459443.474839793518, 114.84454,  58.18005,               11.04265,  20.72742,        11.03377,       20.73829,    114.84454,     +58.18005,     114.85622,      +58.19252,  2749272.84, -2709864.32,  5183886.73,      53.507351,       -1.096574,   98917.94,  265532.42,   14746.42,            14710.49,   157.81,  65034.74,           60755.88,    -22.10,    -59.43,          49.25,  +0.33,  -1.79
  7,     UK003G,       0,  0.280860, 2459443.474840257782, 115.24461,  58.09709,               10.84263,  20.59915,        10.84034,       20.60196,    115.24461,     +58.09709,     115.24856,      +58.10030,  2748662.63, -2710791.38,  5182137.47,      53.496606,       -1.112898,   97640.28,  263737.62,   16818.06,            16782.13,  -230.27,  51656.80,           60295.91,     -5.68,    -15.25,          12.73,  +0.40,  -1.71
  8,     UK003G,       0,  0.320996, 2459443.474840722047, 115.69928,  57.98262,               10.61879,  20.43461,        10.61345,       20.44113,    115.69928,     +57.98262,     115.70717,      +57.99007,  2747954.65, -2711866.99,  5180107.94,      53.484130,       -1.131809,   96158.42,  261660.83,   19221.63,            19185.70,  -288.40,  59885.64,           60053.88,    -13.10,    -35.19,          29.59,  +0.65,  -1.44

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.