Orbital Analysis for matched events on 20210813_224719.031_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 64.58° Bg 37.80° Vg 58.62km/s
mass 0.01285g, abs. mag 0.2
Path Details
------------
start -1.70° 52.63° 110.34km
end   -1.83° 52.52° 99.59km

Orbit Details
-------------
Semimajor axis 8.35A.U., eccentricity 0.89, inclination 113.53°, Period 24.13Y, LA Sun 141.10°, last Perihelion 2021-07-22

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: 2459440.449525822420
Time: 2021-08-13 22:47:19.031057 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002H and UK003G
 Convergence angle = 67.48837 deg
 R.A. =  50.18614  Dec = +58.24151 deg

Best intersection: Stations UK002H and UK003G with Qconv = 67.49 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2133056.21 +/- 26.93 m
 Y =  -3320367.91 +/- 30.97 m
 Z =   5133437.35 +/- 61.66 m
 Vx =    20105.70 +/- 216.38 m/s
 Vy =    24124.20 +/- 207.62 m/s
 Vz =    50727.37 +/- 241.91 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+7.526265e+02, -1.079502e+02, +2.590970e+02, +1.571287e+03, -2.979413e+03, -3.818129e+03
-1.079502e+02, +9.975184e+02, +1.270591e+03, -1.930079e+03, +3.686522e+03, +3.252125e+03
+2.590970e+02, +1.270591e+03, +4.053519e+03, -1.042734e+03, +1.622650e+03, +9.590690e+03
+1.571287e+03, -1.930079e+03, -1.042734e+03, +7.104748e+03, -1.359343e+04, -1.140152e+04
-2.979413e+03, +3.686522e+03, +1.622650e+03, -1.359343e+04, +2.614253e+04, +1.994352e+04
-3.818129e+03, +3.252125e+03, +9.590690e+03, -1.140152e+04, +1.994352e+04, +5.718871e+04

Timing offsets (from input data):
    UK002H: -0.001053 s
    UK003G: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 22:47:19.031057 UTC
  Lon     = +-1.697918 +/- 0.0004 deg
  Lat     = +52.630239 +/- 0.0005 deg
  Lat geo = +52.447605 +/- 0.0005 deg
  Ht      =  110381.13 +/- 43.78 m

  JD dynamic   = 2459440.450326563325 
  LST apparent = 302.7173227343 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  50.19135 +/- 0.2978 deg
  Dec       = +58.23936 +/- 0.1010 deg
  Azimuth   =  38.04136 +/- 0.1681 deg
  Elevation = +35.43607 +/- 0.1255 deg
  Vavg      =  59.48486 +/- 0.1091 km/s
  Vinit     =  59.66139 +/- 0.2197 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  50.03506 +/- 0.2978 deg
  Dec       = +58.01566 +/- 0.1010 deg
  Azimuth   =  38.30753 +/- 0.1681 deg
  Elevation = +35.33727 +/- 0.1255 deg
  Vavg      =  59.62986 +/- 0.1091 km/s
  Vinit     =  59.80640 +/- 0.2197 km/s
Radiant (geocentric, J2000):
  R.A.   =  50.46501 +/- 0.2934 deg
  Dec    = +57.79501 +/- 0.1039 deg
  Vg     =  58.62054 +/- 0.2236 km/s
  Vinf   =  59.66139 +/- 0.2197 km/s
  Zc     =  54.70785 +/- 0.1256 deg
  Zg     =  55.22951 +/- 0.1265 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  64.57565 +/- 0.1952 deg
  Bg     = +37.79557 +/- 0.1063 deg
  Vh     =  40.56044 +/- 0.2412 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  84.90810 +/- 0.2891 deg
  Bh     = +62.34160 +/- 0.1961 deg
  Vh_x   =  -1.67106 +/- 0.0785 km/s
  Vh_y   = -18.75381 +/- 0.2103 km/s
  Vh_z   = -35.92563 +/- 0.1913 km/s
Orbit:
  La Sun = 141.100338 +/- 0.0000 deg
  a      =   8.350569 +/- 3.9932 AU
  e      =   0.887290 +/- 0.0210
  i      = 113.531221 +/- 0.1061 deg
  peri   = 148.111725 +/- 0.3909 deg
  node   = 141.098914 +/- 0.0000 deg
  Pi     = 289.210639 +/- 0.3909 deg
  q      =   0.941197 +/- 0.0016 AU
  f      =  31.884190 +/- 0.3909 deg
  M      =   0.923071 +/- 0.2143 deg
  Q      =  15.759941 +/- 7.9869 AU
  n      =   0.040844 +/- 0.0095 deg/day
  T      =  24.130967 +/- 23.2149 years
  Last perihelion JD = 2459417.850510 (2021-07-22 08:24:44.022702) +/- 0.3149 days
  Tj     =   0.156721 +/- 0.1191
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +4.594028e-04, -5.318419e-06, +4.828242e-03, -1.061790e-09, +5.179500e-05, +1.366063e-05
q   , -5.318419e-06, +2.972361e-06, +3.592095e-04, +2.526307e-10, +1.103149e-05, -3.253876e-06
Tp  , +4.828242e-03, +3.592095e-04, +1.099661e-01, +2.310831e-08, +2.203446e-03, -2.978249e-04
node, -1.061790e-09, +2.526307e-10, +2.310831e-08, +2.234750e-14, +8.405410e-10, -2.878083e-10
peri, +5.179500e-05, +1.103149e-05, +2.203446e-03, +8.405410e-10, +5.232209e-05, -1.082866e-05
i   , +1.366063e-05, -3.253876e-06, -2.978249e-04, -2.878083e-10, -1.082866e-05, +3.706626e-06

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 29.116477
 a2 = 2.323193

Mean time residuals from time vs. length:
  Station with reference time: UK003G
  Avg. res. = 5.732e-06 s
  Stddev    = 2.39e-03 s

Begin point on the trajectory:
  Lon =    -1.698487 +/- 0.0001 deg
  Lat =    52.629797 +/- 0.0005 deg
  Ht  = 110335.86 +/- 36.83 m
End point on the trajectory:
  Lon =    -1.834947 +/- 0.0002 deg
  Lat =    52.524356 +/- 0.0002 deg
  Ht  = 99593.84 +/- 17.55 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
    UK002H,   False,    -2.412630,    53.386080,   20.00,   0.000025,  48.082681,   109310.87,    99593.84,          0.013035,     31.79,      9.72,              76.48, 1.0000,    True,    True, {"ff_name": "FF_UK002H_20210813_224716_992_0218880.fits"}
    UK003G,   False,    -1.802002,    51.351948,  130.00,  49.667434,   0.000000,   110335.86,   100605.24,          0.008993,     17.25,     20.84,              28.18, 1.0000,    True,    True, {"ff_name": "FF_UK003G_20210813_224717_129_0236288.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,     UK002H,       0,  0.023468, 2459440.449526106939, 321.77912,  14.00288,              150.84768,  47.62826,       150.82391,       47.60912,    321.77912,     +14.00288,     321.80089,      +13.98941,  2132434.04, -3321114.43,  5131867.60,      52.619772,       -1.711477,  109310.87,  146951.10,       0.00,             1846.21,   136.71,      0.00,           56615.66,    -18.72,     61.23,          89.87,  +2.48,  +1.64
  1,     UK002H,       0,  0.064152, 2459440.449526577722, 321.29270,  13.22794,              151.85068,  47.02672,       151.84855,       47.02503,    321.29270,     +13.22794,     321.29491,      +13.22674,  2131634.54, -3322073.72,  5129850.43,      52.606314,       -1.728936,  107936.07,  146444.06,    2372.43,             4218.64,    81.88,  58313.58,           56615.66,     -1.67,      5.45,           8.03,  +1.68,  +0.85
  2,     UK002H,       0,  0.104824, 2459440.449527048506, 320.78126,  12.47336,              152.86081,  46.44470,       152.84733,       46.43416,    320.78126,     +12.47336,     320.79385,      +12.46584,  2130843.19, -3323023.24,  5127853.82,      52.592985,       -1.746216,  106575.83,  145978.58,    4720.67,             6566.89,     3.57,  57736.11,           56615.66,    -10.46,     34.21,          50.55,  +1.46,  +0.64
  3,     UK002H,       0,  0.145452, 2459440.449527518824, 320.31709,  11.76544,              153.77105,  45.88817,       153.75698,       45.87731,    320.31709,     +11.76544,     320.33033,      +11.75762,  2130111.81, -3323900.80,  5126008.52,      52.580659,       -1.762196,  105319.16,  145580.61,    6890.96,             8737.18,  -250.06,  53418.61,           56615.66,    -10.87,     35.53,          52.65,  +1.66,  +0.84
  4,     UK002H,       0,  0.186236, 2459440.449527990539, 319.74485,  10.88207,              154.87616,  45.18389,       154.86286,       45.17378,    319.74485,     +10.88207,     319.75752,      +10.87472,  2129206.45, -3324987.11,  5123724.27,      52.565391,       -1.781933,  103764.22,  145132.46,    9577.52,            11423.73,     3.26,  65872.68,           58190.46,    -10.22,     33.41,          49.65,  +1.75,  +0.94
  5,     UK002H,       0,  0.226904, 2459440.449528461322, 319.27857,  10.13123,              155.77042,  44.57363,       155.77197,       44.57480,    319.27857,     +10.13123,     319.27814,      +10.13208,  2128449.82, -3325894.96,  5121815.28,      52.552624,       -1.798453,  102465.26,  144794.71,   11822.71,            13668.93,  -177.85,  55208.00,           58213.80,      1.19,     -3.89,           5.80,  +1.78,  +0.98
  6,     UK002H,       0,  0.267696, 2459440.449528933503, 318.72158,   9.24486,              156.81424,  43.84745,       156.82474,       43.85523,    318.72158,      +9.24486,     318.71338,       +9.25062,  2127556.99, -3326966.25,  5119562.62,      52.537548,       -1.817912,  100933.13,  144440.84,   14472.11,            16318.32,    37.84,  64948.89,           58945.75,      8.00,    -26.19,          39.11,  +1.95,  +1.15
  7,     UK002H,       0,  0.308380, 2459440.449529404286, 318.21526,   8.47735,              157.73216,  43.21776,       157.72922,       43.21561,    318.21526,      +8.47735,     318.21916,       +8.47574,  2126776.20, -3327903.10,  5117592.66,      52.524356,       -1.834947,   99593.84,  144170.34,   16789.01,            18635.23,   -72.52,  56948.77,           59084.05,     -2.24,      7.31,          10.94,  +3.62,  +2.83
  8,     UK002H,       1,  0.348928, 2459440.449529873673, 317.69082,   7.86591,              158.61091,  42.73816,       158.49793,       42.65626,    317.69082,      +7.86591,     317.79224,       +7.80429,  2126102.32, -3328711.66,  5115892.45,      52.512964,       -1.849669,   98438.35,  143966.18,   18788.66,            20634.88,  -492.02,  49315.60,           58500.00,    -86.28,    280.07,         419.87,  +6.02,  +5.23
  0,     UK003G,       0,  0.000000, 2459440.449525822420, 113.63758,  75.37712,                2.82192,  36.86722,         2.82218,       36.86502,    113.63758,     +75.37712,     113.63782,      +75.37492,  2133029.90, -3320399.47,  5133370.97,      52.629797,       -1.698487,  110335.86,  181004.90,       0.00,               78.07,  -231.31,      0.00,           60950.24,      5.36,      4.43,           7.93,  +3.87,  +2.58
  1,     UK003G,       0,  0.039980, 2459440.449526285287, 115.21742,  75.38719,                2.32537,  36.83291,         2.32612,       36.82683,    115.21742,     +75.38719,     115.21762,      +75.38107,  2132148.18, -3321457.42,  5131146.36,      52.614961,       -1.717723,  108819.25,  178700.79,    2616.40,             2694.47,    -0.17,  65442.73,           60950.24,     14.71,     12.16,          22.02,  +1.80,  +0.54
  2,     UK003G,       0,  0.079968, 2459440.449526748154, 116.59985,  75.38426,                1.89183,  36.79824,         1.89267,       36.79180,    116.59985,     +75.38426,     116.59962,      +75.37779,  2131396.33, -3322359.54,  5129249.41,      52.602302,       -1.734148,  107526.55,  176743.00,    4847.43,             4925.51,  -154.87,  55792.58,           60950.24,     15.39,     12.72,          23.30,  +1.48,  +0.24
  3,     UK003G,       0,  0.119968, 2459440.449527211022, 118.20105,  75.35846,                1.39056,  36.74386,         1.38984,       36.74908,    118.20105,     +75.35846,     118.20259,      +75.36371,  2130542.58, -3323383.93,  5127095.38,      52.587920,       -1.752773,  106059.27,  174528.04,    7380.83,             7458.90,    -7.93,  63334.93,           60950.24,    -12.34,    -10.21,          18.93,  +1.04,  -0.17
  4,     UK003G,       0,  0.159964, 2459440.449527673889, 119.78708,  75.32103,                0.89273,  36.68673,         0.89017,       36.70450,    119.78708,     +75.32103,     119.79317,      +75.33887,  2129714.39, -3324377.65,  5125005.83,      52.573958,       -1.770841,  104636.51,  172387.91,    9838.40,             9916.47,    63.41,  61445.27,           61115.89,    -41.45,    -34.32,          64.39,  +2.10,  +0.92
  5,     UK003G,       0,  0.199952, 2459440.449528136756, 121.32067,  75.29134,                0.40901,  36.64617,         0.40702,       36.65938,    121.32067,     +75.29134,     121.32687,      +75.30458,  2128932.17, -3325316.21,  5123032.25,      52.560764,       -1.787913,  103293.28,  170374.58,   12159.55,            12237.63,    -1.17,  58046.31,           60724.73,    -30.48,    -25.22,          47.90,  +1.71,  +0.55
  6,     UK003G,       0,  0.239924, 2459440.449528599158, 122.93990,  75.26045,              359.89646,  36.61258,       359.89693,       36.60955,    122.93990,     +75.26045,     122.93936,      +75.25742,  2128124.63, -3326285.15,  5120994.81,      52.547134,       -1.805528,  101907.15,  168304.57,   14555.82,            14633.90,    10.32,  59948.74,           60501.94,      6.91,      5.71,          10.98,  +1.44,  +0.31
  7,     UK003G,       0,  0.279924, 2459440.449529062491, 124.47693,  75.19624,              359.40730,  36.55421,       359.40643,       36.55955,    124.47693,     +75.19624,     124.48136,      +75.20156,  2127365.86, -3327195.58,  5119080.41,      52.534319,       -1.822087,  100605.24,  166367.70,   16807.39,            16885.47,  -124.57,  56289.21,           60057.95,    -12.04,     -9.96,          19.38,  +3.56,  +2.45

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.