Orbital Analysis for matched events on 20210813_003107.352_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 62.33° Bg 38.73° Vg 58.54km/s
mass 0.05690g, abs. mag -1.3
Path Details
------------
start -0.63° 54.32° 108.51km
end   -0.76° 54.26° 95.95km

Orbit Details
-------------
Semimajor axis 9.73A.U., eccentricity 0.90, inclination 112.60°, Period 30.35Y, LA Sun 140.21°, 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: 2459439.521612870973
Time: 2021-08-13 00:31:07.352052 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0026 and UK003B
 Convergence angle = 28.33572 deg
 R.A. =  47.31820  Dec = +58.42207 deg

Best intersection: Stations UK0026 and UK003B with Qconv = 28.34 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3243579.70 +/- 66.15 m
 Y =  -1962924.92 +/- 19.79 m
 Z =   5246007.06 +/- 142.98 m
 Vx =    21500.87 +/- 807.19 m/s
 Vy =    22688.42 +/- 429.10 m/s
 Vz =    50720.62 +/- 827.11 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+3.061995e+03, -7.541222e+02, -4.805825e+03, +1.222497e+04, -3.396384e+03, -2.268906e+04
-7.541222e+02, +4.177773e+02, +1.698752e+03, -3.114752e+03, +2.569273e+03, +6.223692e+03
-4.805825e+03, +1.698752e+03, +9.527244e+03, -1.692639e+04, +9.063734e+03, +3.749375e+04
+1.222497e+04, -3.114752e+03, -1.692639e+04, +6.344751e+04, -1.654394e+04, -9.996506e+04
-3.396384e+03, +2.569273e+03, +9.063734e+03, -1.654394e+04, +1.810882e+04, +3.501229e+04
-2.268906e+04, +6.223692e+03, +3.749375e+04, -9.996506e+04, +3.501229e+04, +1.965241e+05

Timing offsets (from input data):
    UK001L: 0.000000 s
    UK0026: 0.000000 s
    UK003B: 0.000234 s

Reference point on the trajectory:
  Time: 2021-08-13 00:31:07.352052 UTC
  Lon     = +-0.633168 +/- 0.0004 deg
  Lat     = +54.323809 +/- 0.0012 deg
  Lat geo = +54.144352 +/- 0.0012 deg
  Ht      =  108480.99 +/- 84.16 m

  JD dynamic   = 2459439.522413611878 
  LST apparent = 328.8188312453 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  46.53940 +/- 0.6460 deg
  Dec       = +58.35553 +/- 0.5773 deg
  Azimuth   =  51.63189 +/- 0.9967 deg
  Elevation = +49.16749 +/- 0.1283 deg
  Vavg      =  57.86019 +/- 0.6246 km/s
  Vinit     =  59.57879 +/- 0.6085 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  46.64625 +/- 0.6460 deg
  Dec       = +58.13485 +/- 0.5773 deg
  Azimuth   =  51.88289 +/- 0.9967 deg
  Elevation = +49.00987 +/- 0.1283 deg
  Vavg      =  58.00239 +/- 0.6246 km/s
  Vinit     =  59.72099 +/- 0.6085 km/s
Radiant (geocentric, J2000):
  R.A.   =  46.74644 +/- 0.6410 deg
  Dec    = +58.08792 +/- 0.5832 deg
  Vg     =  58.53606 +/- 0.6189 km/s
  Vinf   =  59.57879 +/- 0.6085 km/s
  Zc     =  40.94410 +/- 0.1282 deg
  Zg     =  41.32177 +/- 0.1305 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  62.33219 +/- 0.6459 deg
  Bg     = +38.73258 +/- 0.4472 deg
  Vh     =  40.74209 +/- 0.8219 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  81.53684 +/- 1.3196 deg
  Bh     = +64.02216 +/- 0.1492 deg
  Vh_x   =  -2.62646 +/- 0.3835 km/s
  Vh_y   = -17.65166 +/- 0.4073 km/s
  Vh_z   = -36.62565 +/- 0.7464 km/s
Orbit:
  La Sun = 140.209253 +/- 0.0000 deg
  a      =   9.729917 +/- 40.6859 AU
  e      =   0.901559 +/- 0.0743
  i      = 112.597745 +/- 0.3294 deg
  peri   = 152.207729 +/- 0.4207 deg
  node   = 140.208620 +/- 0.0000 deg
  Pi     = 292.416349 +/- 0.4207 deg
  q      =   0.957827 +/- 0.0024 AU
  f      =  27.788381 +/- 0.4207 deg
  M      =   0.646467 +/- nan deg
  Q      =  18.502006 +/- 81.3716 AU
  n      =   0.032474 +/- 0.0170 deg/day
  T      =  30.350394 +/- 498887512.3176 years
  Last perihelion JD = 2459419.615410 (2021-07-24 02:46:11.448670) +/- 0.2472 days
  Tj     =   0.080227 +/- 0.4070
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.507964e-03, -5.691424e-05, +6.953375e-03, +6.724825e-09, -4.190943e-05, -9.117452e-05
q   , -5.691424e-05, +3.617918e-06, -2.114041e-05, -2.797116e-10, +8.081811e-06, +3.797089e-06
Tp  , +6.953375e-03, -2.114041e-05, +7.172377e-02, +2.725010e-08, +8.746142e-04, -3.686612e-04
node, +6.724825e-09, -2.797116e-10, +2.725010e-08, +7.679818e-14, -2.934959e-10, -1.041170e-09
peri, -4.190943e-05, +8.081811e-06, +8.746142e-04, -2.934959e-10, +2.992238e-05, +4.000465e-06
i   , -9.117452e-05, +3.797089e-06, -3.686612e-04, -1.041170e-09, +4.000465e-06, +1.411539e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.000000
 a2 = 97.710222

Mean time residuals from time vs. length:
  Station with reference time: UK0026
  Avg. res. = 1.317e-05 s
  Stddev    = 3.63e-03 s

Begin point on the trajectory:
  Lon =    -0.632898 +/- 0.0004 deg
  Lat =    54.323935 +/- 0.0012 deg
  Ht  = 108507.43 +/- 78.41 m
End point on the trajectory:
  Lon =    -0.762804 +/- 0.0003 deg
  Lat =    54.264219 +/- 0.0010 deg
  Ht  = 95951.82 +/- 73.42 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
    UK001L,    True,    -1.306160,    51.883100,   80.00,  41.548901,   0.000000,   105834.19,    96914.34,          0.114308,       nan,       nan,              41.61, 0.0000,    True,    True, {"ff_name": "FF_UK001L_20210813_003106_984_0367872.fits"}
    UK0026,   False,    -0.023645,    52.984073,    6.00,   0.091689,  28.342338,   108507.43,    96007.72,          0.010602,     20.46,     27.08,              49.02, 1.0000,    True,    True, {"ff_name": "FF_UK0026_20210813_003106_210_0388864.fits"}
    UK003B,   False,    -1.072290,    52.276980,  129.00,   0.000046,  56.815815,   106353.03,    95951.82,          0.010508,     41.40,     19.08,              40.33, 1.0000,    True,    True, {"ff_name": "FF_UK003B_20210813_003100_192_0387072.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,     UK001L,       1,  0.054138, 2459439.521613497753, 132.54601,  57.01706,                8.94287,  19.65151,         8.83541,       19.73714,    132.54601,     +57.01706,     132.70183,      +57.11911,  3242317.11, -1964257.24,  5243028.60,      54.311258,       -0.660502,  105834.19,  295478.39,       0.00,             3498.63,   238.71,      0.00,           57447.61,   -219.64,   -647.32,         477.18,  +3.07,  +0.72
  1,     UK001L,       1,  0.094326, 2459439.521613962483, 132.93858,  56.88815,                8.74294,  19.48732,         8.66429,       19.55000,    132.93858,     +56.88815,     133.05314,      +56.96260,  3241646.98, -1964964.39,  5241447.77,      54.304590,       -0.675060,  104429.69,  294116.46,    1856.92,             5355.55,  -298.72,  46205.88,           57447.61,   -160.58,   -471.76,         349.49,  +1.72,  -0.62
  2,     UK001L,       1,  0.134602, 2459439.521614429075, 133.40381,  56.66433,                8.51676,  19.22363,         8.43043,       19.29234,    133.40381,     +56.66433,     133.53004,      +56.74560,  3240735.41, -1965926.31,  5239297.36,      54.295512,       -0.694805,  102519.50,  292273.27,    4382.89,             7881.53,  -172.34,  62716.55,           57447.61,   -175.13,   -514.79,         383.75,  +1.66,  -0.67
  3,     UK001L,       1,  0.174870, 2459439.521614894737, 133.89371,  56.46078,                8.27015,  18.97868,         8.19846,       19.03571,    133.89371,     +56.46078,     133.99910,      +56.52793,  3239839.75, -1966871.44,  5237184.49,      54.286584,       -0.714212,  100643.05,  290472.33,    6864.77,            10363.40,   -89.59,  61633.84,           57447.61,   -144.86,   -425.07,         318.89,  +1.63,  -0.69
  4,     UK001L,       1,  0.215162, 2459439.521615361329, 134.33032,  56.21062,                8.05945,  18.69339,         7.96085,       18.77167,    134.33032,     +56.21062,     134.47548,      +56.30242,  3238930.69, -1967830.71,  5235040.03,      54.277514,       -0.733909,   98738.95,  288654.90,    9383.75,            12882.39,    28.85,  62518.31,           59057.15,   -197.57,   -581.23,         438.67,  +1.09,  -1.21
  5,     UK001L,       1,  0.255434, 2459439.521615827456, 134.77525,  55.98325,                7.83745,  18.43072,         7.73091,       18.51519,    134.77525,     +55.98325,     134.93251,      +56.08189,  3238059.41, -1968750.11,  5232984.67,      54.268813,       -0.752797,   96914.34,  286922.98,   11798.07,            15296.70,    43.81,  59950.30,           59644.26,   -212.15,   -624.50,         474.14,  +1.32,  -0.97
  0,     UK0026,       0,  0.000000, 2459439.521612870973, 184.65049,  68.40484,              345.13706,  34.15339,       345.12907,       34.16190,    184.65049,     +68.40484,     184.67649,      +68.40980,  3243592.31, -1962911.61,  5246036.80,      54.323935,       -0.632898,  108507.43,  189837.38,       0.00,               34.93,     0.47,      0.00,           59444.26,    -28.47,    -21.53,          38.79,  +3.04,  +1.65
  1,     UK0026,       0,  0.040180, 2459439.521613336168, 185.36607,  67.91377,              344.59586,  33.82076,       344.59688,       33.81967,    185.36607,     +67.91377,     185.36296,      +67.91315,  3242727.47, -1963824.22,  5243996.65,      54.315339,       -0.651633,  106694.36,  188296.25,    2396.45,             2361.52,   -66.82,  59642.98,           59444.26,      3.62,      2.74,           4.97,  +1.60,  +0.23
  2,     UK0026,       0,  0.080388, 2459439.521613801364, 186.03929,  67.38151,              344.04442,  33.44920,       344.03871,       33.45521,    186.03929,     +67.38151,     186.05753,      +67.38488,  3241827.69, -1964773.69,  5241874.06,      54.306389,       -0.671121,  104808.41,  186712.04,    4889.74,             4854.81,    30.92,  62009.71,           59444.26,    -19.93,    -15.07,          27.61,  +1.08,  -0.28
  3,     UK0026,       0,  0.120576, 2459439.521614266559, 186.64004,  66.89425,              343.54062,  33.11081,       343.53208,       33.11974,    186.64004,     +66.89425,     186.66686,      +66.89918,  3241018.09, -1965628.02,  5239964.20,      54.298328,       -0.688676,  103111.80,  185304.09,    7133.16,             7098.22,  -120.01,  55823.07,           59444.26,    -29.52,    -22.32,          41.19,  +1.14,  -0.20
  4,     UK0026,       0,  0.160780, 2459439.521614731755, 187.28139,  66.35321,              342.98631,  32.73534,       342.97603,       32.74602,    187.28139,     +66.35321,     187.31313,      +66.35900,  3240135.78, -1966559.06,  5237882.83,      54.289535,       -0.707794,  101263.21,  183788.51,    9578.03,             9543.09,   -70.45,  60811.61,           59441.27,    -35.15,    -26.58,          49.46,  +1.13,  -0.19
  5,     UK0026,       0,  0.200976, 2459439.521615196951, 187.95364,  65.80379,              342.40836,  32.36276,       342.41076,       32.36029,    187.95364,     +65.80379,     187.94739,      +65.80248,  3239245.85, -1967498.14,  5235783.49,      54.280659,       -0.727079,   99399.04,  182280.43,   12044.01,            12009.07,     0.70,  61348.86,           59712.93,      8.10,      6.12,          11.49,  +1.14,  -0.16
  6,     UK0026,       0,  0.241172, 2459439.521615662146, 188.56926,  65.26148,              341.85298,  31.99109,       341.86289,       31.98092,    188.56926,     +65.26148,     188.54143,      +65.25615,  3238390.14, -1968401.11,  5233764.88,      54.272116,       -0.745631,   97606.91,  180850.44,   14415.17,            14380.24,   -22.96,  58990.04,           59732.49,     33.23,     25.10,          47.50,  +1.09,  -0.20
  7,     UK0026,       0,  0.281356, 2459439.521616127342, 189.09002,  64.76494,              341.35896,  31.64653,       341.37008,       31.63518,    189.09002,     +64.76494,     189.05937,      +64.75909,  3237626.42, -1969207.01,  5231963.26,      54.264486,       -0.762209,   96007.72,  179591.44,   16531.44,            16496.50,  -300.81,  52664.35,           59151.83,     36.97,     27.91,          53.20,  +1.85,  +0.58
  8,     UK0026,       1,  0.321484, 2459439.521616592072, 189.64219,  64.33843,              340.88412,  31.37392,       340.93254,       31.32470,    189.64219,     +64.33843,     189.50687,      +64.31338,  3236953.14, -1969917.48,  5230374.99,      54.257753,       -0.776846,   94598.12,  178495.46,   18397.09,            18362.16,  -825.94,  46492.61,           58038.48,    159.97,    120.50,         231.44,  +5.39,  +4.13
  0,     UK003B,       0,  0.045104, 2459439.521613390651, 135.40918,  60.98273,                6.83049,  23.73280,         6.82847,       23.73457,    135.40918,     +60.98273,     135.41260,      +60.98476,  3242564.64, -1963996.04,  5243612.53,      54.313720,       -0.655149,  106353.03,  253580.15,       0.00,             2812.72,    91.03,      0.00,           59431.36,     -4.74,    -10.31,           9.23,  +1.90,  -0.12
  1,     UK003B,       0,  0.085296, 2459439.521613855846, 135.89614,  60.81831,                6.60121,  23.53532,         6.60973,       23.52786,    135.89614,     +60.81831,     135.88286,      +60.80980,  3241877.89, -1964720.72,  5241992.49,      54.306888,       -0.670063,  104913.62,  252155.84,    1902.98,             4715.70,  -400.59,  47347.21,           59431.36,     19.90,     43.17,          38.88,  +1.22,  -0.79
  2,     UK003B,       0,  0.125612, 2459439.521614322439, 136.62978,  60.54243,                6.25575,  23.21191,         6.26783,       23.20134,    136.62978,     +60.54243,     136.61085,      +60.53046,  3240810.86, -1965846.69,  5239475.35,      54.296263,       -0.693146,  102677.60,  249956.27,    4859.73,             7672.45,   154.19,  73339.40,           59431.36,     28.00,     60.72,          55.18,  +1.39,  -0.60
  3,     UK003B,       0,  0.165844, 2459439.521614788100, 137.15484,  60.33558,                6.00642,  22.97256,         6.01822,       22.96225,    137.15484,     +60.33558,     137.13645,      +60.32395,  3240042.63, -1966657.35,  5237663.10,      54.288607,       -0.709815,  101068.07,  248382.17,    6988.48,             9801.20,  -114.04,  52911.82,           59431.36,     27.19,     58.96,          53.91,  +1.23,  -0.75
  4,     UK003B,       0,  0.206136, 2459439.521615254227, 137.78560,  60.07127,                5.70508,  22.67098,         5.71108,       22.66574,    137.78560,     +60.07127,     137.77671,      +60.06540,  3239104.96, -1967646.81,  5235451.13,      54.279253,       -0.730126,   99103.95,  246472.53,    9586.76,            12399.48,    83.70,  64486.34,           60255.59,     13.73,     29.78,          27.45,  +0.97,  -0.99
  5,     UK003B,       0,  0.246392, 2459439.521615720354, 138.33572,  59.84020,                5.43867,  22.40885,         5.44262,       22.40541,    138.33572,     +59.84020,     138.33031,      +59.83636,  3238294.93, -1968501.58,  5233540.27,      54.271165,       -0.747698,   97407.52,  244833.01,   11831.35,            14644.07,   -70.12,  55757.78,           59848.49,      8.97,     19.46,          18.05,  +1.25,  -0.69
  6,     UK003B,       0,  0.286620, 2459439.521616185550, 138.79142,  59.62766,                5.21792,  22.17177,         5.20976,       22.17886,    138.79142,     +59.62766,     138.80592,      +59.63553,  3237599.73, -1969235.17,  5231900.29,      54.264219,       -0.762804,   95951.82,  243433.54,   13757.74,            16570.46,  -540.47,  47886.83,           58422.68,    -18.40,    -39.96,          37.28,  +2.70,  +0.77

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.