Orbital Analysis for matched events on 20210813_215859.671_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 64.76° Bg 38.44° Vg 58.57km/s
mass 0.03388g, abs. mag -0.8
Path Details
------------
start -2.01° 51.87° 112.24km
end   -2.22° 51.66° 95.47km

Orbit Details
-------------
Semimajor axis 10.57A.U., eccentricity 0.91, inclination 112.62°, Period 34.34Y, LA Sun 141.07°, 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: 2459440.415968417190
Time: 2021-08-13 21:58:59.710915 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000S and UK0027
 Convergence angle = 47.92761 deg
 R.A. =  49.69123  Dec = +58.74269 deg

Best intersection: Stations UK000S and UK0027 with Qconv = 47.93 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   1393313.47 +/- 40.26 m
 Y =  -3765443.80 +/- 34.31 m
 Z =   5083923.13 +/- 136.54 m
 Vx =    19720.28 +/- 338.44 m/s
 Vy =    23564.31 +/- 311.06 m/s
 Vz =    51086.94 +/- 505.84 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.736834e+03, +1.107946e+03, +1.515054e+03, +2.483424e+03, -7.629403e+01, -6.026349e+03
+1.107946e+03, +1.259786e+03, +2.796851e+03, +4.192945e+02, +3.782667e+02, +1.435030e+03
+1.515054e+03, +2.796851e+03, +1.973471e+04, -3.363390e+03, +2.081361e+03, +5.484669e+04
+2.483424e+03, +4.192945e+02, -3.363390e+03, +1.202724e+04, +4.492045e+03, -1.962751e+04
-7.629403e+01, +3.782667e+02, +2.081361e+03, +4.492045e+03, +7.339807e+03, +1.852955e+04
-6.026349e+03, +1.435030e+03, +5.484669e+04, -1.962751e+04, +1.852955e+04, +2.544949e+05

Timing offsets (from input data):
    UK000S: -0.000437 s
    UK0027: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 21:58:59.710915 UTC
  Lon     = +-1.995863 +/- 0.0007 deg
  Lat     = +51.884347 +/- 0.0009 deg
  Lat geo = +51.700572 +/- 0.0009 deg
  Ht      =  113139.16 +/- 99.14 m

  JD dynamic   = 2459440.416769617237 
  LST apparent = 290.3058021885 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  50.07501 +/- 0.1364 deg
  Dec       = +58.97433 +/- 0.2607 deg
  Azimuth   =  31.49330 +/- 0.2449 deg
  Elevation = +31.08088 +/- 0.1704 deg
  Vavg      =  59.07373 +/- 0.3314 km/s
  Vinit     =  59.61578 +/- 0.4265 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  49.80618 +/- 0.1364 deg
  Dec       = +58.76521 +/- 0.2607 deg
  Azimuth   =  31.77262 +/- 0.2449 deg
  Elevation = +31.00486 +/- 0.1704 deg
  Vavg      =  59.20529 +/- 0.3314 km/s
  Vinit     =  59.74734 +/- 0.4265 km/s
Radiant (geocentric, J2000):
  R.A.   =  50.33355 +/- 0.1307 deg
  Dec    = +58.45047 +/- 0.2684 deg
  Vg     =  58.57461 +/- 0.4342 km/s
  Vinf   =  59.61578 +/- 0.4265 km/s
  Zc     =  59.07587 +/- 0.1700 deg
  Zg     =  59.64788 +/- 0.1794 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  64.76061 +/- 0.1830 deg
  Bg     = +38.43844 +/- 0.2369 deg
  Vh     =  40.83392 +/- 0.5006 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  85.85871 +/- 0.3306 deg
  Bh     = +63.09678 +/- 0.1097 deg
  Vh_x   =  -1.33432 +/- 0.1035 km/s
  Vh_y   = -18.42849 +/- 0.2425 km/s
  Vh_z   = -36.41455 +/- 0.4457 km/s
Orbit:
  La Sun = 141.068109 +/- -0.0000 deg
  a      =  10.565040 +/- 10.8767 AU
  e      =   0.910814 +/- 0.0430
  i      = 112.620999 +/- 0.1611 deg
  peri   = 148.574448 +/- 0.7197 deg
  node   = 141.066434 +/- 0.0000 deg
  Pi     = 289.640882 +/- 0.7197 deg
  q      =   0.942250 +/- 0.0014 AU
  f      =  31.421442 +/- 0.7197 deg
  M      =   0.635852 +/- 0.5508 deg
  Q      =  20.187830 +/- 21.7523 AU
  n      =   0.028701 +/- 0.0229 deg/day
  T      =  34.340559 +/- 86.7532 years
  Last perihelion JD = 2459418.262440 (2021-07-22 18:17:54.837220) +/- 0.7368 days
  Tj     =   0.040123 +/- 0.2432
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.946298e-03, +5.644357e-05, +3.304661e-02, +1.857147e-09, +5.554146e-04, -2.397334e-05
q   , +5.644357e-05, +2.132948e-06, +1.022172e-03, -4.225674e-11, +1.798964e-05, +5.421362e-07
Tp  , +3.304661e-02, +1.022172e-03, +5.703630e-01, +1.949273e-08, +9.688353e-03, -2.519835e-04
node, +1.857147e-09, -4.225674e-11, +1.949273e-08, +5.097124e-14, +1.698708e-10, -6.562703e-10
peri, +5.554146e-04, +1.798964e-05, +9.688353e-03, +1.698708e-10, +1.658770e-04, -2.204428e-06
i   , -2.397334e-05, +5.421362e-07, -2.519835e-04, -6.562703e-10, -2.204428e-06, +8.449707e-06

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.000470
 a2 = 23.869133

Mean time residuals from time vs. length:
  Station with reference time: UK0027
  Avg. res. = 3.081e-06 s
  Stddev    = 1.76e-03 s

Begin point on the trajectory:
  Lon =    -2.006986 +/- 0.0003 deg
  Lat =    51.873108 +/- 0.0005 deg
  Ht  = 112239.80 +/- 73.56 m
End point on the trajectory:
  Lon =    -2.217062 +/- 0.0005 deg
  Lat =    51.662052 +/- 0.0009 deg
  Ht  = 95474.21 +/- 111.76 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
    UK000S,   False,    -1.778230,    50.857470,   24.00,   0.000425,  24.039727,   112116.62,    95474.21,          0.011292,     12.47,     27.11,              33.37, 1.0000,    True,    True, {"ff_name": "FF_UK000S_20210813_215859_555_0165376.fits"}
    UK0027,   False,    -2.374601,    51.371449,   48.00,   0.192299,  20.503996,   112239.80,   103653.92,          0.015690,     13.43,     30.73,              30.15, 1.0000,    True,   False, {"ff_name": "FF_UK0027_20210813_215853_501_0158976.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,     UK000S,       0,  0.033785, 2459440.415969077498, 150.92332,  81.07156,              351.99499,  43.75465,       351.99720,       43.76353,    150.92332,     +81.07156,     150.94729,      +81.07978,  1392658.14, -3766226.87,  5082225.45,      51.871568,       -2.008582,  112116.62,  160561.23,       0.00,             1981.10,   307.49,      0.00,           57552.95,    -22.96,    -10.57,          32.48,  +3.03,  +2.00
  1,     UK000S,       0,  0.073681, 2459440.415969539434, 153.42848,  80.90646,              351.41972,  43.84838,       351.41679,       43.83614,    153.42848,     +80.90646,     153.39330,      +80.89537,  1391963.05, -3767057.45,  5080424.78,      51.858008,       -2.022160,  111032.52,  158819.55,    2101.29,             4082.40,    30.35,  52669.30,           57552.95,     31.28,     14.38,          44.71,  +2.81,  +1.81
  2,     UK000S,       0,  0.113573, 2459440.415970000904, 156.26344,  80.66808,              350.71928,  43.93765,       350.71525,       43.91998,    156.26344,     +80.66808,     156.20936,      +80.65250,  1391143.63, -3768036.60,  5078302.00,      51.842015,       -2.038132,  109755.13,  156777.57,    4578.47,             6559.57,   129.33,  62097.00,           57552.95,     44.53,     20.47,          64.48,  +1.67,  +0.69
  3,     UK000S,       0,  0.153481, 2459440.415970462840, 158.73010,  80.41516,              350.06182,  44.00347,       350.05979,       43.99411,    158.73010,     +80.41516,     158.70046,      +80.40712,  1390399.36, -3768925.94,  5076373.92,      51.827481,       -2.052650,  108595.48,  154934.14,    6828.44,             8809.54,     0.15,  56378.89,           57552.95,     23.28,     10.71,          34.11,  +1.23,  +0.28
  4,     UK000S,       0,  0.193373, 2459440.415970924776, 161.13770,  80.16299,              349.40693,  44.08640,       349.40242,       44.06449,    161.13770,     +80.16299,     161.06533,      +80.14470,  1389672.15, -3769794.91,  5074490.02,      51.813273,       -2.066835,  107462.94,  153143.64,    9026.84,            11007.95,  -179.63,  55108.98,           57098.24,     53.79,     24.72,          79.73,  +1.17,  +0.24
  5,     UK000S,       0,  0.233269, 2459440.415971386246, 163.64982,  79.83716,              348.65425,  44.15280,       348.65182,       44.14019,    163.64982,     +79.83716,     163.60740,      +79.82697,  1388863.27, -3770761.46,  5072394.56,      51.797462,       -2.082590,  106203.84,  151164.68,   11472.14,            13453.24,  -112.77,  61291.80,           57567.38,     30.53,     14.04,          45.85,  +0.78,  -0.12
  6,     UK000S,       0,  0.273157, 2459440.415971848182, 166.08768,  79.49220,              347.88397,  44.22459,       347.88181,       44.21254,    166.08768,     +79.49220,     166.04655,      +79.48278,  1388056.86, -3771725.06,  5070305.49,      51.781691,       -2.098292,  104949.26,  149205.71,   13909.97,            15891.07,   -52.90,  61116.76,           58115.12,     28.75,     13.22,          43.75,  +0.68,  -0.19
  7,     UK000S,       0,  0.313053, 2459440.415972309653, 168.38474,  79.11311,              347.09161,  44.28235,       347.09143,       44.28125,    168.38474,     +79.11311,     168.38199,      +79.11227,  1387252.41, -3772686.32,  5068221.50,      51.765951,       -2.113952,  103698.37,  147265.91,   16341.88,            18322.98,     0.58,  60956.19,           58580.12,      2.60,      1.20,           4.01,  +0.54,  -0.30
  8,     UK000S,       0,  0.352937, 2459440.415972771589, 170.57179,  78.71615,              346.28761,  44.34024,       346.28838,       44.34530,    170.57179,     +78.71615,     170.59112,      +78.71983,  1386457.99, -3773635.60,  5066163.49,      51.750398,       -2.129414,  102463.71,  145365.00,   18743.47,            20724.57,    24.46,  60214.55,           58906.05,    -11.74,     -5.41,          18.35,  +0.46,  -0.35
  9,     UK000S,       0,  0.392805, 2459440.415973232593, 172.70164,  78.32528,              345.48876,  44.42019,       345.48644,       44.40349,    172.70164,     +78.32528,     172.64382,      +78.31356,  1385686.55, -3774557.41,  5064165.00,      51.735288,       -2.144429,  101265.38,  143533.66,   21075.60,            23056.70,   -20.17,  58496.21,           59049.65,     38.18,     17.56,          60.40,  +0.41,  -0.37
 10,     UK000S,       0,  0.432689, 2459440.415973694529, 174.70135,  77.86760,              344.62811,  44.46444,       344.62751,       44.45953,    174.70135,     +77.86760,     174.68568,      +77.86429,  1384882.77, -3775517.86,  5062082.76,      51.719536,       -2.160062,  100017.48,  141641.32,   23505.46,            25486.56,    31.97,  60923.23,           59213.12,     11.06,      5.09,          17.74,  +0.30,  -0.46
 11,     UK000S,       0,  0.472573, 2459440.415974156000, 176.54506,  77.40289,              343.77530,  44.50401,       343.77580,       44.50859,    176.54506,     +77.40289,     176.56294,      +77.40588,  1384107.92, -3776443.76,  5060075.43,      51.704344,       -2.175133,   98815.08,  139833.03,   25847.91,            27829.01,    -3.29,  58731.54,           59288.93,    -10.20,     -4.70,          16.56,  +0.30,  -0.43
 12,     UK000S,       0,  0.512433, 2459440.415974617470, 178.42321,  76.90851,              342.87077,  44.55762,       342.87041,       44.55377,    178.42321,     +76.90851,     178.41191,      +76.90610,  1383306.61, -3777401.26,  5057999.59,      51.688625,       -2.190709,   97572.29,  137980.03,   28270.31,            30251.41,    42.82,  60772.63,           59383.61,      8.44,      3.89,          13.89,  +0.42,  -0.28
 13,     UK000S,       0,  0.552333, 2459440.415975079406, 179.82543,  76.47956,              342.11804,  44.58144,       342.11837,       44.58555,    179.82543,     +76.47956,     179.84165,      +76.48205,  1382658.86, -3778175.28,  5056321.54,      51.675912,       -2.203328,   96568.09,  136495.74,   30228.50,            32209.61,  -377.66,  49077.62,           59148.62,     -8.93,     -4.11,          14.85,  +1.13,  +0.45
 14,     UK000S,       0,  0.592217, 2459440.415975540876, 181.30130,  75.99558,              341.27916,  44.60633,       341.27975,       44.61526,    181.30130,     +75.99558,     181.33360,      +76.00081,  1381952.94, -3779018.80,  5054492.80,      51.662052,       -2.217062,   95474.21,  134891.88,   32362.55,            34343.66,  -621.32,  53506.43,           58854.83,    -19.12,     -8.81,          32.19,  +2.75,  +2.10
  0,     UK0027,       1,  0.000000, 2459440.415968417190, 336.76964,  73.66264,               24.57266,  60.43295,        24.55275,       60.43098,    336.76964,     +73.66264,     336.76240,      +73.67246,  1393350.56, -3765399.48,  5084019.22,      51.885070,       -1.994981,  113197.04,  129728.57,       0.00,              112.13,   452.63,      0.00,           58592.03,     20.77,     -9.10,          36.06,  +3.97,  +3.40
  1,     UK0027,       0,  0.039704, 2459440.415968876332, 335.28294,  73.61117,               24.32878,  60.83763,        24.37444,       60.84218,    335.28294,     +73.61117,     335.30053,      +73.58902,  1392737.10, -3766132.52,  5082430.01,      51.873108,       -2.006986,  112239.80,  128127.36,    1854.52,             1742.40,  -284.09,  46708.73,           58592.03,    -46.54,     20.31,          81.75,  +2.38,  +1.84
  2,     UK0027,       0,  0.079248, 2459440.415969334077, 333.17969,  73.45805,               24.08551,  61.44178,        24.10870,       61.44409,    333.17969,     +73.45805,     333.18989,      +73.44710,  1391864.08, -3767175.71,  5080168.39,      51.856077,       -2.023995,  110878.21,  125861.88,    4493.71,             4381.58,    -2.35,  66740.52,           58592.03,    -22.80,      9.96,          40.78,  +1.66,  +1.16
  3,     UK0027,       0,  0.118824, 2459440.415969792288, 331.27774,  73.28769,               23.87355,  62.00310,        23.85229,       62.00099,    331.27774,     +73.28769,     331.26787,      +73.29747,  1391082.93, -3768109.13,  5078144.76,      51.840830,       -2.039227,  109660.53,  123847.28,    6855.18,             6743.05,    -0.23,  59669.29,           58592.03,     20.20,     -8.84,          36.72,  +1.20,  +0.74
  4,     UK0027,       0,  0.158388, 2459440.415970250033, 329.31044,  73.10825,               23.60523,  62.58620,        23.57395,       62.58308,    329.31044,     +73.10825,     329.29479,      +73.12223,  1390291.91, -3769054.34,  5076095.57,      51.825382,       -2.054645,  108428.11,  121820.14,    9246.49,             9134.36,    32.43,  60441.44,           59341.01,     28.70,    -12.56,          53.05,  +0.75,  +0.32
  5,     UK0027,       0,  0.197944, 2459440.415970707778, 327.35674,  72.89970,               23.33608,  63.18163,        23.27860,       63.17590,    327.35674,     +72.89970,     327.32589,      +72.92460,  1389511.68, -3769986.66,  5074074.31,      51.810137,       -2.069850,  107213.10,  119833.96,   11605.19,            11493.06,    32.97,  59629.49,           59596.36,     50.89,    -22.28,          95.62,  +0.73,  +0.34
  6,     UK0027,       0,  0.237516, 2459440.415971165989, 325.43740,  72.69897,               23.00207,  63.76486,        22.97367,       63.76201,    325.43740,     +72.69897,     325.42182,      +72.71089,  1388764.12, -3770879.94,  5072137.70,      51.795524,       -2.084421,  106049.55,  117943.93,   13865.11,            13752.98,   -66.22,  57109.01,           59421.19,     24.28,    -10.61,          46.34,  +0.37,  +0.01
  7,     UK0027,       0,  0.277056, 2459440.415971623734, 323.39834,  72.47028,               22.60367,  64.39284,        22.62968,       64.39547,    323.39834,     +72.47028,     323.41486,      +72.45974,  1387981.12, -3771815.57,  5070109.27,      51.780210,       -2.099670,  104831.45,  115978.78,   16232.18,            16120.05,   -56.36,  59865.12,           59385.14,    -21.41,      9.33,          41.54,  +0.11,  -0.21
  8,     UK0027,       0,  0.316588, 2459440.415972081013, 321.46334,  72.18931,               22.26858,  65.02797,        22.26910,       65.02802,    321.46334,     +72.18931,     321.46475,      +72.18910,  1387223.83, -3772720.48,  5068147.44,      51.765391,       -2.114420,  103653.92,  114092.79,   18521.53,            18409.40,  -123.74,  57911.43,           59270.18,     -0.41,      0.18,           0.82,  +0.03,  -0.26

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.