Orbital Analysis for matched events on 20210810_000951.077_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 56.31° Bg 37.45° Vg 59.11km/s
mass 0.13411g, abs. mag -1.7
Path Details
------------
start -0.76° 49.10° 108.33km
end   -0.96° 48.99° 90.18km

Orbit Details
-------------
Semimajor axis 7.34A.U., eccentricity 0.87, inclination 115.25°, Period 19.90Y, LA Sun 137.32°, last Perihelion 2021-07-25

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: 2459436.506841173396
Time: 2021-08-10 00:09:51.077381 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002D and UK0038
 Convergence angle = 6.07146 deg
 R.A. =  41.17874  Dec = +55.95767 deg

Best intersection: Stations UK002D and UK0038 with Qconv = 6.07 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3278767.66 +/- 233.07 m
 Y =  -2712105.52 +/- 73.50 m
 Z =   4879665.11 +/- 71.56 m
 Vx =    26400.48 +/- 1024.82 m/s
 Vy =    21615.88 +/- 365.90 m/s
 Vz =    49525.70 +/- 374.56 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+5.757403e+04, -1.772280e+04, -1.729757e+04, +1.726546e+05, -5.650885e+04, -5.782045e+04
-1.772280e+04, +5.714293e+03, +5.367901e+03, -5.625854e+04, +1.914903e+04, +1.878458e+04
-1.729757e+04, +5.367901e+03, +5.446383e+03, -5.265337e+04, +1.695594e+04, +1.780719e+04
+1.726546e+05, -5.625854e+04, -5.265337e+04, +1.031136e+06, -3.722861e+05, -3.779449e+05
-5.650885e+04, +1.914903e+04, +1.695594e+04, -3.722861e+05, +1.380769e+05, +1.364548e+05
-5.782045e+04, +1.878458e+04, +1.780719e+04, -3.779449e+05, +1.364548e+05, +1.400712e+05

Timing offsets (from input data):
    UK002D: -0.000401 s
    UK0038: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-10 00:09:51.077381 UTC
  Lon     = +-0.759370 +/- 0.0013 deg
  Lat     = +49.098750 +/- 0.0019 deg
  Lat geo = +48.911391 +/- 0.0019 deg
  Ht      =  108319.71 +/- 95.57 m

  JD dynamic   = 2459436.507641914301 
  LST apparent = 320.4033925361 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  39.30953 +/- 1.6263 deg
  Dec       = +55.43501 +/- 0.5676 deg
  Azimuth   =  50.63940 +/- 1.2457 deg
  Elevation = +43.93947 +/- 0.5226 deg
  Vavg      =  58.79857 +/- 0.0662 km/s
  Vinit     =  60.14172 +/- 0.0592 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  39.40890 +/- 1.6263 deg
  Dec       = +55.19678 +/- 0.5676 deg
  Azimuth   =  50.89831 +/- 1.2457 deg
  Elevation = +43.78104 +/- 0.5226 deg
  Vavg      =  58.97187 +/- 0.0662 km/s
  Vinit     =  60.31502 +/- 0.0592 km/s
Radiant (geocentric, J2000):
  R.A.   =  39.58521 +/- 1.6345 deg
  Dec    = +55.15114 +/- 0.5642 deg
  Vg     =  59.10920 +/- 0.0602 km/s
  Vinf   =  60.14172 +/- 0.0592 km/s
  Zc     =  46.17953 +/- 0.5255 deg
  Zg     =  46.60252 +/- 0.5303 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  56.30724 +/- 1.3229 deg
  Bg     = +37.45391 +/- 0.2009 deg
  Vh     =  40.36567 +/- 0.2818 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  69.88868 +/- 3.1998 deg
  Bh     = +62.93976 +/- 0.2227 deg
  Vh_x   =  -6.31418 +/- 0.9720 km/s
  Vh_y   = -17.24375 +/- 0.4731 km/s
  Vh_z   = -35.94679 +/- 0.1883 km/s
Orbit:
  La Sun = 137.315702 +/- -0.0000 deg
  a      =   7.343555 +/- 6.7642 AU
  e      =   0.866486 +/- 0.0257
  i      = 115.253785 +/- 0.5236 deg
  peri   = 158.319896 +/- 2.4996 deg
  node   = 137.314662 +/- 0.0000 deg
  Pi     = 295.634559 +/- 2.4996 deg
  q      =   0.980471 +/- 0.0107 AU
  f      =  21.676067 +/- 2.4996 deg
  M      =   0.791576 +/- 0.1750 deg
  Q      =  13.706639 +/- 13.5380 AU
  n      =   0.049527 +/- 0.0106 deg/day
  T      =  19.900325 +/- 45.2178 years
  Last perihelion JD = 2459420.525010 (2021-07-25 00:36:00.821150) +/- 1.4689 days
  Tj     =   0.202709 +/- 0.1264
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +7.010874e-04, -2.892137e-04, -3.963804e-02, +1.874849e-08, -1.179709e-03, -2.458796e-04
q   , -2.892137e-04, +1.216835e-04, +1.671137e-02, -7.837716e-09, +4.965984e-04, +1.028047e-04
Tp  , -3.963804e-02, +1.671137e-02, +2.324227e+00, -1.088267e-06, +6.876375e-02, +1.426599e-02
node, +1.874849e-08, -7.837716e-09, -1.088267e-06, +5.224987e-13, -3.222664e-08, -6.850116e-09
peri, -1.179709e-03, +4.965984e-04, +6.876375e-02, -3.222664e-08, +2.037607e-03, +4.225384e-04
i   , -2.458796e-04, +1.028047e-04, +1.426599e-02, -6.850116e-09, +4.225384e-04, +8.980998e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.000000
 a2 = 70.659298

Mean time residuals from time vs. length:
  Station with reference time: UK0038
  Avg. res. = 4.901e-06 s
  Stddev    = 2.21e-03 s

Begin point on the trajectory:
  Lon =    -0.759231 +/- 0.0013 deg
  Lat =    49.098826 +/- 0.0019 deg
  Ht  = 108332.64 +/- 97.72 m
End point on the trajectory:
  Lon =    -0.957636 +/- 0.0013 deg
  Lat =    48.992579 +/- 0.0029 deg
  Ht  = 90179.57 +/- 101.79 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
    UK002D,   False,    -1.801980,    51.351940,  129.00,   0.000000,   0.000000,   108233.90,    90179.57,          0.013927,     68.97,      7.05,              92.19, 1.0000,    True,    True, {"ff_name": "FF_UK002D_20210810_000949_133_0346368.fits"}
    UK0038,   False,    -2.379250,    51.361350,  169.00,   0.000003,  42.853203,   108332.64,    90266.64,          0.003409,     17.40,      3.67,              88.01, 1.0000,    True,    True, {"ff_name": "FF_UK0038_20210810_000944_320_0343040.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,     UK002D,       0,  0.004054, 2459436.506841224153, 335.73945, -16.00986,              163.10657,  21.13394,       163.08270,       21.11430,    335.73945,     -16.00986,     335.76607,      -16.02495,  3278713.37, -2712149.96,  4879563.28,      49.098251,       -0.760316,  108233.90,  284964.94,       0.00,              123.66,    -1.70,      0.00,           60521.02,     14.97,    146.88,         106.87,  +2.38,  +0.11
  1,     UK002D,       0,  0.044398, 2459436.506841691211, 335.51387, -16.42236,              163.41714,  20.76932,       163.41360,       20.76641,    335.51387,     -16.42236,     335.51801,      -16.42461,  3277700.48, -2712979.29,  4877663.14,      49.088930,       -0.777783,  106632.97,  284935.12,    2307.44,             2431.10,  -120.61,  57194.12,           60521.02,      2.23,     21.82,          15.88,  +1.96,  -0.31
  2,     UK002D,       0,  0.084782, 2459436.506842158269, 335.22898, -16.89301,              163.79616,  20.35692,       163.79827,       20.35865,    335.22898,     -16.89301,     335.22697,      -16.89167,  3276515.90, -2713949.18,  4875440.96,      49.078021,       -0.798186,  104761.24,  284924.59,    5005.96,             5129.62,   149.14,  66821.46,           60521.02,     -1.33,    -13.03,           9.48,  +1.59,  -0.68
  3,     UK002D,       0,  0.125102, 2459436.506842625327, 334.98510, -17.27893,              164.11470,  20.01944,       164.11578,       20.02033,    334.98510,     -17.27893,     334.98441,      -17.27824,  3275534.76, -2714752.51,  4873600.39,      49.068978,       -0.815115,  103211.36,  284934.80,    7241.06,             7364.72,   -40.67,  55433.99,           60521.02,     -0.68,     -6.68,           4.86,  +1.24,  -1.03
  4,     UK002D,       0,  0.165438, 2459436.506843091920, 334.71247, -17.69227,              164.46467,  19.65875,       164.45792,       19.65324,    334.71247,     -17.69227,     334.72074,      -17.69658,  3274471.94, -2715622.72,  4871606.60,      49.059174,       -0.833442,  101532.90,  284965.99,    9662.22,             9785.88,   -45.39,  60024.90,           60123.62,      4.25,     41.61,          30.28,  +0.94,  -1.33
  5,     UK002D,       0,  0.205798, 2459436.506843558978, 334.45576, -18.12691,              164.79998,  19.27323,       164.80556,       19.27779,    334.45576,     -18.12691,     334.45033,      -18.12333,  3273386.53, -2716511.41,  4869570.44,      49.049153,       -0.852157,   99819.25,  285019.25,   12134.84,            12258.50,    -0.09,  61264.02,           60173.00,     -3.53,    -34.49,          25.09,  +0.70,  -1.57
  6,     UK002D,       0,  0.246134, 2459436.506844026037, 334.17866, -18.54106,              165.14900,  18.91001,       165.14615,       18.90769,    334.17866,     -18.54106,     334.18291,      -18.54289,  3272317.96, -2717386.33,  4867565.86,      49.039280,       -0.870587,   98132.63,  285092.68,   14569.10,            14692.77,     8.30,  60349.77,           60209.57,      1.80,     17.64,          12.83,  +0.76,  -1.51
  7,     UK002D,       0,  0.286494, 2459436.506844493095, 333.89260, -18.98022,              165.50843,  18.52227,       165.50271,       18.51762,    333.89260,     -18.98022,     333.90026,      -18.98391,  3271193.02, -2718307.39,  4865455.55,      49.028877,       -0.889983,   96357.55,  285192.68,   17131.78,            17255.44,   143.65,  63495.35,           60498.72,      3.61,     35.33,          25.69,  +0.47,  -1.81
  8,     UK002D,       0,  0.326846, 2459436.506844960153, 333.64980, -19.40775,              165.82046,  18.13805,       165.83617,       18.15080,    333.64980,     -19.40775,     333.63337,      -19.39759,  3270136.03, -2719172.82,  4863472.70,      49.019095,       -0.908219,   94690.16,  285307.52,   19539.65,            19663.31,   124.69,  59671.69,           60578.51,     -9.97,    -97.23,          70.66,  +0.28,  -2.00
  9,     UK002D,       0,  0.367186, 2459436.506845427211, 333.37873, -19.82771,              166.15625,  17.76453,       166.17298,       17.77809,    333.37873,     -19.82771,     333.36126,      -19.81685,  3269062.81, -2720051.54,  4861459.41,      49.009154,       -0.926736,   92997.62,  285445.01,   21984.50,            22108.17,   143.42,  60606.22,           60620.63,    -10.63,   -103.66,          75.29,  +0.34,  -1.94
 10,     UK002D,       0,  0.407510, 2459436.506845893804, 333.10584, -20.22207,              166.48690,  17.41538,       166.49393,       17.42106,    333.10584,     -20.22207,     333.09955,      -20.21749,  3268035.23, -2720892.89,  4859531.74,      48.999628,       -0.944474,   91377.50,  285596.19,   24325.38,            24449.04,    59.14,  58051.61,           60526.91,     -4.46,    -43.57,          31.63,  +0.61,  -1.67
 11,     UK002D,       0,  0.447754, 2459436.506846359465, 332.91950, -20.52284,              166.71628,  17.14517,       166.73091,       17.15699,    332.91950,     -20.52284,     332.90469,      -20.51330,  3267275.30, -2721515.10,  4858106.14,      48.992579,       -0.957636,   90179.57,  285719.67,   26056.56,            26180.22,  -630.02,  43017.10,           59801.28,     -9.30,    -90.81,          65.90,  +2.79,  +0.51
  0,     UK0038,       0,  0.000000, 2459436.506841173396, 343.40548, -15.34521,              154.70103,  19.91898,       154.70576,       19.92332,    343.40548,     -15.34521,     343.39980,      -15.34228,  3278775.84, -2712098.82,  4879680.45,      49.098826,       -0.759231,  108332.64,  299469.77,       0.00,               18.63,   137.06,      0.00,           59578.24,     -6.71,    -31.78,          22.37,  +2.63,  +0.25
  1,     UK0038,       0,  0.040264, 2459436.506841639522, 343.17017, -15.74055,              155.04821,  19.60129,       155.04430,       19.59772,    343.17017,     -15.74055,     343.17504,      -15.74298,  3277730.14, -2712955.01,  4877718.78,      49.089203,       -0.777258,  106679.85,  299263.03,    2382.16,             2363.53,    60.42,  59163.54,           59578.24,      5.53,     26.23,          18.48,  +2.18,  -0.20
  2,     UK0038,       0,  0.080536, 2459436.506842105649, 342.94238, -16.15129,              155.39026,  19.26567,       155.38879,       19.26433,    342.94238,     -16.15129,     342.94449,      -16.15221,  3276662.96, -2713828.78,  4875716.83,      49.079376,       -0.795655,  104993.57,  299071.65,    4813.24,             4794.62,    69.48,  60366.56,           59578.24,      2.08,      9.87,           6.96,  +1.84,  -0.54
  3,     UK0038,       0,  0.120800, 2459436.506842571776, 342.71668, -16.55144,              155.72500,  18.93862,       155.72418,       18.93788,    342.71668,     -16.55144,     342.71818,      -16.55195,  3275621.18, -2714681.75,  4873762.52,      49.069774,       -0.813619,  103347.87,  298903.77,    7186.47,             7167.84,    21.16,  58941.61,           59578.24,      1.16,      5.49,           3.87,  +1.24,  -1.14
  4,     UK0038,       0,  0.161060, 2459436.506843037438, 342.49509, -16.94548,              156.05189,  18.61534,       156.05283,       18.61620,    342.49509,     -16.94548,     342.49463,      -16.94489,  3274597.58, -2715519.85,  4871842.29,      49.060333,       -0.831276,  101731.29,  298757.12,    9518.30,             9499.67,   -68.32,  57919.24,           59209.12,     -1.33,     -6.30,           4.45,  +1.24,  -1.14
  5,     UK0038,       0,  0.201336, 2459436.506843503565, 342.25593, -17.36643,              156.40116,  18.26946,       156.40309,       18.27121,    342.25593,     -17.36643,     342.25444,      -17.36522,  3273502.91, -2716416.13,  4869788.76,      49.050228,       -0.850149,  100002.96,  298620.76,   12012.01,            11993.39,     3.13,  61915.69,           59490.40,     -2.73,    -12.93,           9.13,  +1.01,  -1.37
  6,     UK0038,       0,  0.241620, 2459436.506843969692, 341.99791, -17.79920,              156.76951,  17.91563,       156.76552,       17.91202,    341.99791,     -17.79920,     342.00376,      -17.80170,  3272366.33, -2717346.72,  4867656.61,      49.039727,       -0.869740,   98208.98,  298501.45,   14601.20,            14582.57,   169.56,  64273.28,           60103.55,      5.64,     26.74,          18.88,  +0.84,  -1.53
  7,     UK0038,       0,  0.281860, 2459436.506844435818, 341.79530, -18.16423,              157.06371,  17.61249,       157.06520,       17.61384,    341.79530,     -18.16423,     341.79467,      -18.16329,  3271424.90, -2718117.54,  4865890.54,      49.031022,       -0.885999,   96723.39,  298418.93,   16745.84,            16727.21,  -105.90,  53296.16,           59792.11,     -2.11,     -9.99,           7.06,  +0.74,  -1.63
  8,     UK0038,       0,  0.322156, 2459436.506844901945, 341.53611, -18.61440,              157.43308,  17.23973,       157.43595,       17.24232,    341.53611,     -18.61440,     341.53396,      -18.61259,  3270254.74, -2719075.62,  4863695.39,      49.020194,       -0.906169,   94877.40,  298338.99,   19411.52,            19392.89,   136.31,  66152.52,           60071.09,     -4.06,    -19.23,          13.59,  +0.61,  -1.76
  9,     UK0038,       1,  0.362408, 2459436.506845368072, 341.27918, -19.01348,              157.78423,  16.91457,       157.77219,       16.90374,    341.27918,     -19.01348,     341.29536,      -19.02109,  3269190.56, -2719946.94,  4861699.06,      49.010338,       -0.924530,   93199.07,  298286.68,   21835.77,            21817.14,   139.74,  60226.85,           60221.59,     16.97,     80.59,          56.95,  +0.64,  -1.73
 10,     UK0038,       0,  0.402652, 2459436.506845833734, 341.08470, -19.38091,              158.06539,  16.60430,       158.06699,       16.60574,    341.08470,     -19.38091,     341.08443,      -19.37990,  3268255.53, -2720712.52,  4859944.99,      49.001671,       -0.940685,   91724.77,  298256.54,   23965.83,            23947.21,  -150.54,  52928.75,           59972.40,     -2.26,    -10.71,           7.57,  +0.85,  -1.52
 11,     UK0038,       0,  0.442880, 2459436.506846299395, 340.87293, -19.73466,              158.35780,  16.31050,       158.35779,       16.31049,    340.87293,     -19.73466,     340.87479,      -19.73466,  3267330.53, -2721469.87,  4858209.76,      48.993091,       -0.956670,   90266.64,  298241.73,   26073.02,            26054.39,  -462.73,  52381.14,           59536.99,      0.02,      0.07,           0.05,  +1.59,  -0.78

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.