Orbital Analysis for matched events on 20210813_222252.148_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 64.97° Bg 36.63° Vg 57.22km/s
mass 0.00270g, abs. mag 1.5
Path Details
------------
start -1.03° 50.96° 108.67km
end   -1.12° 50.87° 101.58km

Orbit Details
-------------
Semimajor axis 3.68A.U., eccentricity 0.75, inclination 113.97°, Period 7.07Y, LA Sun 141.08°, last Perihelion 2021-07-17

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: 2459440.432548018638
Time: 2021-08-13 22:22:52.148810 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0001 and UK0038
 Convergence angle = 23.48969 deg
 R.A. =  53.12744  Dec = +56.76709 deg

Best intersection: Stations UK0001 and UK0038 with Qconv = 23.49 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   1875411.45 +/- 93.26 m
 Y =  -3639604.68 +/- 23.57 m
 Z =   5014920.65 +/- 104.07 m
 Vx =    19652.93 +/- 547.84 m/s
 Vy =    24596.40 +/- 594.70 m/s
 Vz =    49053.43 +/- 443.57 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+8.875735e+03, -1.585858e+03, +9.667780e+03, +4.094081e+04, -2.550895e+04, +2.472419e+04
-1.585858e+03, +5.649271e+02, -1.661738e+03, -7.272572e+03, +4.452486e+03, -6.340140e+03
+9.667780e+03, -1.661738e+03, +1.117320e+04, +4.126303e+04, -2.912887e+04, +2.479645e+04
+4.094081e+04, -7.272572e+03, +4.126303e+04, +2.638950e+05, -1.198416e+05, +1.735862e+05
-2.550895e+04, +4.452486e+03, -2.912887e+04, -1.198416e+05, +1.081784e+05, -4.699491e+04
+2.472419e+04, -6.340140e+03, +2.479645e+04, +1.735862e+05, -4.699491e+04, +1.612504e+05

Timing offsets (from input data):
    UK0001: 0.000000 s
    UK0038: 0.000464 s

Reference point on the trajectory:
  Time: 2021-08-13 22:22:52.148810 UTC
  Lon     = +-1.025402 +/- 0.0011 deg
  Lat     = +50.955730 +/- 0.0002 deg
  Lat geo = +50.770485 +/- 0.0002 deg
  Ht      =  108723.47 +/- 116.78 m

  JD dynamic   = 2459440.433348759543 
  LST apparent = 297.2610954609 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  51.37456 +/- 1.0153 deg
  Dec       = +57.30669 +/- 0.1417 deg
  Azimuth   =  35.09876 +/- 0.4163 deg
  Elevation = +30.97141 +/- 0.4438 deg
  Vavg      =  58.15449 +/- 0.3992 km/s
  Vinit     =  58.28773 +/- 0.4338 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  51.15448 +/- 1.0153 deg
  Dec       = +57.08163 +/- 0.1417 deg
  Azimuth   =  35.37785 +/- 0.4163 deg
  Elevation = +30.88449 +/- 0.4438 deg
  Vavg      =  58.30226 +/- 0.3992 km/s
  Vinit     =  58.43550 +/- 0.4338 km/s
Radiant (geocentric, J2000):
  R.A.   =  51.69109 +/- 1.0166 deg
  Dec    = +56.78563 +/- 0.1506 deg
  Vg     =  57.22172 +/- 0.4419 km/s
  Vinf   =  58.28773 +/- 0.4338 km/s
  Zc     =  59.18021 +/- 0.4445 deg
  Zg     =  59.78073 +/- 0.4563 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  64.96780 +/- 0.6254 deg
  Bg     = +36.62930 +/- 0.2871 deg
  Vh     =  38.86448 +/- 0.4067 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  86.27038 +/- 1.5368 deg
  Bh     = +61.45678 +/- 0.4736 deg
  Vh_x   =  -1.20796 +/- 0.5101 km/s
  Vh_y   = -18.53096 +/- 0.2706 km/s
  Vh_z   = -34.14077 +/- 0.4457 km/s
Orbit:
  La Sun = 141.084032 +/- 0.0000 deg
  a      =   3.682079 +/- 0.5040 AU
  e      =   0.749263 +/- 0.0294
  i      = 113.966957 +/- 0.2780 deg
  peri   = 142.461632 +/- 2.8486 deg
  node   = 141.082410 +/- 0.0000 deg
  Pi     = 283.544042 +/- 2.8486 deg
  q      =   0.923235 +/- 0.0120 AU
  f      =  37.534262 +/- 2.8486 deg
  M      =   3.795544 +/- 1.0977 deg
  Q      =   6.440924 +/- 0.9987 AU
  n      =   0.139497 +/- 0.0277 deg/day
  T      =   7.065458 +/- 1.5006 years
  Last perihelion JD = 2459413.224534 (2021-07-17 17:23:19.731427) +/- 1.9456 days
  Tj     =   0.960836 +/- 0.1946
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +8.659604e-04, +2.768896e-04, +4.976452e-02, -7.963309e-09, +1.216598e-03, +1.006370e-04
q   , +2.768896e-04, +1.441379e-04, +2.290126e-02, -1.359197e-09, +5.918414e-04, +1.716285e-05
Tp  , +4.976452e-02, +2.290126e-02, +3.738895e+00, -3.075445e-07, +9.542036e-02, +3.884898e-03
node, -7.963309e-09, -1.359197e-09, -3.075445e-07, +1.601068e-13, -6.843077e-09, -2.023731e-09
peri, +1.216598e-03, +5.918414e-04, +9.542036e-02, -6.843077e-09, +2.449320e-03, +8.642928e-05
i   , +1.006370e-04, +1.716285e-05, +3.884898e-03, -2.023731e-09, +8.642928e-05, +2.557986e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 12.544329
 a2 = 12.415572

Mean time residuals from time vs. length:
  Station with reference time: UK0001
  Avg. res. = 5.385e-06 s
  Stddev    = 2.32e-03 s

Begin point on the trajectory:
  Lon =    -1.026113 +/- 0.0009 deg
  Lat =    50.955091 +/- 0.0001 deg
  Ht  = 108670.44 +/- 108.27 m
End point on the trajectory:
  Lon =    -1.122258 +/- 0.0007 deg
  Lat =    50.869381 +/- 0.0001 deg
  Ht  = 101578.21 +/- 72.27 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
    UK0001,   False,    -1.778230,    50.857470,   24.00,  12.889874,  12.311905,   108670.44,   101578.21,          0.010974,     19.61,     11.84,              43.04, 1.0000,    True,    True, {"ff_name": "FF_UK0001_20210813_222242_846_0202240.fits"}
    UK0038,   False,    -2.379250,    51.361350,  169.00,  12.361271,  12.458746,   107714.84,   101654.34,          0.012501,     32.19,      4.27,              62.68, 1.0000,    True,    True, {"ff_name": "FF_UK0038_20210813_222249_805_0196096.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,     UK0001,       0,  0.000000, 2459440.432548018638, 338.54665,  48.62882,               78.13203,  63.11202,        78.10722,       63.13229,    338.54665,     +48.62882,     338.52400,      +48.64650,  1875376.71, -3639648.17,  5014833.93,      50.955091,       -1.026113,  108670.44,  121532.07,       0.00,              103.05,  -158.44,      0.00,           59047.88,     25.38,    -42.08,          83.40,  +4.31,  +3.89
  1,     UK0001,       0,  0.039644, 2459440.432548477314, 337.59926,  48.13227,               79.66894,  63.51966,        79.67293,       63.51626,    337.59926,     +48.13227,     337.60319,      +48.12937,  1874543.49, -3640690.98,  5012754.22,      50.939765,       -1.043325,  107399.08,  119717.43,    2471.21,             2574.26,     2.01,  62335.11,           59047.88,     -4.15,      6.86,          13.81,  +2.00,  +1.61
  2,     UK0001,       0,  0.079316, 2459440.432548936456, 336.72439,  47.63586,               81.20170,  63.87948,        81.21400,       63.86850,    336.72439,     +47.63586,     336.73678,      +47.62669,  1873767.08, -3641662.69,  5010816.31,      50.925476,       -1.059371,  106215.01,  118047.82,    4773.94,             4876.99,    -7.66,  58044.08,           59047.88,    -13.06,     21.59,          44.09,  +1.57,  +1.21
  3,     UK0001,       0,  0.118996, 2459440.432549396064, 335.87228,  47.11473,               82.80799,  64.21170,        82.81206,       64.20788,    335.87228,     +47.11473,     335.87693,      +47.11161,  1873003.10, -3642618.83,  5008909.44,      50.911408,       -1.075159,  105050.48,  116426.17,    7039.77,             7142.82,   -54.68,  57102.62,           59047.88,     -4.43,      7.33,          15.17,  +1.35,  +1.02
  4,     UK0001,       0,  0.158644, 2459440.432549854741, 334.96689,  46.55584,               84.56472,  64.55697,        84.56979,       64.55189,    334.96689,     +46.55584,     334.97302,      +46.55178,  1872206.18, -3643616.21,  5006920.33,      50.896727,       -1.091616,  103836.32,  114758.28,    9403.34,             9506.39,    -2.11,  59613.75,           58932.99,     -5.74,      9.49,          19.93,  +1.38,  +1.08
  5,     UK0001,       0,  0.198336, 2459440.432550314348, 334.17311,  46.03102,               86.21334,  64.83951,        86.20646,       64.84685,    334.17311,     +46.03102,     334.16612,      +46.03676,  1871500.68, -3644499.16,  5005159.43,      50.883723,       -1.106201,  102761.98,  113302.02,   11495.72,            11598.77,  -223.28,  52715.59,           58011.30,      8.08,    -13.36,          28.43,  +1.70,  +1.43
  6,     UK0001,       0,  0.237972, 2459440.432550773025, 333.27571,  45.44258,               88.10670,  65.15284,        88.10217,       65.15806,    333.27571,     +45.44258,     333.27119,      +45.44658,  1870722.96, -3645472.51,  5003218.24,      50.869381,       -1.122258,  101578.21,  111720.83,   13802.34,            13905.39,  -226.95,  58195.08,           57701.91,      5.61,     -9.27,          20.01,  +2.83,  +2.59
  0,     UK0038,       0,  0.031348, 2459440.432548210025, 338.88607,  21.13527,              115.83518,  45.05067,       115.84283,       45.06769,    338.88607,     +21.13527,     338.87052,      +21.14560,  1874750.47, -3640431.93,  5013270.85,      50.943573,       -1.038994,  107714.84,  150677.46,       0.00,             1960.38,  -128.30,      0.00,           59379.39,      6.17,    -46.56,          64.30,  +3.99,  +3.10
  1,     UK0038,       0,  0.071832, 2459440.432548678480, 338.32548,  20.42203,              117.03083,  44.79247,       117.03305,       44.79719,    338.32548,     +20.42203,     338.32138,      +20.42490,  1873877.22, -3641524.83,  5011091.23,      50.927503,       -1.057025,  106382.95,  149509.26,    2589.92,             4550.31,   101.91,  63974.00,           59379.39,      1.71,    -12.87,          17.91,  +2.43,  +1.56
  2,     UK0038,       0,  0.112288, 2459440.432549146935, 337.84313,  19.76485,              118.08991,  44.52859,       118.09698,       44.54307,    337.84313,     +19.76485,     337.83018,      +19.77364,  1873101.12, -3642496.15,  5009154.09,      50.913214,       -1.073065,  105199.86,  148500.55,    4891.73,             6852.11,    45.63,  56896.56,           59379.39,      5.23,    -39.39,          55.20,  +2.26,  +1.40
  3,     UK0038,       0,  0.152752, 2459440.432549615391, 337.34029,  19.08835,              119.18013,  44.25360,       119.18827,       44.26965,    337.34029,     +19.08835,     337.32603,      +19.09810,  1872308.56, -3643488.07,  5007175.88,      50.898613,       -1.089437,  103992.28,  147500.75,    7242.35,             9202.73,    37.69,  58091.57,           59379.39,      5.79,    -43.59,          61.49,  +1.84,  +1.00
  4,     UK0038,       0,  0.193112, 2459440.432550082449, 336.91200,  18.55350,              120.07046,  44.04789,       120.06677,       44.04081,    336.91200,     +18.55350,     336.91931,      +18.54919,  1871673.23, -3644283.22,  5005590.09,      50.886904,       -1.102591,  103024.68,  146720.24,    9126.66,            11087.04,  -430.49,  46687.63,           56636.19,     -2.56,     19.19,          27.22,  +3.58,  +2.75
  5,     UK0038,       0,  0.233660, 2459440.432550551835, 336.33808,  17.76142,              121.31556,  43.70255,       121.31397,       43.69962,    336.33808,     +17.76142,     336.34171,      +17.75964,  1870772.99, -3645409.90,  5003343.11,      50.870303,       -1.121156,  101654.34,  145652.13,   11796.63,            13757.02,  -123.97,  65847.24,           57170.40,     -1.06,      7.92,          11.31,  +4.48,  +3.66

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.