Orbital Analysis for matched events on 20210816_001542.623_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 70.53° Bg 27.42° Vg 63.51km/s
mass 0.00348g, abs. mag 0.7
Path Details
------------
start -5.05° 50.24° 109.51km
end   -5.19° 50.16° 101.50km

Orbit Details
-------------
Semimajor axis 31.87A.U., eccentricity 0.97, inclination 129.80°, Period 179.96Y, LA Sun 143.08°, last Perihelion 2021-07-16

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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: 2459442.510909993201
Time: 2021-08-16 00:15:42.623413 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0021 and UK0024
 Convergence angle = 1.40966 deg
 R.A. =  42.50928  Dec = +61.95227 deg

Best intersection: Stations UK0021 and UK0024 with Qconv = 1.41 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3341914.28 +/- 312.44 m
 Y =  -2473239.35 +/- 2168.60 m
 Z =   4964029.75 +/- 762.35 m
 Vx =    19024.64 +/- 2735.48 m/s
 Vy =    37350.40 +/- 16431.08 m/s
 Vz =    48986.86 +/- 7002.50 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+3.122825e+04, -2.010925e+05, +6.883447e+04, +1.194824e+05, -1.475456e+06, +2.370773e+05
-2.010925e+05, +1.314240e+06, -4.498295e+05, -7.366763e+05, +9.448759e+06, -1.555967e+06
+6.883447e+04, -4.498295e+05, +1.539648e+05, +2.522307e+05, -3.234437e+06, +5.325535e+05
+1.194824e+05, -7.366763e+05, +2.522307e+05, +5.125892e+05, -5.733938e+06, +8.574071e+05
-1.475456e+06, +9.448759e+06, -3.234437e+06, -5.733938e+06, +6.985348e+07, -1.112183e+07
+2.370773e+05, -1.555967e+06, +5.325535e+05, +8.574071e+05, -1.112183e+07, +1.844342e+06

Timing offsets (from input data):
    UK000T: 0.000000 s
    UK0021: 0.000000 s
    UK0024: -0.003584 s

Reference point on the trajectory:
  Time: 2021-08-16 00:15:42.623413 UTC
  Lon     = +-5.049246 +/- 0.0214 deg
  Lat     = +50.238699 +/- 0.0062 deg
  Lat geo = +50.052571 +/- 0.0061 deg
  Ht      =  109501.95 +/- 1571.43 m

  JD dynamic   = 2459442.511710734107 
  LST apparent = 323.4960908484 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  63.00772 +/- 25.7229 deg
  Dec       = +49.44748 +/- 7.6043 deg
  Azimuth   =  48.43677 +/- 9.0242 deg
  Elevation = +31.02177 +/- 13.1042 deg
  Vavg      =  64.14409 +/- 2.8217 km/s
  Vinit     =  64.47249 +/- 3.0579 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  62.93972 +/- 25.7229 deg
  Dec       = +49.24617 +/- 7.6043 deg
  Azimuth   =  48.64450 +/- 9.0242 deg
  Elevation = +30.91802 +/- 13.1042 deg
  Vavg      =  64.33891 +/- 2.8217 km/s
  Vinit     =  64.66730 +/- 3.0579 km/s
Radiant (geocentric, J2000):
  R.A.   =  63.15709 +/- 25.7401 deg
  Dec    = +49.06267 +/- 7.7222 deg
  Vg     =  63.51053 +/- 3.1045 km/s
  Vinf   =  64.47249 +/- 3.0579 km/s
  Zc     =  59.10182 +/- 13.0889 deg
  Zg     =  59.59013 +/- 13.1901 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  70.52934 +/- 11.0420 deg
  Bg     = +27.42333 +/- 12.1761 deg
  Vh     =  41.52369 +/- 5.2726 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  87.29364 +/- 45.2765 deg
  Bh     = +44.78357 +/- 15.5275 deg
  Vh_x   =  -1.39161 +/- 1.3147 km/s
  Vh_y   = -29.43951 +/- 12.4538 km/s
  Vh_z   = -29.25056 +/- 9.1788 km/s
Orbit:
  La Sun = 143.080699 +/- -0.0000 deg
  a      =  31.874739 +/- 9.8761 AU
  e      =   0.973358 +/- 0.5893
  i      = 129.801139 +/- 15.1629 deg
  peri   = 132.275542 +/- 19.6102 deg
  node   = 143.078405 +/- 0.0013 deg
  Pi     = 275.353947 +/- 19.6115 deg
  q      =   0.849217 +/- 0.0646 AU
  f      =  47.719835 +/- 19.6097 deg
  M      =   0.166825 +/- nan deg
  Q      =  62.900262 +/- 19.7838 AU
  n      =   0.005477 +/- 0.8012 deg/day
  T      = 179.957768 +/- 399999964.5215 years
  Last perihelion JD = 2459412.051916 (2021-07-16 13:14:45.505463) +/- 5.6224 days
  Tj     =  -0.563213 +/- 2.8823
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +3.536490e-03, -2.862168e-03, -2.439667e-01, -6.098702e-07, -8.647231e-03, +6.829517e-03
q   , -2.862168e-03, +4.834762e-03, +4.929526e-01, +1.058343e-06, +1.594034e-02, -1.222703e-02
Tp  , -2.439667e-01, +4.929526e-01, +5.150494e+01, +1.083417e-04, +1.645788e+00, -1.257291e+00
node, -6.098702e-07, +1.058343e-06, +1.083417e-04, +2.318250e-10, +3.496528e-06, -2.680229e-06
peri, -8.647231e-03, +1.594034e-02, +1.645788e+00, +3.496528e-06, +5.289404e-02, -4.048805e-02
i   , +6.829517e-03, -1.222703e-02, -1.257291e+00, -2.680229e-06, -4.048805e-02, +3.101267e-02

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 24.308017
 a2 = 8.732843

Mean time residuals from time vs. length:
  Station with reference time: UK0021
  Avg. res. = 7.830e-06 s
  Stddev    = 2.80e-03 s

Begin point on the trajectory:
  Lon =    -5.049121 +/- 0.0215 deg
  Lat =    50.238770 +/- 0.0062 deg
  Ht  = 109509.22 +/- 1563.43 m
End point on the trajectory:
  Lon =    -5.187609 +/- 0.0257 deg
  Lat =    50.160395 +/- 0.0086 deg
  Ht  = 101502.66 +/- 1231.58 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
    UK000T,    True,    -3.557111,    51.483925,   37.50, 162168.882162,   0.132026,   110516.04,   106925.08,          0.105220,       nan,       nan,              91.46, 0.0000,    True,   False, {"ff_name": "FF_UK000T_20210816_001544_301_0362752.fits"}
    UK0021,   False,    -3.515726,    50.691998,   17.00,  39.511526,   5.362212,   109509.22,   102746.78,          0.019295,     33.47,     44.33,              79.39, 1.0000,    True,    True, {"ff_name": "FF_UK0021_20210816_001540_306_0368384.fits"}
    UK0024,   False,    -2.949770,    50.877440,   82.00,  16.001859,  10.926454,   109479.29,   101502.66,          0.012799,     26.29,     36.74,              87.72, 1.0000,    True,    True, {"ff_name": "FF_UK0024_20210816_001540_548_0370944.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,     UK000T,       1,  4.680393, 2459442.510964164510, 293.40213,  -0.48386,              217.94321,  31.59101,       218.00261,       31.60084,    293.40213,      -0.48386,     293.37872,       -0.45539,  3342554.35, -2471982.73,  4965677.88,      50.249598,       -5.049633,  110516.04,  206432.99,       0.00,             2169.13, -299587.12,      0.00,           57943.03,     93.33,   -160.60,         185.54,  +3.28,  +1.71
  1,     UK000T,       1,  4.720925, 2459442.510964633431, 293.16359,  -0.87922,              218.02375,  31.13442,       218.10786,       31.14836,    293.16359,      -0.87922,     293.12219,       -0.83870,  3342013.43, -2473044.69,  4964285.06,      50.240390,       -5.066001,  109569.24,  207216.74,    1833.11,              336.02, -304033.44,  45226.36,           57943.03,    133.20,   -229.42,         263.99,  +1.71,  +0.13
  2,     UK000T,       1,  4.761717, 2459442.510965105612, 292.83774,  -1.46765,              218.11085,  30.46600,       218.25777,       30.49043,    292.83774,      -1.46765,     292.75015,       -1.39634,  3341219.03, -2474604.30,  4962239.56,      50.226858,       -5.089959,  108180.27,  208389.47,    4525.24,             2356.11, -304643.31,  65996.36,           57943.03,    235.15,   -405.97,         464.24,  +1.23,  -0.36
  3,     UK000T,       1,  4.802397, 2459442.510965576395, 292.51373,  -1.97248,              218.23174,  29.87539,       218.39041,       29.90179,    292.51373,      -1.97248,     292.41703,       -1.89499,  3340500.85, -2476014.28,  4960390.30,      50.214616,       -5.111632,  106925.08,  209474.50,    6959.08,             4789.95, -304832.20,  59829.04,           57943.03,    256.67,   -443.32,         504.27,  +1.48,  -0.13
  0,     UK0021,       0,  0.000000, 2459442.510909993201, 279.01962,  18.61283,              245.75317,  41.60000,       245.74407,       41.60173,    279.01962,     +18.61283,     279.02642,      +18.61005,  3341918.44, -2473231.18,  4964040.47,      50.238770,       -5.049121,  109509.22,  163186.43,       0.00,               14.11,    14.43,      0.00,           62964.92,    -15.96,     12.06,          25.29,  +2.25,  +1.19
  1,     UK0021,       0,  0.040772, 2459442.510910464916, 278.63516,  17.79543,              245.47906,  40.72882,       245.45638,       40.73313,    278.63516,     +17.79543,     278.65244,      +17.78845,  3341138.70, -2474762.01,  4962032.71,      50.225486,       -5.072640,  108147.77,  163890.79,    2642.45,             2628.34,    -0.00,  64810.40,           62964.92,    -40.45,     30.55,          63.80,  +1.56,  +0.49
  2,     UK0021,       0,  0.081536, 2459442.510910937097, 278.24995,  16.99252,              245.22821,  39.86675,       245.17997,       39.87592,    278.24995,     +16.99252,     278.28699,      +16.97759,  3340363.00, -2476284.92,  4960035.34,      50.212261,       -5.096035,  106794.13,  164630.88,    5271.22,             5257.11,     0.61,  64487.51,           62964.92,    -87.48,     66.02,         137.31,  +1.41,  +0.33
  3,     UK0021,       0,  0.122228, 2459442.510911407880, 277.95572,  16.24271,              244.93808,  39.09762,       244.93553,       39.09810,    277.95572,     +16.24271,     277.95819,      +16.24191,  3339653.60, -2477677.66,  4958208.70,      50.200158,       -5.117442,  105556.86,  165342.32,    7675.30,             7661.19,  -218.82,  59079.95,           62964.92,     -4.70,      3.55,           7.35,  +1.56,  +0.47
  4,     UK0021,       0,  0.162984, 2459442.510911879595, 277.59800,  15.44046,              244.67976,  38.24829,       244.67470,       38.24925,    277.59800,     +15.44046,     277.60259,      +15.43887,  3338872.52, -2479211.12,  4956197.49,      50.186822,       -5.140991,  104195.32,  166161.76,   10322.29,            10308.19,  -199.47,  64947.30,           63024.18,     -9.46,      7.15,          14.72,  +1.80,  +0.70
  5,     UK0021,       0,  0.203784, 2459442.510912351776, 277.24919,  14.58463,              244.38197,  37.35914,       244.40629,       37.35454,    277.24919,     +14.58463,     277.23111,      +14.59233,  3338041.04, -2480843.53,  4954056.50,      50.172614,       -5.166046,  102746.78,  167075.47,   13140.08,            13125.97,   -12.16,  69063.40,           63905.13,     46.21,    -34.94,          71.52,  +2.57,  +1.46
  0,     UK0024,       0,  0.000696, 2459442.510910040699, 274.31012,  11.27758,              245.26939,  32.59780,       245.28029,       32.59548,    274.31012,     +11.27758,     274.30115,      +11.28107,  3341901.30, -2473264.83,  4963996.34,      50.238478,       -5.049652,  109479.29,  199061.19,       0.00,               43.97,    -0.59,      0.00,           63655.73,     26.76,    -19.17,          34.11,  +2.98,  +1.49
  1,     UK0024,       0,  0.041200, 2459442.510910509620, 274.05808,  10.64745,              245.07239,  31.94164,       245.08704,       31.93852,    274.05808,     +10.64745,     274.04613,      +10.65216,  3341142.98, -2474753.62,  4962043.72,      50.225559,       -5.072528,  108155.23,  200102.43,    2569.87,             2613.85,   -42.11,  63447.40,           63655.73,     36.40,    -26.07,          46.16,  +3.04,  +1.53
  2,     UK0024,       0,  0.081720, 2459442.510910978541, 273.79747,  10.00320,              244.87775,  31.26836,       244.89187,       31.26535,    273.79747,     +10.00320,     273.78607,      +10.00776,  3340357.83, -2476295.06,  4960022.04,      50.212173,       -5.096205,  106785.12,  201209.28,    5230.65,             5274.62,     6.24,  65665.77,           63655.73,     35.51,    -25.43,          44.77,  +2.32,  +0.80
  3,     UK0024,       0,  0.122208, 2459442.510911446996, 273.53492,   9.41865,              244.72890,  30.64196,       244.71469,       30.64498,    273.53492,      +9.41865,     273.54733,       +9.41405,  3339626.88, -2477730.12,  4958139.90,      50.199702,       -5.118256,  105510.27,  202266.56,    7707.77,             7751.74,  -127.00,  61181.56,           63655.73,    -36.15,     25.86,          45.32,  +4.14,  +2.61
  4,     UK0024,       0,  0.162756, 2459442.510911916383, 273.25456,   8.74876,              244.54272,  29.93517,       244.51607,       29.94084,    273.25456,      +8.74876,     273.27766,       +8.74009,  3338787.81, -2479377.44,  4955979.35,      50.185375,       -5.143540,  104047.70,  203509.50,   10551.30,            10595.27,   102.30,  70127.52,           64771.14,    -68.70,     49.13,          85.60,  +2.76,  +1.22
  5,     UK0024,       0,  0.203148, 2459442.510912383907, 273.07725,   8.23779,              244.36924,  29.41639,       244.37049,       29.41613,    273.07725,      +8.23779,     273.07706,       +8.23820,  3338156.42, -2480617.01,  4954353.60,      50.174586,       -5.162605,  102947.73,  204468.28,   12690.98,            12734.96,  -362.19,  52972.95,           63409.40,      3.27,     -2.34,           4.05,  +3.77,  +2.22
  6,     UK0024,       0,  0.243668, 2459442.510912852827, 272.81994,   7.58435,              244.17895,  28.73501,       244.18289,       28.73418,    272.81994,      +7.58435,     272.81764,       +7.58564,  3337326.50, -2482246.36,  4952216.62,      50.160395,       -5.187609,  101502.66,  205752.93,   15503.50,            15547.47,  -162.10,  69410.57,           63565.78,     10.38,     -7.43,          12.80,  +4.95,  +3.38

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.