Orbital Analysis for matched events on 20210813_211135.043_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 65.84° Bg 37.84° Vg 57.64km/s
mass 0.00900g, abs. mag 0.9
Path Details
------------
start -2.87° 50.87° 109.30km
end   -2.98° 50.72° 100.15km

Orbit Details
-------------
Semimajor axis 5.55A.U., eccentricity 0.83, inclination 112.44°, Period 13.09Y, LA Sun 141.04°, last Perihelion 2021-07-19

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: 2459440.383044485934
Time: 2021-08-13 21:11:35.047890 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000T and UK003J
 Convergence angle = 35.28846 deg
 R.A. =  51.50924  Dec = +58.64819 deg

Best intersection: Stations UK000T and UK003J with Qconv = 35.29 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =    539175.83 +/- 18.54 m
 Y =  -4066283.00 +/- 33.56 m
 Z =   5009761.85 +/- 18.56 m
 Vx =    18704.62 +/- 96.25 m/s
 Vy =    23972.27 +/- 161.39 m/s
 Vz =    50205.16 +/- 68.32 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+3.718567e+02, -4.042062e+02, +2.194865e+02, +1.674660e+03, -1.869840e+03, +1.433192e+02
-4.042062e+02, +1.199696e+03, -3.076024e+02, -2.060719e+03, +5.077753e+03, -1.264050e+03
+2.194865e+02, -3.076024e+02, +3.686547e+02, +7.165572e+02, -1.902143e+03, +4.814577e+02
+1.674660e+03, -2.060719e+03, +7.165572e+02, +8.756888e+03, -9.852799e+03, +6.655102e+02
-1.869840e+03, +5.077753e+03, -1.902143e+03, -9.852799e+03, +2.766263e+04, -6.838375e+03
+1.433192e+02, -1.264050e+03, +4.814577e+02, +6.655102e+02, -6.838375e+03, +2.329367e+03

Timing offsets (from input data):
    UK000T: -0.000031 s
    UK003J: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 21:11:35.047890 UTC
  Lon     = +-2.863279 +/- 0.0002 deg
  Lat     = +50.875531 +/- 0.0002 deg
  Lat geo = +50.690200 +/- 0.0002 deg
  Ht      =  109443.92 +/- 31.52 m

  JD dynamic   = 2459440.383845276665 
  LST apparent = 277.5531723283 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  52.03648 +/- 0.2922 deg
  Dec       = +58.79933 +/- 0.1074 deg
  Azimuth   =  24.22744 +/- 0.1130 deg
  Elevation = +25.75465 +/- 0.1546 deg
  Vavg      =  56.37106 +/- 0.0122 km/s
  Vinit     =  58.69489 +/- 0.0136 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  51.64430 +/- 0.2922 deg
  Dec       = +58.62089 +/- 0.1074 deg
  Azimuth   =  24.52239 +/- 0.1130 deg
  Elevation = +25.70239 +/- 0.1546 deg
  Vavg      =  56.48227 +/- 0.0122 km/s
  Vinit     =  58.80610 +/- 0.0136 km/s
Radiant (geocentric, J2000):
  R.A.   =  52.23069 +/- 0.2883 deg
  Dec    = +58.15617 +/- 0.1093 deg
  Vg     =  57.63653 +/- 0.0139 km/s
  Vinf   =  58.69489 +/- 0.0136 km/s
  Zc     =  64.41438 +/- 0.1547 deg
  Zg     =  65.07107 +/- 0.1564 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  65.84453 +/- 0.1563 deg
  Bg     = +37.84395 +/- 0.1405 deg
  Vh     =  39.89508 +/- 0.0394 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  88.81083 +/- 0.2867 deg
  Bh     = +62.41825 +/- 0.2295 deg
  Vh_x   =  -0.38336 +/- 0.0885 km/s
  Vh_y   = -18.46799 +/- 0.1301 km/s
  Vh_z   = -35.36104 +/- 0.1034 km/s
Orbit:
  La Sun = 141.036488 +/- 0.0000 deg
  a      =   5.553039 +/- 0.1158 AU
  e      =   0.833712 +/- 0.0031
  i      = 112.435490 +/- 0.1604 deg
  peri   = 143.638516 +/- 0.5118 deg
  node   = 141.034527 +/- 0.0000 deg
  Pi     = 284.673043 +/- 0.5119 deg
  q      =   0.923404 +/- 0.0023 AU
  f      =  36.357358 +/- 0.5118 deg
  M      =   1.939032 +/- 0.0729 deg
  Q      =  10.182675 +/- 0.2302 AU
  n      =   0.075320 +/- 0.0022 deg/day
  T      =  13.085695 +/- 0.4151 years
  Last perihelion JD = 2459414.639780 (2021-07-19 03:21:16.982170) +/- 0.3259 days
  Tj     =   0.501812 +/- 0.0163
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.005676e-05, +3.689558e-06, +6.363779e-04, +6.577243e-10, +1.592573e-05, -8.487250e-06
q   , +3.689558e-06, +5.674178e-06, +7.987706e-04, +4.034244e-10, +2.204564e-05, -5.203421e-06
Tp  , +6.363779e-04, +7.987706e-04, +1.142450e-01, +6.280434e-08, +3.127966e-03, -8.101271e-04
node, +6.577243e-10, +4.034244e-10, +6.280434e-08, +5.000449e-14, +1.649033e-09, -6.451125e-10
peri, +1.592573e-05, +2.204564e-05, +3.127966e-03, +1.649033e-09, +8.598784e-05, -2.127043e-05
i   , -8.487250e-06, -5.203421e-06, -8.101271e-04, -6.451125e-10, -2.127043e-05, +8.322677e-06

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

Mean time residuals from time vs. length:
  Station with reference time: UK003J
  Avg. res. = 7.534e-06 s
  Stddev    = 2.74e-03 s

Begin point on the trajectory:
  Lon =    -2.865042 +/- 0.0002 deg
  Lat =    50.873051 +/- 0.0002 deg
  Ht  = 109295.48 +/- 30.77 m
End point on the trajectory:
  Lon =    -2.975405 +/- 0.0002 deg
  Lat =    50.719493 +/- 0.0002 deg
  Ht  = 100147.34 +/- 26.81 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,   False,    -3.557111,    51.483925,   37.50,   0.000000,   0.000000,   109295.48,   100147.34,          0.007065,     14.14,      9.41,              85.44, 1.0000,   False,    True, {"ff_name": "FF_UK000T_20210813_211128_167_0081152.fits"}
    UK003J,   False,    -2.379250,    51.361350,  169.00,   0.000000,   0.000000,   108386.78,   101464.34,          0.012146,      9.76,     25.37,              93.98, 1.0000,    True,    True, {"ff_name": "FF_UK003J_20210813_211126_117_0084992.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,       0,  0.007565, 2459440.383044535760, 299.01970,  17.80246,              144.28649,  52.03027,       144.27639,       52.02259,    299.01970,     +17.80246,     299.02883,      +17.79774,   539066.97, -4066422.52,  5009469.64,      50.873051,       -2.865042,  109295.48,  137901.27,       0.00,              341.62,   349.72,      0.00,           55086.79,    -13.17,     19.79,          35.56,  +3.26,  +2.56
  1,     UK000T,       0,  0.048885, 2459440.383045013994, 298.51710,  16.88263,              145.56037,  51.35738,       145.57213,       51.36612,    298.51710,     +16.88263,     298.50679,      +16.88806,   538271.79, -4067441.64,  5007335.30,      50.854935,       -2.878093,  108211.70,  137748.19,    2495.26,             2836.88,   419.71,  60388.74,           55086.79,     15.20,    -22.86,          41.11,  +2.00,  +1.30
  2,     UK000T,       0,  0.089917, 2459440.383045488968, 298.10132,  16.16546,              146.56599,  50.83357,       146.57167,       50.83772,    298.10132,     +16.16546,     298.09666,      +16.16806,   537644.22, -4068245.94,  5005650.85,      50.840632,       -2.888424,  107356.90,  137658.45,    4464.56,             4806.17,   -19.37,  47994.09,           55086.79,      7.30,    -10.97,          19.75,  +1.17,  +0.48
  3,     UK000T,       0,  0.131201, 2459440.383045966737, 297.59588,  15.27072,              147.77568,  50.16629,       147.78006,       50.16943,    297.59588,     +15.27072,     297.59257,      +15.27270,   536865.78, -4069243.61,  5003561.44,      50.822884,       -2.901194,  106297.26,  137587.35,    6907.29,             7248.91,     0.21,  59168.99,           55086.79,      5.60,     -8.41,          15.15,  +1.01,  +0.32
  4,     UK000T,       0,  0.172393, 2459440.383046443574, 297.12562,  14.43994,              148.87502,  49.53825,       148.87373,       49.53734,    297.12562,     +14.43994,     297.12745,      +14.43935,   536142.61, -4070170.44,  5001620.37,      50.806390,       -2.913065,  105313.50,  137559.98,    9176.59,             9518.21,  -148.26,  55090.77,           55260.68,     -1.65,      2.48,           4.46,  +0.91,  +0.22
  5,     UK000T,       0,  0.213797, 2459440.383046922740, 296.58544,  13.45882,              150.12161,  48.78135,       150.12180,       48.78148,    296.58544,     +13.45882,     296.58616,      +13.45891,   535292.93, -4071259.41,  4999339.74,      50.787002,       -2.926976,  104158.46,  137576.50,   11842.88,            12184.50,    87.83,  64396.92,           56622.41,      0.24,     -0.36,           0.65,  +0.74,  +0.05
  6,     UK000T,       0,  0.255013, 2459440.383047400042, 296.11433,  12.60613,              151.18150,  48.11537,       151.17839,       48.11324,    296.11433,     +12.60613,     296.11808,      +12.60475,   534553.06, -4072207.64,  4997353.86,      50.770112,       -2.939106,  103153.40,  137632.60,   14164.57,            14506.19,    -9.64,  56330.00,           57076.30,     -3.96,      5.95,          10.71,  +0.81,  +0.12
  7,     UK000T,       0,  0.296349, 2459440.383047878277, 295.62220,  11.66670,              152.28504,  47.36482,       152.29848,       47.37389,    295.62220,     +11.66670,     295.61180,      +11.67267,   533745.58, -4073242.52,  4995186.50,      50.751672,       -2.952323,  102057.26,  137738.96,   16698.43,            17040.05,    98.01,  61299.08,           57618.16,     17.12,    -25.72,          46.27,  +0.93,  +0.23
  8,     UK000T,       0,  0.337497, 2459440.383048354648, 295.17291,  10.86115,              153.24727,  46.72205,       153.24797,       46.72252,    295.17291,     +10.86115,     295.17370,      +10.86146,   533042.18, -4074144.02,  4993298.49,      50.735603,       -2.963854,  101103.03,  137869.16,   18905.71,            19247.33,  -109.89,  53642.46,           57606.33,      0.89,     -1.34,           2.41,  +1.01,  +0.31
  9,     UK000T,       0,  0.378645, 2459440.383048831020, 294.73023,  10.05280,              154.18183,  46.06821,       154.17465,       46.06348,    294.73023,     +10.05280,     294.73798,      +10.04962,   532337.26, -4075047.46,  4991406.42,      50.719493,       -2.975405,  100147.34,  138035.07,   21117.73,            21459.35,  -313.05,  53757.64,           57390.95,     -9.18,     13.78,          24.74,  +2.39,  +1.69
  0,     UK003J,       1,  0.000000, 2459440.383044485934, 260.70709,  23.63733,              212.23607,  59.23041,       212.27773,       59.22783,    260.70709,     +23.63733,     260.68439,      +23.64268,   539178.92, -4066279.04,  5009770.14,      50.875602,       -2.863211,  109448.13,  126809.37,       0.00,                9.69,   461.82,      0.00,           54668.10,     44.33,    -17.09,          77.28,  +6.08,  +5.56
  1,     UK003J,       0,  0.040948, 2459440.383044959977, 260.39124,  22.57498,              212.01936,  58.13482,       212.03555,       58.13382,    260.39124,     +22.57498,     260.38238,      +22.57710,   538400.28, -4067276.96,  5007680.19,      50.857863,       -2.875993,  108386.78,  127015.50,    2443.37,             2433.68,   482.36,  59670.04,           54668.10,     17.80,     -6.86,          30.98,  +3.17,  +2.65
  2,     UK003J,       0,  0.081768, 2459440.383045432158, 260.13598,  21.65835,              211.82169,  57.19410,       211.84018,       57.19295,    260.13598,     +21.65835,     260.12580,      +21.66082,   537728.88, -4068137.44,  5005878.09,      50.842562,       -2.887034,  107472.19,  127231.24,    4550.20,             4540.51,   193.27,  51612.79,           54668.10,     20.90,     -8.05,          36.31,  +3.01,  +2.49
  3,     UK003J,       0,  0.122616, 2459440.383045905270, 259.88149,  20.70522,              211.61498,  56.21845,       211.64738,       56.21644,    259.88149,     +20.70522,     259.86320,      +20.70964,   537029.58, -4069033.68,  5004001.09,      50.826619,       -2.898522,  106520.16,  127492.58,    6744.60,             6734.91,    -9.90,  53721.15,           54668.10,     37.64,    -14.50,          65.26,  +2.60,  +2.07
  4,     UK003J,       0,  0.163600, 2459440.383046379313, 259.55277,  19.62074,              211.45892,  55.09437,       211.43663,       55.09577,    259.55277,     +19.62074,     259.56667,      +19.61763,   536223.21, -4070067.14,  5001836.70,      50.808228,       -2.911738,  105423.11,  127839.69,    9274.99,             9265.29,   114.94,  61740.75,           55890.12,    -26.72,     10.27,          46.19,  +2.52,  +1.99
  5,     UK003J,       0,  0.204500, 2459440.383046852890, 259.28822,  18.62019,              211.27003,  54.06890,       211.25454,       54.06987,    259.28822,     +18.62019,     259.29844,      +18.61799,   535481.27, -4071018.03,  4999845.26,      50.791300,       -2.923906,  104414.41,  128202.79,   11603.19,            11593.50,    42.52,  56924.31,           56386.58,    -19.10,      7.34,          32.92,  +1.88,  +1.34
  6,     UK003J,       0,  0.245408, 2459440.383047326468, 259.03126,  17.61095,              211.07887,  53.03677,       211.07997,       53.03670,    259.03126,     +17.61095,     259.03161,      +17.61111,   534729.72, -4071981.23,  4997828.02,      50.774146,       -2.936225,  103393.31,  128612.62,   13961.55,            13951.85,    -0.22,  57650.18,           56699.23,      1.39,     -0.54,           2.39,  +1.60,  +1.05
  7,     UK003J,       0,  0.286296, 2459440.383047799580, 258.76200,  16.63410,              210.93668,  52.03030,       210.91817,       52.03146,    258.76200,     +16.63410,     258.77480,      +16.63138,   533993.83, -4072924.37,  4995852.81,      50.757342,       -2.948285,  102394.15,  129054.64,   16270.77,            16261.07,   -90.91,  56476.76,           56810.92,    -24.07,      9.25,          41.21,  +1.61,  +1.06
  8,     UK003J,       0,  0.327116, 2459440.383048272226, 258.52055,  15.72910,              210.80267,  51.09978,       210.77540,       51.10149,    258.52055,     +15.72910,     258.53928,      +15.72503,   533308.58, -4073802.60,  4994013.53,      50.741689,       -2.959523,  101464.34,  129502.30,   18421.07,            18411.37,  -336.54,  52677.63,           56588.05,    -36.31,     13.94,          61.95,  +1.64,  +1.08

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.