Orbital Analysis for matched events on 20210810_205041.791_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 65.84° Bg 30.59° Vg 63.20km/s
mass 0.00650g, abs. mag 0.8
Path Details
------------
start -2.12° 50.03° 108.25km
end   -2.23° 49.86° 102.46km

Orbit Details
-------------
Semimajor axis -17.18A.U., eccentricity 1.05, inclination 124.89°, Period 1000000000.00Y, LA Sun 138.14°, 

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: 2459437.368539249524
Time: 2021-08-10 20:50:41.796792 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000H and UK002D
 Convergence angle = 7.76605 deg
 R.A. =  54.19536  Dec = +53.12609 deg

Best intersection: Stations UK000H and UK002D with Qconv = 7.77 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =      7434.24 +/- 78.10 m
 Y =  -4174831.56 +/- 467.02 m
 Z =   4948207.91 +/- 81.24 m
 Vx =    22274.90 +/- 555.55 m/s
 Vy =    32758.50 +/- 2567.34 m/s
 Vz =    50482.08 +/- 2074.03 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+3.360480e+03, +1.906130e+04, -3.063451e+03, +1.849671e+04, +8.047744e+04, +3.746905e+03
+1.906130e+04, +1.138537e+05, -1.847469e+04, +1.128617e+05, +5.025246e+05, +2.694572e+04
-3.063451e+03, -1.847469e+04, +3.164426e+03, -1.919191e+04, -8.441429e+04, -4.728272e+03
+1.849671e+04, +1.128617e+05, -1.919191e+04, +1.486897e+05, +6.449391e+05, +4.876849e+04
+8.047744e+04, +5.025246e+05, -8.441429e+04, +6.449391e+05, +2.846065e+06, +2.169801e+05
+3.746905e+03, +2.694572e+04, -4.728272e+03, +4.876849e+04, +2.169801e+05, +2.216072e+04

Timing offsets (from input data):
    UK000H: 0.000000 s
    UK002D: -0.000671 s

Reference point on the trajectory:
  Time: 2021-08-10 20:50:41.796792 UTC
  Lon     = +-2.121376 +/- 0.0011 deg
  Lat     = +50.031833 +/- 0.0027 deg
  Lat geo = +49.845436 +/- 0.0027 deg
  Ht      =  108437.36 +/- 361.63 m

  JD dynamic   = 2459437.369340055622 
  LST apparent = 270.1020280956 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  55.78535 +/- 1.7719 deg
  Dec       = +51.87803 +/- 1.6825 deg
  Azimuth   =  21.22517 +/- 0.2046 deg
  Elevation = +15.98580 +/- 1.9406 deg
  Vavg      =  64.37535 +/- 1.1770 km/s
  Vinit     =  64.16954 +/- 1.2891 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  55.42325 +/- 1.7719 deg
  Dec       = +51.75712 +/- 1.6825 deg
  Azimuth   =  21.48828 +/- 0.2046 deg
  Elevation = +15.95859 +/- 1.9406 deg
  Vavg      =  64.48194 +/- 1.1770 km/s
  Vinit     =  64.27613 +/- 1.2891 km/s
Radiant (geocentric, J2000):
  R.A.   =  55.78144 +/- 1.7270 deg
  Dec    = +51.20119 +/- 1.6826 deg
  Vg     =  63.20282 +/- 1.3107 km/s
  Vinf   =  64.16954 +/- 1.2891 km/s
  Zc     =  74.18796 +/- 1.9408 deg
  Zg     =  74.84557 +/- 1.9367 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  65.83606 +/- 0.5344 deg
  Bg     = +30.59488 +/- 1.8990 deg
  Vh     =  42.45099 +/- 0.4891 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  84.04336 +/- 0.9708 deg
  Bh     = +49.26969 +/- 3.2587 deg
  Vh_x   =  -2.87451 +/- 0.5425 km/s
  Vh_y   = -27.54969 +/- 2.1986 km/s
  Vh_z   = -32.16891 +/- 0.9010 km/s
Orbit:
  La Sun = 138.142501 +/- nan deg
  a      = -17.182353 +/- 132.2936 AU
  e      =   1.050564 +/- 0.0416
  i      = 124.894063 +/- 3.2022 deg
  peri   = 136.146715 +/- 1.8407 deg
  node   = 138.139281 +/- 0.0003 deg
  Pi     = 274.285995 +/- 1.8410 deg
  q      =   0.868803 +/- 0.0125 AU
  f      =  43.848576 +/- 1.8406 deg
  M      =        nan +/- nan deg
  Q      = -35.233508 +/- 264.5860 AU
  n      =   0.013838 +/- 0.0117 deg/day
  T      = 1000000000.000000 +/- 462634274.4911 years
  Last perihelion JD = NaN 
  Tj     =  -0.972290 +/- 0.2969
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.049255e-03, -2.718728e-04, -1.389293e-02, -1.034266e-07, -6.970327e-04, +1.247681e-03
q   , -2.718728e-04, +7.460785e-05, +4.045835e-03, +2.797974e-08, +1.944665e-04, -3.376916e-04
Tp  , -1.389293e-02, +4.045835e-03, +2.328584e-01, +1.492925e-06, +1.073440e-02, -1.805011e-02
node, -1.034266e-07, +2.797974e-08, +1.492925e-06, +1.059486e-11, +7.258372e-08, -1.278079e-07
peri, -6.970327e-04, +1.944665e-04, +1.073440e-02, +7.258372e-08, +5.095511e-04, -8.765644e-04
i   , +1.247681e-03, -3.376916e-04, -1.805011e-02, -1.278079e-07, -8.765644e-04, +1.542298e-03

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: UK000H
  Avg. res. = 9.268e-06 s
  Stddev    = 3.04e-03 s

Begin point on the trajectory:
  Lon =    -2.124641 +/- 0.0015 deg
  Lat =    50.026417 +/- 0.0033 deg
  Ht  = 108249.08 +/- 303.14 m
End point on the trajectory:
  Lon =    -2.226757 +/- 0.0013 deg
  Lat =    49.858636 +/- 0.0029 deg
  Ht  = 102456.45 +/- 217.62 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
    UK000H,   False,    -1.778230,    50.857470,   24.00,   0.000000,   0.000000,   107597.27,   102642.58,          0.005921,      4.86,     14.99,             110.68, 1.0000,    True,    True, {"ff_name": "FF_UK000H_20210810_205041_409_0051200.fits"}
    UK002D,   False,    -1.801980,    51.351940,  129.00,   0.000000,   0.000000,   108249.08,   102456.45,          0.021190,     30.43,     63.76,             121.98, 1.0000,    True,    True, {"ff_name": "FF_UK002D_20210810_205032_784_0050432.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,     UK000H,       1,  0.000000, 2459437.368539249524, 260.34689,   9.79056,              194.99417,  48.09955,       194.99401,       48.09954,    260.34689,      +9.79056,     260.34697,       +9.79053,     7435.41, -4174829.84,  4948210.56,      50.031860,       -2.121336,  108438.29,  144691.95,       0.00,                3.37,  -175.35,      0.00,           63964.66,     -0.24,      0.08,           0.37,  +4.50,  +3.70
  1,     UK000H,       0,  0.040948, 2459437.368539723568, 260.02752,   8.74690,              195.19710,  47.01796,       195.19227,       47.01758,    260.02752,      +8.74690,     260.03089,       +8.74597,     6374.59, -4176389.93,  4945806.41,      50.007647,       -2.136099,  107597.27,  146002.52,    3056.00,             3052.63,   246.30,  74631.22,           63964.66,     -8.04,      2.61,          11.94,  +1.94,  +1.12
  2,     UK000H,       0,  0.081672, 2459437.368540194817, 259.78442,   7.94840,              195.34689,  46.19040,       195.33999,       46.18984,    259.78442,      +7.94840,     259.78940,       +7.94704,     5550.17, -4177602.36,  4943938.01,      49.988825,       -2.147601,  106944.56,  147057.43,    5430.99,             5427.62,     8.05,  58319.24,           63964.66,    -11.74,      3.81,          17.31,  +1.45,  +0.61
  3,     UK000H,       0,  0.122412, 2459437.368540666532, 259.54286,   7.12640,              195.48576,  45.33972,       195.48683,       45.33981,    259.54286,      +7.12640,     259.54261,       +7.12661,     4691.02, -4178865.87,  4941990.89,      49.969204,       -2.159574,  106265.20,  148189.33,    7906.04,             7902.68,  -131.17,  60752.38,           63964.66,      1.87,     -0.61,           2.73,  +1.00,  +0.15
  4,     UK000H,       0,  0.163220, 2459437.368541138712, 259.27695,   6.22884,              195.63704,  44.41028,       195.64167,       44.41065,    259.27695,      +6.22884,     259.27439,       +6.22978,     3736.51, -4180269.61,  4939827.67,      49.947399,       -2.172849,  105511.46,  149484.77,   10655.78,            10652.42,    -0.06,  67382.40,           64139.00,      8.26,     -2.68,          11.98,  +1.10,  +0.23
  5,     UK000H,       0,  0.203964, 2459437.368541610427, 259.03187,   5.40644,              195.77453,  43.55822,       195.77977,       43.55864,    259.03187,      +5.40644,     259.02902,       +5.40751,     2846.50, -4181578.51,  4937810.61,      49.927061,       -2.185230,  104809.60,  150728.13,   13219.74,            13216.37,   -50.62,  62928.42,           64016.10,      9.55,     -3.10,          13.74,  +0.93,  +0.04
  6,     UK000H,       0,  0.244672, 2459437.368542081211, 258.79011,   4.62154,              195.91354,  42.74349,       195.90848,       42.74308,    258.79011,      +4.62154,     258.79471,       +4.62050,     1980.59, -4182851.95,  4935848.19,      49.907269,       -2.197273,  104127.63,  151969.76,   15714.25,            15710.88,  -168.33,  61278.15,           63679.41,     -9.43,      3.06,          13.45,  +1.47,  +0.56
  7,     UK000H,       0,  0.285532, 2459437.368542554323, 258.49879,   3.67004,              196.07588,  41.75590,       196.05866,       41.75452,    258.49879,      +3.67004,     258.51238,       +3.66644,      911.38, -4184424.38,  4933425.02,      49.882823,       -2.212094,  103286.78,  153544.59,   18794.42,            18791.05,   289.87,  75383.48,           64516.51,    -32.92,     10.66,          46.49,  +2.06,  +1.13
  8,     UK000H,       0,  0.326176, 2459437.368543024641, 258.29178,   2.94951,              196.17837,  41.01027,       196.17010,       41.00961,    258.29178,      +2.94951,     258.29915,       +2.94776,       91.12, -4185630.70,  4931566.04,      49.864062,       -2.223496,  102642.58,  154784.11,   21157.44,            21154.07,    44.79,  58139.52,           64483.28,    -16.12,      5.22,          22.59,  +3.63,  +2.68
  0,     UK002D,       0,  0.004334, 2459437.368539314717, 263.11166,  -3.26432,              188.92407,  35.02839,       188.91477,       35.02635,    263.11166,      -3.26432,     263.11906,       -3.26710,     7196.89, -4175180.62,  4947670.00,      50.026417,       -2.124641,  108249.08,  185284.77,       0.00,              683.75,   226.93,      0.00,           61905.26,    -23.01,     10.99,          28.38,  +5.52,  +4.18
  1,     UK002D,       0,  0.044846, 2459437.368539783638, 262.85890,  -3.85685,              189.15862,  34.41393,       189.12120,       34.40572,    262.85890,      -3.85685,     262.88904,       -3.86808,     6294.79, -4176507.29,  4945625.55,      50.005825,       -2.137218,  107534.05,  186837.44,    2598.78,             3282.54,   226.08,  64148.48,           61905.26,    -94.02,     44.83,         115.00,  +4.61,  +3.25
  2,     UK002D,       0,  0.085314, 2459437.368540252093, 262.65042,  -4.39589,              189.34301,  33.85670,       189.30433,       33.84823,    262.65042,      -4.39589,     262.68195,       -4.40758,     5471.84, -4177717.56,  4943760.48,      49.987036,       -2.148698,  106882.59,  188274.21,    4969.54,             5653.29,     0.02,  58583.43,           61905.26,    -98.54,     46.98,         119.60,  +3.05,  +1.68
  3,     UK002D,       0,  0.125822, 2459437.368540721014, 262.44094,  -4.98232,              189.51995,  33.25192,       189.49858,       33.24724,    262.44094,      -4.98232,     262.45880,       -4.98883,     4570.70, -4179042.81,  4941718.22,      49.966456,       -2.161246,  106170.14,  189868.94,    7565.53,             8249.28,    -3.37,  64085.81,           61905.26,    -55.24,     26.35,          66.48,  +2.04,  +0.65
  4,     UK002D,       0,  0.166358, 2459437.368541189935, 262.23103,  -5.59886,              189.69074,  32.61690,       189.69857,       32.61861,    262.23103,      -5.59886,     262.22530,       -5.59646,     3611.97, -4180452.77,  4939545.43,      49.944553,       -2.174576,  105413.20,  191589.64,   10327.44,            11011.19,   157.37,  68134.81,           63259.93,     20.57,     -9.82,          24.54,  +1.86,  +0.45
  5,     UK002D,       0,  0.206830, 2459437.368541658390, 262.03337,  -6.14217,              189.85361,  32.05572,       189.87418,       32.06024,    262.03337,      -6.14217,     262.01726,       -6.13581,     2746.06, -4181726.22,  4937582.99,      49.924766,       -2.186625,  104730.45,  193164.79,   12821.97,            13505.72,    54.82,  61635.88,           63414.88,     54.80,    -26.18,          64.85,  +1.66,  +0.23
  6,     UK002D,       0,  0.247286, 2459437.368542126846, 261.83096,  -6.66740,              190.02182,  31.51179,       190.04313,       31.51646,    261.83096,      -6.66740,     261.81431,       -6.66076,     1889.27, -4182986.25,  4935641.22,      49.905182,       -2.198541,  104055.76,  194742.36,   15290.21,            15973.96,   -72.98,  61010.50,           63212.91,     57.54,    -27.49,          67.54,  +2.00,  +0.55
  7,     UK002D,       0,  0.287726, 2459437.368542594835, 261.62343,  -7.17523,              190.19574,  30.98431,       190.20587,       30.98653,    261.62343,      -7.17523,     261.61616,       -7.17206,     1040.99, -4184233.77,  4933718.76,      49.885786,       -2.210333,  103388.61,  196322.46,   17733.92,            18417.68,  -224.28,  60428.19,           62897.03,     27.72,    -13.23,          32.27,  +3.28,  +1.82
  8,     UK002D,       0,  0.328342, 2459437.368543064687, 261.36861,  -7.88316,              190.39480,  30.25244,       190.42472,       30.25899,    261.36861,      -7.88316,     261.34480,       -7.87370,     -146.11, -4185979.57,  4931028.41,      49.858636,       -2.226757,  102456.45,  198562.52,   21153.72,            21837.47,   589.21,  84198.24,           64174.30,     83.36,    -39.83,          95.97,  +3.91,  +2.42

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.