Orbital Analysis for matched events on 20210816_210555.835_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 69.32° Bg 36.63° Vg 58.09km/s
mass 0.00355g, abs. mag 1.3
Path Details
------------
start -0.72° 50.52° 107.54km
end   -0.79° 50.41° 101.65km

Orbit Details
-------------
Semimajor axis 5.40A.U., eccentricity 0.83, inclination 114.14°, Period 12.54Y, LA Sun 143.92°, last Perihelion 2021-07-20

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: 2459443.379118468147
Time: 2021-08-16 21:05:55.875358 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0001 and UK0009
 Convergence angle = 21.95423 deg
 R.A. =  56.13043  Dec = +58.81099 deg
Intersection 2 - Stations: UK0001 and UK0038
 Convergence angle = 11.28081 deg
 R.A. =  55.48072  Dec = +58.93251 deg
Intersection 3 - Stations: UK0009 and UK0038
 Convergence angle = 33.23489 deg
 R.A. =  55.94739  Dec = +58.89637 deg

Best intersection: Stations UK0009 and UK0038 with Qconv = 33.23 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =    805779.55 +/- 40.38 m
 Y =  -4051681.52 +/- 63.47 m
 Z =   4984801.09 +/- 47.17 m
 Vx =    16534.47 +/- 204.37 m/s
 Vy =    26177.08 +/- 442.58 m/s
 Vz =    50392.05 +/- 233.54 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.771901e+03, -2.232967e+03, +1.947083e+03, +7.203476e+03, -9.259569e+03, +6.290629e+03
-2.232967e+03, +4.489333e+03, -2.256359e+03, -1.032210e+04, +1.622799e+04, -1.113662e+04
+1.947083e+03, -2.256359e+03, +2.382345e+03, +7.923559e+03, -1.019735e+04, +7.049994e+03
+7.203476e+03, -1.032210e+04, +7.923559e+03, +4.509301e+04, -7.292025e+04, +4.749147e+04
-9.259569e+03, +1.622799e+04, -1.019735e+04, -7.292025e+04, +1.347307e+05, -8.730004e+04
+6.290629e+03, -1.113662e+04, +7.049994e+03, +4.749147e+04, -8.730004e+04, +5.700299e+04

Timing offsets (from input data):
    UK0001: 0.000000 s
    UK0009: -0.000039 s
    UK0038: -0.000047 s

Reference point on the trajectory:
  Time: 2021-08-16 21:05:55.875358 UTC
  Lon     = +-0.708355 +/- 0.0004 deg
  Lat     = +50.536400 +/- 0.0003 deg
  Lat geo = +50.350608 +/- 0.0003 deg
  Ht      =  108595.33 +/- 74.58 m

  JD dynamic   = 2459443.379919668660 
  LST apparent = 281.2479593830 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  57.72188 +/- 0.6781 deg
  Dec       = +58.43274 +/- 0.2719 deg
  Azimuth   =  23.36372 +/- 0.1960 deg
  Elevation = +24.61628 +/- 0.4055 deg
  Vavg      =  59.05687 +/- 0.0220 km/s
  Vinit     =  59.14378 +/- 0.1046 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  57.32039 +/- 0.6781 deg
  Dec       = +58.26118 +/- 0.2719 deg
  Azimuth   =  23.65774 +/- 0.1960 deg
  Elevation = +24.56788 +/- 0.4055 deg
  Vavg      =  59.16614 +/- 0.0220 km/s
  Vinit     =  59.25305 +/- 0.1046 km/s
Radiant (geocentric, J2000):
  R.A.   =  57.88202 +/- 0.6714 deg
  Dec    = +57.78881 +/- 0.2797 deg
  Vg     =  58.09348 +/- 0.1065 km/s
  Vinf   =  59.14378 +/- 0.1046 km/s
  Zc     =  65.55430 +/- 0.4057 deg
  Zg     =  66.21531 +/- 0.4130 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  69.31899 +/- 0.3329 deg
  Bg     = +36.63471 +/- 0.3635 deg
  Vh     =  39.85018 +/- 0.2047 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  91.70708 +/- 0.6045 deg
  Bh     = +60.44535 +/- 0.5283 deg
  Vh_x   =   0.58556 +/- 0.2034 km/s
  Vh_y   = -19.64752 +/- 0.2291 km/s
  Vh_z   = -34.66510 +/- 0.3561 km/s
Orbit:
  La Sun = 143.915115 +/- -0.0000 deg
  a      =   5.398930 +/- 0.9512 AU
  e      =   0.831348 +/- 0.0163
  i      = 114.136196 +/- 0.3142 deg
  peri   = 141.089212 +/- 1.4982 deg
  node   = 143.913062 +/- 0.0000 deg
  Pi     = 285.002274 +/- 1.4983 deg
  q      =   0.910540 +/- 0.0063 AU
  f      =  38.906632 +/- 1.4982 deg
  M      =   2.140727 +/- 0.3171 deg
  Q      =   9.887320 +/- 1.8963 AU
  n      =   0.078567 +/- 0.0104 deg/day
  T      =  12.544755 +/- 3.8686 years
  Last perihelion JD = 2459416.132913 (2021-07-20 15:11:23.640508) +/- 1.0244 days
  Tj     =   0.501020 +/- 0.0947
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.835801e-04, +1.075286e-04, +1.769608e-02, +7.331956e-09, +4.506407e-04, -9.325936e-05
q   , +1.075286e-04, +4.223259e-05, +6.884500e-03, +2.743893e-09, +1.760290e-04, -3.488767e-05
Tp  , +1.769608e-02, +6.884500e-03, +1.125288e+00, +4.525989e-07, +2.874046e-02, -5.755412e-03
node, +7.331956e-09, +2.743893e-09, +4.525989e-07, +1.989056e-13, +1.151073e-08, -2.529708e-09
peri, +4.506407e-04, +1.760290e-04, +2.874046e-02, +1.151073e-08, +7.343897e-04, -1.463674e-04
i   , -9.325936e-05, -3.488767e-05, -5.755412e-03, -2.529708e-09, -1.463674e-04, +3.217348e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.676684
 a2 = 16.602901

Mean time residuals from time vs. length:
  Station with reference time: UK0001
  Avg. res. = 9.624e-07 s
  Stddev    = 9.81e-04 s

Begin point on the trajectory:
  Lon =    -0.721050 +/- 0.0003 deg
  Lat =    50.517663 +/- 0.0002 deg
  Ht  = 107537.95 +/- 65.15 m
End point on the trajectory:
  Lon =    -0.792748 +/- 0.0003 deg
  Lat =    50.413016 +/- 0.0003 deg
  Ht  = 101654.90 +/- 86.69 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,  35.946327,   0.000000,   107537.95,   101654.90,          0.018082,     39.57,     16.87,              70.90, 0.8929,    True,    True, {"ff_name": "FF_UK0001_20210816_210556_888_0097024.fits"}
    UK0009,   False,    -0.848117,    51.261084,   92.00,   5.112676,   0.000000,   106005.04,   102111.15,          0.005299,      8.97,      8.99,              96.62, 0.9867,    True,    True, {"ff_name": "FF_UK0009_20210816_210552_720_0046592.fits"}
    UK0038,   False,    -2.379250,    51.361350,  169.00,   0.111895,  27.423017,   106761.66,   101834.06,          0.020939,     66.22,     13.78,              85.72, 0.9944,    True,    True, {"ff_name": "FF_UK0038_20210816_210552_783_0090368.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,       1,  0.000000, 2459443.379118468147, 318.97763,  26.40486,              114.91196,  51.77106,       114.91652,       51.78010,    318.97763,     +26.40486,     318.96875,      +26.41002,   805759.94, -4051712.57,  4984741.32,      50.535882,       -0.708540,  108566.11,  137446.65,       0.00,               70.15,  -106.47,      0.00,           59986.88,      8.90,    -20.92,          34.12,  +5.61,  +4.92
  1,     UK0001,       0,  0.039724, 2459443.379118927754, 318.33261,  25.60567,              116.45047,  51.51928,       116.42968,       51.48063,    318.33261,     +25.60567,     318.37081,      +25.58366,   805069.62, -4052805.46,  4982637.44,      50.517663,       -0.721050,  107537.95,  136700.72,    2469.26,             2539.42,    13.36,  62160.45,           59986.88,    -38.14,     89.46,         146.73,  +4.25,  +3.57
  2,     UK0001,       0,  0.079536, 2459443.379119388759, 317.84599,  24.88538,              117.71991,  51.22842,       117.70926,       51.20958,    317.84599,     +24.88538,     317.86491,      +24.87465,   804484.55, -4053731.74,  4980854.33,      50.502216,       -0.731674,  106667.14,  136099.49,    4562.05,             4632.21,  -248.48,  52566.88,           59986.88,    -18.60,     43.67,          71.94,  +2.17,  +1.50
  3,     UK0001,       0,  0.119284, 2459443.379119848832, 317.21695,  23.95089,              119.34734,  50.83608,       119.34726,       50.83595,    317.21695,     +23.95089,     317.21758,      +23.95081,   803731.97, -4054923.21,  4978560.68,      50.482339,       -0.745286,  105547.82,  135371.82,    7254.05,             7324.20,    92.66,  67726.47,           59986.88,     -0.13,      0.31,           0.52,  +1.38,  +0.72
  4,     UK0001,       0,  0.159056, 2459443.379120308906, 316.67493,  23.16601,              120.71504,  50.50216,       120.71505,       50.50219,    316.67493,     +23.16601,     316.67557,      +23.16602,   803100.30, -4055923.26,  4976635.55,      50.465649,       -0.756733,  104609.03,  134798.61,    9513.52,             9583.68,    -0.12,  56810.74,           59877.68,      0.03,     -0.06,           0.10,  +0.97,  +0.32
  5,     UK0001,       0,  0.198816, 2459443.379120769445, 316.11838,  22.34200,              122.12128,  50.13317,       122.12340,       50.13638,    316.11838,     +22.34200,     316.11601,      +22.34383,   802445.65, -4056959.70,  4974640.36,      50.448345,       -0.768585,  103636.75,  134242.47,   11855.22,            11925.38,    -9.98,  58895.86,           59706.24,      3.20,     -7.50,          12.53,  +0.97,  +0.33
  6,     UK0001,       0,  0.238564, 2459443.379121229518, 315.56300,  21.54768,              123.48425,  49.77633,       123.47556,       49.76369,    315.56300,     +21.54768,     315.57666,      +21.54044,   801812.40, -4057962.25,  4972710.40,      50.431601,       -0.780051,  102696.91,  133741.25,   14120.36,            14190.51,   -95.69,  56987.42,           59353.86,    -12.66,     29.69,          49.78,  +1.48,  +0.85
  7,     UK0001,       0,  0.278304, 2459443.379121689126, 314.97550,  20.64271,              124.96504,  49.33285,       124.96181,       49.32836,    314.97550,     +20.64271,     314.98119,      +20.64013,   801109.79, -4059074.60,  4970569.07,      50.413016,       -0.792748,  101654.90,  133228.85,   16633.58,            16703.74,    67.16,  63241.73,           59530.78,     -4.52,     10.61,          17.85,  +2.06,  +1.44
  0,     UK0009,       0,  0.102394, 2459443.379119668622, 284.45740,  11.63360,              174.86259,  50.27856,       174.87281,       50.28175,    284.45740,     +11.63360,     284.45099,      +11.63642,   804039.46, -4054436.40,  4979497.81,      50.490461,       -0.739728,  106005.04,  136924.70,       0.00,             6224.32,    -8.27,      0.00,           59525.93,     12.29,    -12.27,          26.17,  +2.31,  +1.63
  1,     UK0009,       0,  0.142058, 2459443.379120127764, 284.08359,  10.76824,              175.50246,  49.43407,       175.51434,       49.43777,    284.08359,     +10.76824,     284.07615,      +10.77154,   803400.48, -4055448.02,  4977550.41,      50.473581,       -0.751307,  105055.08,  137352.99,    2285.61,             8509.92,   -68.54,  57624.24,           59525.93,     14.53,    -14.51,          30.84,  +0.98,  +0.29
  2,     UK0009,       0,  0.181678, 2459443.379120586440, 283.67491,   9.84110,              176.17963,  48.52647,       176.17935,       48.52638,    283.67491,      +9.84110,     283.67586,       +9.84102,   802708.69, -4056543.24,  4975442.05,      50.455299,       -0.763824,  104027.35,  137858.09,    4760.13,            10984.45,    62.70,  62456.47,           59525.93,     -0.35,      0.35,           0.74,  +0.86,  +0.16
  3,     UK0009,       0,  0.221342, 2459443.379121045582, 283.31017,   8.98885,              176.76790,  47.68890,       176.76794,       47.68891,    283.31017,      +8.98885,     283.31107,       +8.98886,   802070.82, -4057553.12,  4973498.00,      50.438435,       -0.775374,  103080.38,  138361.50,    7041.82,            13266.13,    -1.49,  57525.28,           59525.93,      0.06,     -0.06,           0.12,  +1.41,  +0.70
  4,     UK0009,       0,  0.260998, 2459443.379121504724, 282.94456,   8.12090,              177.34193,  46.83316,       177.34694,       46.83470,    282.94456,      +8.12090,     282.94215,       +8.12234,   801417.50, -4058587.45,  4971506.87,      50.421157,       -0.787194,  102111.15,  138914.20,    9378.75,            15603.07,    -9.96,  58930.20,           59304.26,      6.45,     -6.44,          13.53,  +3.95,  +3.24
  0,     UK0038,       0,  0.073282, 2459443.379119318444, 319.87887,   6.87308,              128.82072,  34.48939,       128.81322,       34.47842,    319.87887,      +6.87308,     319.89001,       +6.86655,   804548.07, -4053631.17,  4981047.92,      50.503893,       -0.730513,  106761.66,  185119.19,       0.00,             4405.00,  -105.78,      0.00,           60157.26,     -8.31,     39.81,          45.32,  +3.56,  +2.22
  1,     UK0038,       0,  0.113774, 2459443.379119786900, 319.48434,   6.19024,              129.63746,  34.08376,       129.64286,       34.09154,    319.48434,      +6.19024,     319.47709,       +6.19489,   803838.22, -4054755.00,  4978884.49,      50.485146,       -0.743366,  105705.79,  185050.24,    2539.15,             6944.15,    38.52,  62707.50,           60157.26,      5.92,    -28.38,          32.31,  +2.28,  +0.94
  2,     UK0038,       0,  0.154234, 2459443.379120255355, 319.07347,   5.53907,              130.44626,  33.70911,       130.44579,       33.70843,    319.07347,      +5.53907,     319.07479,       +5.53867,   803145.38, -4055851.89,  4976772.93,      50.466840,       -0.755909,  104676.01,  185016.45,    5017.44,             9422.44,   123.85,  61252.81,           60157.26,     -0.52,      2.47,           2.81,  +2.08,  +0.74
  3,     UK0038,       0,  0.194666, 2459443.379120723344, 318.71717,   4.93058,              131.16732,  33.34191,       131.17528,       33.35309,    318.71717,      +4.93058,     318.70681,       +4.93731,   802510.81, -4056856.53,  4974838.96,      50.450068,       -0.767406,  103733.50,  185014.09,    7287.29,            11692.29,     2.40,  56139.88,           60157.26,      8.57,    -41.13,          46.84,  +1.98,  +0.64
  4,     UK0038,       0,  0.235078, 2459443.379121190868, 318.33044,   4.34514,              131.90206,  33.00558,       131.89482,       32.99553,    318.33044,      +4.34514,     318.34151,       +4.33907,   801879.68, -4057855.73,  4972915.45,      50.433381,       -0.778837,  102796.73,  185039.43,    9544.86,            13949.85,  -130.15,  55863.78,           58934.60,     -7.76,     37.12,          42.28,  +4.09,  +2.75
  5,     UK0038,       0,  0.275546, 2459443.379121659324, 318.00472,   3.70038,              132.59998,  32.58475,       132.62829,       32.62368,    318.00472,      +3.70038,     317.96669,       +3.72395,   801230.64, -4058883.28,  4970937.38,      50.416214,       -0.790582,  101834.06,  185094.50,   11866.46,            16271.46,  -201.97,  57368.96,           58361.17,     30.03,   -144.39,         164.34,  +5.36,  +4.02

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.