Orbital Analysis for matched events on 20210810_011441.040_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 64.59° Bg 38.54° Vg 59.76km/s
mass 0.00338g, abs. mag 1.2
Path Details
------------
start -2.21° 52.01° 108.26km
end   -2.28° 51.97° 100.43km

Orbit Details
-------------
Semimajor axis -16.74A.U., eccentricity 1.05, inclination 112.27°, Period 1000000000.00Y, LA Sun 137.36°, 

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: 2459436.551863892004
Time: 2021-08-10 01:14:41.042522 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000S and UK001Z
 Convergence angle = 29.63106 deg
 R.A. =  50.71237  Dec = +58.37023 deg

Best intersection: Stations UK000S and UK001Z with Qconv = 29.63 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3632396.84 +/- 43.91 m
 Y =  -1677798.69 +/- 41.17 m
 Z =   5088596.54 +/- 189.87 m
 Vx =    20350.40 +/- 1177.10 m/s
 Vy =    24107.05 +/- 830.98 m/s
 Vz =    51953.29 +/- 1552.36 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.308695e+03, -1.168609e+03, -8.448153e+03, +9.691093e+02, -1.236860e+04, -4.490457e+04
-1.168609e+03, +6.110529e+02, +4.162936e+03, -3.293522e+02, +6.238697e+03, +1.888527e+04
-8.448153e+03, +4.162936e+03, +3.157173e+04, -4.481576e+03, +4.538783e+04, +1.866263e+05
+9.691093e+02, -3.293522e+02, -4.481576e+03, +1.737164e+03, -5.373536e+03, -5.057895e+04
-1.236860e+04, +6.238697e+03, +4.538783e+04, -5.373536e+03, +6.628834e+04, +2.449037e+05
-4.490457e+04, +1.888527e+04, +1.866263e+05, -5.057895e+04, +2.449037e+05, +1.630162e+06

Timing offsets (from input data):
    UK000S: 0.002904 s
    UK001Z: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-10 01:14:41.042522 UTC
  Lon     = +-2.207471 +/- 0.0004 deg
  Lat     = +52.005747 +/- 0.0014 deg
  Lat geo = +51.822025 +/- 0.0014 deg
  Ht      =  108315.63 +/- 122.20 m

  JD dynamic   = 2459436.552664658986 
  LST apparent = 335.2078552125 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  49.83001 +/- 0.8043 deg
  Dec       = +58.73214 +/- 0.7059 deg
  Azimuth   =  50.15049 +/- 1.2134 deg
  Elevation = +49.31757 +/- 0.1976 deg
  Vavg      =  61.64364 +/- 1.3945 km/s
  Vinit     =  60.78185 +/- 1.3624 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  49.96928 +/- 0.8043 deg
  Dec       = +58.50594 +/- 0.7059 deg
  Azimuth   =  50.41932 +/- 1.2134 deg
  Elevation = +49.15752 +/- 0.1976 deg
  Vavg      =  61.79018 +/- 1.3945 km/s
  Vinit     =  60.92839 +/- 1.3624 km/s
Radiant (geocentric, J2000):
  R.A.   =  50.03398 +/- 0.7904 deg
  Dec    = +58.50558 +/- 0.7148 deg
  Vg     =  59.76022 +/- 1.3858 km/s
  Vinf   =  60.78185 +/- 1.3624 km/s
  Zc     =  40.80036 +/- 0.1984 deg
  Zg     =  41.16154 +/- 0.1972 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  64.59431 +/- 0.7642 deg
  Bg     = +38.54151 +/- 0.5679 deg
  Vh     =  42.46413 +/- 1.5509 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  89.00635 +/- 1.0971 deg
  Bh     = +61.27007 +/- 0.4098 deg
  Vh_x   =  -0.35397 +/- 0.4072 km/s
  Vh_y   = -20.40866 +/- 0.9359 km/s
  Vh_z   = -37.23660 +/- 1.2737 km/s
Orbit:
  La Sun = 137.358896 +/- 0.0000 deg
  a      = -16.740232 +/- 13.2548 AU
  e      =   1.054540 +/- 0.1348
  i      = 112.274554 +/- 0.4971 deg
  peri   = 143.741890 +/- 1.9537 deg
  node   = 137.358493 +/- 0.0000 deg
  Pi     = 281.100384 +/- 1.9536 deg
  q      =   0.913005 +/- 0.0047 AU
  f      =  36.254255 +/- 1.9537 deg
  M      =        nan +/- nan deg
  Q      = -34.393469 +/- 26.5109 AU
  n      =   0.014390 +/- 0.0575 deg/day
  T      = 1000000000.000000 +/- 399999961.1556 years
  Last perihelion JD = NaN 
  Tj     =  -0.766013 +/- 0.7878
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.131004e-02, +6.441228e-04, +2.529317e-01, -8.770977e-09, +4.677146e-03, +1.201601e-04
q   , +6.441228e-04, +3.915020e-05, +1.471928e-02, -9.269912e-11, +2.753642e-04, +1.247209e-06
Tp  , +2.529317e-01, +1.471928e-02, +5.696521e+00, -1.442829e-07, +1.057439e-01, +1.973738e-03
node, -8.770977e-09, -9.269912e-11, -1.442829e-07, +7.390265e-14, -2.143671e-09, -1.016199e-09
peri, +4.677146e-03, +2.753642e-04, +1.057439e-01, -2.143671e-09, +1.966981e-03, +2.928480e-05
i   , +1.201601e-04, +1.247209e-06, +1.973738e-03, -1.016199e-09, +2.928480e-05, +1.397326e-05

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: UK001Z
  Avg. res. = 3.672e-05 s
  Stddev    = 6.06e-03 s

Begin point on the trajectory:
  Lon =    -2.207985 +/- 0.0003 deg
  Lat =    52.005482 +/- 0.0013 deg
  Ht  = 108261.31 +/- 103.50 m
End point on the trajectory:
  Lon =    -2.282696 +/- 0.0003 deg
  Lat =    51.967290 +/- 0.0011 deg
  Ht  = 100432.85 +/- 61.77 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
    UK000S,   False,    -1.778230,    50.857470,   24.00,   0.000000,   0.000000,   108261.31,   100432.85,          0.024424,     25.17,     66.36,              44.73, 1.0000,    True,    True, {"ff_name": "FF_UK000S_20210810_011440_413_0443904.fits"}
    UK001Z,   False,    -2.949729,    50.877448,   82.00,   0.000000,   0.000000,   108257.01,   101049.29,          0.016986,     39.57,     31.68,              21.84, 1.0000,    True,    True, {"ff_name": "FF_UK001Z_20210810_011437_139_0439808.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,     UK000S,       0,  0.004226, 2459436.551863918081, 197.63009,  74.78422,              346.99725,  38.70094,       346.99817,       38.69987,    197.63009,     +74.78422,     197.62560,      +74.78371,  3632372.85, -1677827.10,  5088535.31,      52.005482,       -2.207985,  108261.31,  170921.30,       0.00,               71.64,    -0.03,      0.00,           58723.39,      3.58,      1.36,           4.62,  +2.56,  +1.40
  1,     UK000S,       0,  0.044498, 2459436.551864384208, 198.67543,  74.14180,              346.24976,  38.31502,       346.25784,       38.30582,    198.67543,     +74.14180,     198.63773,      +74.13759,  3631396.68, -1678983.47,  5086043.21,      51.994714,       -2.229049,  106050.56,  168867.36,    2915.58,             2987.22,   467.75,  72397.32,           58723.39,     30.79,     11.70,          40.23,  +2.01,  +0.87
  2,     UK000S,       0,  0.084674, 2459436.551864849404, 199.38767,  73.71049,              345.73772,  38.06412,       345.76148,       38.03726,    199.38767,     +73.71049,     199.27949,      +73.69849,  3630751.48, -1679747.77,  5084396.05,      51.987591,       -2.243031,  104589.65,  167524.70,    4842.66,             4914.29,   -47.15,  47965.76,           58723.39,     89.48,     33.95,         117.83,  +2.21,  +1.09
  3,     UK000S,       0,  0.124906, 2459436.551865315065, 200.17070,  73.15704,              345.11206,  37.72889,       345.14171,       37.69569,    200.17070,     +73.15704,     200.04010,      +73.14262,  3629951.99, -1680694.84,  5082355.01,      51.978758,       -2.260319,  102779.72,  165876.57,    7230.54,             7302.17,  -104.65,  59352.73,           58723.39,    110.04,     41.72,         146.34,  +3.19,  +2.09
  4,     UK000S,       0,  0.165246, 2459436.551865781657, 201.00922,  72.40586,              344.32124,  37.24711,       344.32969,       37.23777,    201.00922,     +72.40586,     200.97411,      +72.40194,  3628915.08, -1681923.17,  5079707.83,      51.967290,       -2.282696,  100432.85,  163765.66,   10327.55,            10399.19,   540.43,  76772.85,           62048.34,     30.74,     11.68,          41.42,  +5.13,  +4.06
  0,     UK001Z,       0,  0.000000, 2459436.551863892004,  96.08310,  69.58048,               22.05777,  37.70817,        22.04877,       37.71761,     96.08310,     +69.58048,      96.07967,      +69.59224,  3632370.95, -1677829.35,  5088530.46,      52.005461,       -2.208016,  108257.01,  174421.96,       0.00,               77.31,   262.52,      0.00,           61412.81,    -22.52,    -28.10,          42.58,  +2.91,  +1.70
  1,     UK001Z,       0,  0.040160, 2459436.551864356734,  96.79923,  69.58888,               21.81812,  37.54554,        21.79502,       37.56970,     96.79923,     +69.58888,      96.79166,      +69.61908,  3631709.51, -1678612.89,  5086841.85,      51.998166,       -2.222342,  106758.98,  172590.20,    1975.56,             2052.87,  -202.92,  49192.28,           61412.81,    -57.06,    -71.30,         109.14,  +2.37,  +1.18
  2,     UK001Z,       0,  0.080368, 2459436.551864822395,  97.88222,  69.65433,               21.40941,  37.34257,        21.41038,       37.34155,     97.88222,     +69.65433,      97.88282,      +69.65305,  3630722.45, -1679782.17,  5084321.93,      51.987270,       -2.243643,  104523.92,  169864.59,    4923.70,             5001.01,   301.31,  73322.23,           61412.81,      2.38,      2.96,           4.62,  +2.46,  +1.31
  3,     UK001Z,       0,  0.120556, 2459436.551865287125,  98.77053,  69.67138,               21.10334,  37.15220,        21.09962,       37.15606,     98.77053,     +69.67138,      98.77022,      +69.67624,  3629945.61, -1680702.41,  5082338.71,      51.978687,       -2.260446,  102765.27,  167724.21,    7243.94,             7321.24,   178.84,  57734.48,           61412.81,     -8.92,    -11.12,          17.53,  +3.18,  +2.06
  4,     UK001Z,       0,  0.160752, 2459436.551865752786,  99.66194,  69.67613,               20.80450,  36.95466,        20.79000,       36.96963,     99.66194,     +69.67613,      99.66027,      +69.69504,  3629187.47, -1681600.49,  5080403.23,      51.970304,       -2.276851,  101049.29,  165640.08,    9508.31,             9585.62,     0.03,  56333.38,           60425.90,    -34.23,    -42.70,          68.15,  +3.66,  +2.56

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.