Orbital Analysis for matched events on 20210810_013306.225_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 61.70° Bg 37.01° Vg 54.43km/s
mass 0.00628g, abs. mag 0.9
Path Details
------------
start -3.68° 51.04° 107.26km
end   -3.75° 51.01° 100.34km

Orbit Details
-------------
Semimajor axis 2.19A.U., eccentricity 0.59, inclination 111.22°, Period 3.24Y, LA Sun 137.37°, last Perihelion 2021-07-07

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: 2459436.564655392431
Time: 2021-08-10 01:33:06.258978 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0020 and UK003H
 Convergence angle = 24.63883 deg
 R.A. =  45.58694  Dec = +56.87338 deg

Best intersection: Stations UK0020 and UK003H with Qconv = 24.64 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3798751.58 +/- 87.90 m
 Y =  -1506903.20 +/- 49.26 m
 Z =   5021117.23 +/- 208.73 m
 Vx =    21010.86 +/- 525.69 m/s
 Vy =    22288.99 +/- 1312.67 m/s
 Vz =    46344.93 +/- 1176.67 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.030141e+04, -6.456448e+03, +2.582003e+04, +5.852501e+04, -6.808761e+04, +1.468883e+05
-6.456448e+03, +4.479253e+03, -1.697246e+04, -3.954574e+04, +4.492936e+04, -1.041636e+05
+2.582003e+04, -1.697246e+04, +6.816533e+04, +1.555928e+05, -1.864427e+05, +4.164618e+05
+5.852501e+04, -3.954574e+04, +1.555928e+05, +3.817209e+05, -4.342088e+05, +1.009110e+06
-6.808761e+04, +4.492936e+04, -1.864427e+05, -4.342088e+05, +5.603996e+05, -1.217571e+06
+1.468883e+05, -1.041636e+05, +4.164618e+05, +1.009110e+06, -1.217571e+06, +2.888199e+06

Timing offsets (from input data):
    UK0020: 0.000000 s
    UK003H: -0.003834 s

Reference point on the trajectory:
  Time: 2021-08-10 01:33:06.258978 UTC
  Lon     = +-3.670428 +/- 0.0003 deg
  Lat     = +51.042768 +/- 0.0005 deg
  Lat geo = +50.857641 +/- 0.0005 deg
  Ht      =  108715.73 +/- 223.10 m

  JD dynamic   = 2459436.565456516109 
  LST apparent = 338.3625745194 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  46.69076 +/- 1.4002 deg
  Dec       = +56.53792 +/- 0.7530 deg
  Azimuth   =  54.44890 +/- 0.8212 deg
  Elevation = +50.96405 +/- 0.9327 deg
  Vavg      =  52.63127 +/- 0.7654 km/s
  Vinit     =  55.55275 +/- 0.9457 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  46.89477 +/- 1.4002 deg
  Dec       = +56.30012 +/- 0.7530 deg
  Azimuth   =  54.73070 +/- 0.8212 deg
  Elevation = +50.77001 +/- 0.9327 deg
  Vavg      =  52.78456 +/- 0.7654 km/s
  Vinit     =  55.70604 +/- 0.9457 km/s
Radiant (geocentric, J2000):
  R.A.   =  46.97750 +/- 1.4186 deg
  Dec    = +56.30104 +/- 0.7687 deg
  Vg     =  54.43320 +/- 0.9639 km/s
  Vinf   =  55.55275 +/- 0.9457 km/s
  Zc     =  39.14383 +/- 0.9308 deg
  Zg     =  39.55853 +/- 0.9524 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  61.70097 +/- 0.5769 deg
  Bg     = +37.01200 +/- 0.9804 deg
  Vh     =  36.67898 +/- 1.2120 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  86.83062 +/- 1.5743 deg
  Bh     = +63.30342 +/- 0.9008 deg
  Vh_x   =  -0.91107 +/- 0.4452 km/s
  Vh_y   = -16.45340 +/- 0.2283 km/s
  Vh_z   = -32.76893 +/- 1.3456 km/s
Orbit:
  La Sun = 137.371168 +/- 0.0000 deg
  a      =   2.191172 +/- 3.4571 AU
  e      =   0.588819 +/- 0.0956
  i      = 111.218901 +/- 0.4571 deg
  peri   = 134.410267 +/- 5.0126 deg
  node   = 137.370939 +/- 0.0000 deg
  Pi     = 271.781206 +/- 5.0126 deg
  q      =   0.900969 +/- 0.0160 AU
  f      =  45.585959 +/- 5.0126 deg
  M      =  10.339661 +/- 2.6591 deg
  Q      =   3.481374 +/- 6.9012 AU
  n      =   0.303871 +/- 0.0784 deg/day
  T      =   3.243510 +/- 14.9415 years
  Last perihelion JD = 2459402.538994 (2021-07-07 00:56:09.099851) +/- 3.9990 days
  Tj     =   1.995469 +/- 0.5617
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.765103e-02, +3.111816e-03, +7.791230e-01, +6.264146e-08, +1.703387e-02, -8.909744e-04
q   , +3.111816e-03, +5.611935e-04, +1.396868e-01, +1.037137e-08, +3.061077e-03, -1.475019e-04
Tp  , +7.791230e-01, +1.396868e-01, +3.483507e+01, +2.619154e-06, +7.627811e-01, -3.724818e-02
node, +6.264146e-08, +1.037137e-08, +2.619154e-06, +3.092398e-13, +5.711835e-08, -4.404792e-09
peri, +1.703387e-02, +3.061077e-03, +7.627811e-01, +5.711835e-08, +1.670793e-02, -8.123230e-04
i   , -8.909744e-04, -1.475019e-04, -3.724818e-02, -4.404792e-09, -8.123230e-04, +6.274231e-05

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.069823
 a2 = 42.745626

Mean time residuals from time vs. length:
  Station with reference time: UK0020
  Avg. res. = 7.423e-06 s
  Stddev    = 2.72e-03 s

Begin point on the trajectory:
  Lon =    -3.683940 +/- 0.0004 deg
  Lat =    51.036679 +/- 0.0003 deg
  Ht  = 107255.01 +/- 145.14 m
End point on the trajectory:
  Lon =    -3.748703 +/- 0.0003 deg
  Lat =    51.007770 +/- 0.0004 deg
  Ht  = 100336.21 +/- 166.78 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
    UK0020,   False,    -3.515726,    50.691998,   17.00,   2.863077,   0.000000,   107157.57,   100336.21,          0.012774,      8.70,     22.60,              34.78, 1.0000,    True,    True, {"ff_name": "FF_UK0020_20210810_013300_581_0463360.fits"}
    UK003H,   False,    -2.379250,    51.361350,  169.00,   0.000000,   0.000000,   107255.01,   100851.61,          0.018836,     33.88,     33.64,              78.03, 1.0000,    True,    True, {"ff_name": "FF_UK003H_20210810_013304_696_0467968.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,     UK0020,       1,  0.000000, 2459436.564655392431, 322.36612,  70.02531,              344.45026,  69.23907,       344.45743,       69.21755,    322.36612,     +70.02531,     322.34124,      +70.04524,  3798741.32, -1506914.09,  5021094.59,      51.042680,       -3.670485,  108694.66,  116101.53,       0.00,               27.13,   132.20,      0.00,           54847.56,     40.95,    -15.83,          77.99,  +5.24,  +4.92
  1,     UK0020,       0,  0.040236, 2459436.564655858092, 320.74300,  69.81089,              342.79690,  69.13226,       342.79434,       69.13850,    320.74300,     +69.81089,     320.75077,      +69.80515,  3797992.84, -1507708.09,  5019443.63,      51.036273,       -3.684872,  107157.57,  114520.36,    1978.97,             2006.10,  -124.05,  49184.01,           54847.56,    -11.77,      4.54,          22.72,  +1.32,  +1.03
  2,     UK0020,       0,  0.080484, 2459436.564656323753, 318.86824,  69.48615,              340.77795,  69.02801,       340.78170,       69.02053,    318.86824,     +69.48615,     318.85896,      +69.49296,  3797104.66, -1508650.30,  5017484.52,      51.028664,       -3.701916,  105333.88,  112660.36,    4327.32,             4354.45,   -11.58,  58347.10,           54847.56,     13.93,     -5.37,          27.33,  +0.87,  +0.61
  3,     UK0020,       0,  0.120748, 2459436.564656789880, 317.04748,  69.16120,              338.81201,  68.88463,       338.81425,       68.88083,    317.04748,     +69.16120,     317.04286,      +69.16462,  3796254.27, -1509552.42,  5015608.76,      51.021372,       -3.718245,  103588.09,  110897.17,    6575.75,             6602.89,     0.08,  55842.24,           54847.56,      7.01,     -2.71,          13.98,  +0.69,  +0.47
  4,     UK0020,       0,  0.161032, 2459436.564657256007, 315.22949,  68.81895,              336.83830,  68.70489,       336.83146,       68.71492,    315.22949,     +68.81895,     315.24433,      +68.80997,  3795412.33, -1510445.58,  5013751.65,      51.014147,       -3.734418,  101859.94,  109169.32,    8801.84,             8828.97,   -11.73,  55259.78,           55146.19,    -18.38,      7.08,          37.21,  +0.91,  +0.72
  5,     UK0020,       0,  0.201288, 2459436.564657722134, 313.62374,  68.49245,              335.07344,  68.52056,       335.05554,       68.54409,    313.62374,     +68.49245,     313.65905,      +68.47155,  3794669.87, -1511233.20,  5012113.96,      51.007770,       -3.748703,  100336.21,  107661.22,   10764.90,            10792.03,  -285.00,  48764.42,           54319.80,    -42.83,     16.48,          87.92,  +2.08,  +1.92
  6,     UK0020,       1,  0.241688, 2459436.564658189658, 311.30855,  68.00046,              332.54026,  68.19580,       332.48528,       68.25865,    311.30855,     +68.00046,     311.40614,      +67.94520,  3793607.33, -1512360.38,  5009770.25,      50.998636,       -3.769078,   98156.01,  105528.53,   13574.26,            13601.39,   280.03,  69538.65,           55661.34,   -113.62,     43.59,         237.86,  +6.09,  +5.97
  0,     UK003H,       0,  0.029270, 2459436.564655775204, 295.06480,  24.58534,              248.92110,  46.83117,       248.90077,       46.83326,    295.06480,     +24.58534,     295.07815,      +24.57804,  3798040.29, -1507657.76,  5019548.29,      51.036679,       -3.683940,  107255.01,  145775.43,       0.00,             1880.65,   359.68,      0.00,           53365.81,    -25.21,     25.38,          50.61,  +3.06,  +2.24
  1,     UK003H,       0,  0.069878, 2459436.564656245057, 294.62926,  23.96081,              248.78532,  46.09705,       248.74561,       46.10113,    294.62926,     +23.96081,     294.65564,      +23.94642,  3797323.08, -1508418.59,  5017966.30,      51.030536,       -3.697737,  105782.34,  145487.31,    1896.29,             3776.95,     0.09,  46697.56,           53365.81,    -49.82,     50.14,         100.21,  +1.63,  +0.82
  2,     UK003H,       0,  0.110658, 2459436.564656717237, 294.09914,  23.13409,              248.57233,  45.14972,       248.54963,       45.15205,    294.09914,     +23.13409,     294.11471,      +23.12579,  3796396.74, -1509401.28,  5015923.02,      51.022594,       -3.715511,  103880.56,  145149.00,    4345.53,             6226.19,   183.88,  60059.77,           53365.81,    -28.88,     29.07,          58.23,  +1.13,  +0.32
  3,     UK003H,       0,  0.151326, 2459436.564657188021, 293.65258,  22.42853,              248.39658,  44.34241,       248.38824,       44.34326,    293.65258,     +22.42853,     293.65883,      +22.42545,  3795611.25, -1510234.56,  5014190.42,      51.015854,       -3.730612,  102268.22,  144895.28,    6422.37,             8303.02,     1.50,  51068.09,           53365.81,    -10.74,     10.82,          21.71,  +1.25,  +0.44
  4,     UK003H,       0,  0.191910, 2459436.564657657407, 293.28037,  21.79552,              248.21924,  43.63294,       248.24993,       43.62979,    293.28037,     +21.79552,     293.26038,      +21.80693,  3794921.02, -1510966.77,  5012667.94,      51.009927,       -3.743904,  100851.61,  144697.64,    8247.34,            10127.99,  -428.08,  44967.70,           51684.43,     39.91,    -40.23,          80.78,  +3.80,  +3.00

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.