Orbital Analysis for matched events on 20210813_005309.150_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 67.54° Bg 41.64° Vg 55.38km/s
mass 0.03077g, abs. mag -1.2
Path Details
------------
start 2.05° 52.28° 109.66km
end   1.97° 52.23° 100.41km

Orbit Details
-------------
Semimajor axis 5.89A.U., eccentricity 0.84, inclination 105.37°, Period 14.31Y, LA Sun 140.22°, last Perihelion 2021-07-17

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: 2459439.536911464762
Time: 2021-08-13 00:53:09.168258 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000Z and UK002K
 Convergence angle = 19.30605 deg
 R.A. =  52.11817  Dec = +62.55527 deg
Intersection 2 - Stations: UK000Z and UK0032
 Convergence angle = 17.88563 deg
 R.A. =  50.21373  Dec = +59.50035 deg
Intersection 3 - Stations: UK002K and UK0032
 Convergence angle = 1.74679 deg
 R.A. = 144.86292  Dec = +70.27792 deg

Best intersection: Stations UK000Z and UK002K with Qconv = 19.31 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3662201.51 +/- 174.85 m
 Y =  -1552144.97 +/- 111.14 m
 Z =   5109454.89 +/- 43.73 m
 Vx =    16140.00 +/- 1307.02 m/s
 Vy =    20617.43 +/- 726.30 m/s
 Vz =    50048.87 +/- 1187.25 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+3.252057e+04, +2.005695e+04, +6.881730e+03, +2.306734e+05, +1.236453e+05, +4.536687e+02
+2.005695e+04, +1.322148e+04, +4.329328e+03, +1.417867e+05, +8.096386e+04, -8.470610e+02
+6.881730e+03, +4.329328e+03, +2.143978e+03, +4.748370e+04, +2.435824e+04, +3.731272e+02
+2.306734e+05, +1.417867e+05, +4.748370e+04, +1.956178e+06, +1.039999e+06, +6.251493e+03
+1.236453e+05, +8.096386e+04, +2.435824e+04, +1.039999e+06, +5.892515e+05, -4.062935e+03
+4.536687e+02, -8.470610e+02, +3.731272e+02, +6.251493e+03, -4.062935e+03, +3.119559e+03

Timing offsets (from input data):
    UK000Z: -0.000079 s
    UK002K: 0.000166 s
    UK0032: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 00:53:09.168258 UTC
  Lon     = ++2.056744 +/- 0.0024 deg
  Lat     = +52.283609 +/- 0.0007 deg
  Lat geo = +52.100390 +/- 0.0007 deg
  Ht      =  110295.94 +/- 103.46 m

  JD dynamic   = 2459439.537712410558 
  LST apparent = 337.0313902395 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  51.94501 +/- 1.2400 deg
  Dec       = +62.38326 +/- 1.2263 deg
  Azimuth   =  45.06181 +/- 2.1381 deg
  Elevation = +50.78075 +/- 0.1880 deg
  Vavg      =  54.80236 +/- 0.7728 km/s
  Vinit     =  56.48422 +/- 0.6782 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  52.10845 +/- 1.2400 deg
  Dec       = +62.13203 +/- 1.2263 deg
  Azimuth   =  45.38860 +/- 2.1381 deg
  Elevation = +50.61931 +/- 0.1880 deg
  Vavg      =  54.93277 +/- 0.7728 km/s
  Vinit     =  56.61464 +/- 0.6782 km/s
Radiant (geocentric, J2000):
  R.A.   =  52.29642 +/- 1.2794 deg
  Dec    = +62.16521 +/- 1.2282 deg
  Vg     =  55.38370 +/- 0.6913 km/s
  Vinf   =  56.48422 +/- 0.6782 km/s
  Zc     =  39.34885 +/- 0.1903 deg
  Zg     =  39.75192 +/- 0.1972 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  67.53732 +/- 1.2908 deg
  Bg     = +41.63619 +/- 0.9671 deg
  Vh     =  40.00713 +/- 0.0488 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     = 100.10716 +/- 4.8487 deg
  Bh     = +66.89215 +/- 0.8865 deg
  Vh_x   =   2.75542 +/- 1.3330 km/s
  Vh_y   = -15.45766 +/- 0.6653 km/s
  Vh_z   = -36.79727 +/- 0.2841 km/s
Orbit:
  La Sun = 140.223943 +/- 0.0000 deg
  a      =   5.893536 +/- 0.1438 AU
  e      =   0.844993 +/- 0.0047
  i      = 105.373184 +/- 2.0562 deg
  peri   = 141.734217 +/- 1.9722 deg
  node   = 140.224041 +/- 0.0001 deg
  Pi     = 281.958258 +/- 1.9721 deg
  q      =   0.913541 +/- 0.0096 AU
  f      =  38.262171 +/- 1.9723 deg
  M      =   1.844816 +/- 0.0982 deg
  Q      =  10.873531 +/- 0.2900 AU
  n      =   0.068888 +/- 0.0027 deg/day
  T      =  14.307525 +/- 0.5162 years
  Last perihelion JD = 2459412.757568 (2021-07-17 06:10:53.895628) +/- 1.1600 days
  Tj     =   0.581309 +/- 0.0362
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.357287e-05, -2.712399e-05, -2.989273e-03, +9.178307e-09, -9.320593e-05, -1.368418e-04
q   , -2.712399e-05, +1.009475e-04, +1.211965e-02, -2.424239e-08, +3.606733e-04, +3.620965e-04
Tp  , -2.989273e-03, +1.211965e-02, +1.461443e+00, -2.861290e-06, +4.339913e-02, +4.272772e-02
node, +9.178307e-09, -2.424239e-08, -2.861290e-06, +6.353858e-12, -8.590838e-08, -9.490675e-08
peri, -9.320593e-05, +3.606733e-04, +4.339913e-02, -8.590838e-08, +1.290148e-03, +1.282971e-03
i   , -1.368418e-04, +3.620965e-04, +4.272772e-02, -9.490675e-08, +1.282971e-03, +1.417730e-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: UK0032
  Avg. res. = 9.797e-07 s
  Stddev    = 9.90e-04 s

Begin point on the trajectory:
  Lon =     2.051471 +/- 0.0019 deg
  Lat =    52.280382 +/- 0.0007 deg
  Ht  = 109662.35 +/- 56.46 m
End point on the trajectory:
  Lon =     1.973490 +/- 0.0022 deg
  Lat =    52.233146 +/- 0.0007 deg
  Ht  = 100412.33 +/- 96.18 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
    UK000Z,   False,    -1.740490,    53.069201,  230.00,   0.000000,   0.000000,   107780.75,   100852.79,          0.007862,     15.38,     36.63,              55.17, 0.6737,    True,    True, {"ff_name": "FF_UK000Z_20210813_005304_034_0410368.fits"}
    UK002K,   False,    -0.382860,    53.537770,   34.00,   0.000000,   0.000000,   109662.35,   101032.12,          0.015532,     43.77,     48.37,              64.97, 0.8210,    True,    True, {"ff_name": "FF_UK002K_20210813_005301_788_0415744.fits"}
    UK0032,   False,    -0.023645,    52.984073,    6.00,   0.000000,   0.000000,   108713.35,   100412.33,          0.013323,     28.89,     34.40,              52.99, 0.6376,    True,    True, {"ff_name": "FF_UK0032_20210813_005308_259_0421888.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,     UK000Z,       0,  0.062072, 2459439.536912183743,  37.22164,   6.10610,              107.67018,  20.30672,       107.67082,       20.30729,     37.22164,      +6.10610,      37.22107,       +6.10622,  3661273.73, -1553330.13,  5106577.91,      52.270792,       +2.035623,  107780.75,  293116.52,       0.00,             3246.91,   159.65,      0.00,           57007.19,     -3.93,     -1.65,           3.00,  +4.29,  +1.95
  1,     UK000Z,       0,  0.102212, 2459439.536912648473,  37.17755,   5.80676,              107.89188,  20.08709,       107.89223,       20.08740,     37.17755,      +5.80676,      37.17753,       +5.80682,  3660749.97, -1553999.20,  5104953.75,      52.263550,       +2.023635,  106361.10,  292120.64,    1832.99,             5079.90,  -274.64,  45664.96,           57007.19,     -2.15,     -0.90,           1.65,  +1.73,  -0.60
  2,     UK000Z,       0,  0.142420, 2459439.536913113669,  37.11799,   5.37593,              108.20656,  19.76833,       108.20903,       19.77050,     37.11799,      +5.37593,      37.11542,       +5.37638,  3660003.27, -1554953.04,  5102638.30,      52.253218,       +2.006612,  104337.55,  290719.34,    4446.17,             7693.08,    67.42,  64991.53,           57007.19,    -14.89,     -6.25,          11.46,  +1.46,  -0.86
  3,     UK000Z,       0,  0.182612, 2459439.536913578864,  37.07590,   4.98868,              108.47848,  19.47488,       108.49166,       19.48643,     37.07590,      +4.98868,      37.05979,       +4.99105,  3659340.83, -1555799.24,  5100584.14,      52.244045,       +1.991490,  102542.69,  289489.18,    6764.46,            10011.36,   115.49,  57680.29,           57007.19,    -79.04,    -33.18,          61.08,  +1.78,  -0.53
  4,     UK000Z,       0,  0.222772, 2459439.536914043594,  37.00922,   4.62477,              108.75666,  19.21419,       108.75914,       19.21637,     37.00922,      +4.62477,      37.00698,       +4.62521,  3658717.03, -1556596.10,  5098649.77,      52.235400,       +1.977237,  100852.79,  288342.49,    8947.55,            12194.46,    30.18,  54359.86,           56811.44,    -14.82,     -6.23,          11.50,  +2.74,  +0.44
  0,     UK002K,       0,  0.017910, 2459439.536911669653,  18.54487,   0.55458,              129.55329,  25.82348,       129.53520,       25.80808,     18.54487,      +0.55458,      18.56648,       +0.54835,  3661967.82, -1552443.49,  5108730.22,      52.280382,       +2.051471,  109662.35,  243320.20,       0.00,              817.84,   225.03,      0.00,           54175.00,     70.59,     63.87,          80.70,  +4.26,  +2.33
  1,     UK002K,       0,  0.058174, 2459439.536912135780,  18.44168,   0.10944,              129.88083,  25.47476,       129.88409,       25.47753,     18.44168,      +0.10944,      18.43804,       +0.11056,  3661367.77, -1553210.01,  5106869.51,      52.272091,       +2.037763,  108035.65,  242489.48,    2099.97,             2917.81,    50.72,  52155.02,           54175.00,    -12.68,    -11.46,          14.53,  +2.09,  +0.17
  2,     UK002K,       0,  0.098438, 2459439.536912601907,  18.30517,  -0.35767,              130.25028,  25.12084,       130.25400,       25.12399,     18.30517,      -0.35767,      18.30116,       -0.35639,  3660732.19, -1554021.91,  5104898.62,      52.263304,       +2.023250,  106312.92,  241626.91,    4324.27,             5142.11,     0.74,  55242.93,           54175.00,    -14.40,    -13.02,          16.57,  +1.44,  -0.48
  3,     UK002K,       0,  0.138694, 2459439.536913067568,  18.16337,  -0.82237,              130.62160,  24.77054,       130.62115,       24.77016,     18.16337,      -0.82237,      18.16449,       -0.82253,  3660102.16, -1554826.71,  5102944.96,      52.254587,       +2.008861,  104605.53,  240789.14,    6529.14,             7346.99,   -68.22,  54771.26,           54175.00,      1.74,      1.57,           2.01,  +1.13,  -0.78
  4,     UK002K,       0,  0.178974, 2459439.536913533695,  18.01485,  -1.32488,              131.01600,  24.38854,       131.01469,       24.38744,     18.01485,      -1.32488,      18.01716,       -1.32533,  3659427.40, -1555688.66,  5100852.58,      52.245244,       +1.993460,  102777.23,  239911.74,    8890.56,             9708.41,    18.02,  58625.18,           55160.66,      5.05,      4.57,           5.85,  +1.29,  -0.61
  5,     UK002K,       0,  0.219222, 2459439.536913999822,  17.84556,  -1.80037,              131.41513,  24.03893,       131.39090,       24.01857,     17.84556,      -1.80037,      17.87538,       -1.80873,  3658783.23, -1556511.53,  5098855.06,      52.236318,       +1.978748,  101032.12,  239092.62,   11144.92,            11962.76,    -1.00,  56011.59,           55563.72,     93.04,     84.23,         108.27,  +2.18,  +0.29
  0,     UK0032,       1,  0.000000, 2459439.536911464762,  23.65426,  11.73004,              118.14698,  33.45973,       118.14193,       33.45497,     23.65426,     +11.73004,      23.66052,      +11.72833,  3662186.73, -1552163.86,  5109409.03,      52.283405,       +2.056485,  110255.85,  196242.64,       0.00,               51.75,   470.58,      0.00,           52163.55,     16.69,     14.02,          22.91,  +4.84,  +3.38
  1,     UK0032,       0,  0.040188, 2459439.536911929958,  23.55032,  11.26363,              118.55119,  33.12245,       118.56996,       33.14004,     23.55032,     +11.26363,      23.52732,      +11.26997,  3661617.77, -1552890.66,  5107644.73,      52.275546,       +2.043478,  108713.35,  195086.62,    1991.16,             2042.91,   191.75,  49546.08,           52163.55,    -61.54,    -51.64,          84.93,  +2.83,  +1.38
  2,     UK0032,       0,  0.080348, 2459439.536912394688,  23.39415,  10.78486,              119.01200,  32.80115,       119.01769,       32.80646,     23.39415,     +10.78486,      23.38747,      +10.78678,  3661025.24, -1553647.55,  5105807.36,      52.267356,       +2.029939,  107107.20,  193897.58,    4064.78,             4116.53,    -3.04,  51634.01,           52163.55,    -18.54,    -15.57,          25.75,  +1.60,  +0.16
  3,     UK0032,       0,  0.120536, 2459439.536912859883,  23.24474,  10.25788,              119.49367,  32.43415,       119.50132,       32.44126,     23.24474,     +10.25788,      23.23585,      +10.26046,  3660388.07, -1554461.49,  5103831.53,      52.258544,       +2.015390,  105380.30,  192636.39,    6294.67,             6346.42,   -43.13,  55486.49,           52163.55,    -24.72,    -20.76,          34.57,  +1.30,  -0.12
  4,     UK0032,       0,  0.160716, 2459439.536913325079,  23.06742,   9.70853,              120.01340,  32.06122,       120.00628,       32.05464,     23.06742,      +9.70853,      23.07682,       +9.70613,  3659725.94, -1555307.30,  5101778.32,      52.249379,       +2.000275,  103586.10,  191344.98,    8611.88,             8663.63,     4.54,  57670.67,           53579.80,     22.83,     19.19,          32.15,  +1.08,  -0.33
  5,     UK0032,       0,  0.200904, 2459439.536913789809,  22.90331,   9.16226,              120.51447,  31.68235,       120.50149,       31.67041,     22.90331,      +9.16226,      22.92002,       +9.15791,  3659079.78, -1556132.72,  5099774.63,      52.240428,       +1.985519,  101835.45,  190103.41,   10873.21,            10924.96,    -4.12,  56268.86,           54368.66,     41.30,     34.73,          58.55,  +1.37,  -0.02
  6,     UK0032,       0,  0.241072, 2459439.536914255004,  22.78549,   8.70816,              120.90987,  31.35654,       120.90622,       31.35320,     22.78549,      +8.70816,      22.79096,       +8.70693,  3658554.43, -1556803.80,  5098145.56,      52.233146,       +1.973490,  100412.33,  189106.42,   12711.75,            12763.49,  -434.44,  45771.14,           53729.47,     11.55,      9.71,          16.45,  +2.94,  +1.56

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.