Orbital Analysis for matched events on 20210813_005105.273_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 63.14° Bg 37.00° Vg 59.33km/s
mass 0.04482g, abs. mag -0.8
Path Details
------------
start 0.20° 54.49° 110.02km
end   0.05° 54.43° 95.00km

Orbit Details
-------------
Semimajor axis 10.01A.U., eccentricity 0.91, inclination 115.17°, Period 31.69Y, LA Sun 140.22°, last Perihelion 2021-07-22

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: 2459439.535477698781
Time: 2021-08-13 00:51:05.273175 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000Z and UK0026
 Convergence angle = 49.70457 deg
 R.A. =  48.71178  Dec = +56.55352 deg

Best intersection: Stations UK000Z and UK0026 with Qconv = 49.70 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3413169.46 +/- 44.76 m
 Y =  -1616330.50 +/- 37.63 m
 Z =   5258454.97 +/- 127.86 m
 Vx =    21702.99 +/- 661.26 m/s
 Vy =    24777.52 +/- 321.44 m/s
 Vz =    50580.65 +/- 698.85 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.357032e+03, -1.410543e+03, -5.812504e+03, +1.009423e+04, -1.552355e+03, -1.342194e+04
-1.410543e+03, +1.315054e+03, +4.204366e+03, -6.804820e+03, +1.220139e+03, +8.106965e+03
-5.812504e+03, +4.204366e+03, +1.765377e+04, -2.884055e+04, -1.637971e+03, +2.914101e+04
+1.009423e+04, -6.804820e+03, -2.884055e+04, +6.125988e+04, -7.944001e+02, -6.931673e+04
-1.552355e+03, +1.220139e+03, -1.637971e+03, -7.944001e+02, +2.902717e+04, +4.591093e+04
-1.342194e+04, +8.106965e+03, +2.914101e+04, -6.931673e+04, +4.591093e+04, +1.619996e+05

Timing offsets (from input data):
    UK000Z: -0.000318 s
    UK0026: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 00:51:05.273175 UTC
  Lon     = ++0.202771 +/- 0.0003 deg
  Lat     = +54.493744 +/- 0.0010 deg
  Lat geo = +54.314689 +/- 0.0010 deg
  Ht      =  110020.13 +/- 75.56 m

  JD dynamic   = 2459439.536278439686 
  LST apparent = 334.6597743669 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  48.78441 +/- 0.5580 deg
  Dec       = +56.92752 +/- 0.3779 deg
  Azimuth   =  55.17274 +/- 0.7363 deg
  Elevation = +50.25137 +/- 0.1083 deg
  Vavg      =  60.30186 +/- 0.6529 km/s
  Vinit     =  60.36014 +/- 0.5742 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  48.91440 +/- 0.5580 deg
  Dec       = +56.71725 +/- 0.3779 deg
  Azimuth   =  55.40485 +/- 0.7363 deg
  Elevation = +50.08655 +/- 0.1083 deg
  Vavg      =  60.44686 +/- 0.6529 km/s
  Vinit     =  60.50515 +/- 0.5742 km/s
Radiant (geocentric, J2000):
  R.A.   =  48.93906 +/- 0.5521 deg
  Dec    = +56.67505 +/- 0.3818 deg
  Vg     =  59.33138 +/- 0.5840 km/s
  Vinf   =  60.36014 +/- 0.5742 km/s
  Zc     =  39.85112 +/- 0.1096 deg
  Zg     =  40.20815 +/- 0.1048 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  63.13567 +/- 0.5084 deg
  Bg     = +37.00337 +/- 0.2695 deg
  Vh     =  40.77386 +/- 0.6820 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  81.70398 +/- 0.9287 deg
  Bh     = +61.13976 +/- 0.2377 deg
  Vh_x   =  -2.83965 +/- 0.2794 km/s
  Vh_y   = -19.47457 +/- 0.4743 km/s
  Vh_z   = -35.70973 +/- 0.5454 km/s
Orbit:
  La Sun = 140.222566 +/- -0.0000 deg
  a      =  10.013818 +/- 29.1720 AU
  e      =   0.905579 +/- 0.0601
  i      = 115.173573 +/- 0.2683 deg
  peri   = 149.242664 +/- 0.3160 deg
  node   = 140.221897 +/- 0.0000 deg
  Pi     = 289.464560 +/- 0.3160 deg
  q      =   0.945513 +/- 0.0020 AU
  f      =  30.753420 +/- 0.3160 deg
  M      =   0.677323 +/- nan deg
  Q      =  19.082123 +/- 58.3441 AU
  n      =   0.031103 +/- 0.0175 deg/day
  T      =  31.688390 +/- 339934595.1108 years
  Last perihelion JD = 2459417.759620 (2021-07-22 06:13:51.133372) +/- 0.3191 days
  Tj     =   0.019149 +/- 0.3370
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.236855e-03, -4.028787e-05, +9.139320e-03, +2.638013e-09, +3.274125e-05, -3.460968e-05
q   , -4.028787e-05, +3.029060e-06, -4.159243e-05, -4.886099e-10, +5.998316e-06, +6.417824e-06
Tp  , +9.139320e-03, -4.159243e-05, +1.060060e-01, -3.958214e-08, +1.299864e-03, +5.203521e-04
node, +2.638013e-09, -4.886099e-10, -3.958214e-08, +1.522933e-13, -1.573283e-09, -2.002512e-09
peri, +3.274125e-05, +5.998316e-06, +1.299864e-03, -1.573283e-09, +2.999982e-05, +2.067065e-05
i   , -3.460968e-05, +6.417824e-06, +5.203521e-04, -2.002512e-09, +2.067065e-05, +2.633119e-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: UK0026
  Avg. res. = 6.900e-06 s
  Stddev    = 2.63e-03 s

Begin point on the trajectory:
  Lon =     0.202750 +/- 0.0003 deg
  Lat =    54.493736 +/- 0.0010 deg
  Ht  = 110018.07 +/- 75.74 m
End point on the trajectory:
  Lon =     0.045653 +/- 0.0006 deg
  Lat =    54.430467 +/- 0.0014 deg
  Ht  = 95004.17 +/- 110.89 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,   109907.54,    95004.17,          0.022994,     88.42,     21.37,              24.12, 1.0000,    True,    True, {"ff_name": "FF_UK000Z_20210813_005101_171_0407296.fits"}
    UK0026,   False,    -0.023645,    52.984073,    6.00,   0.000000,   0.000000,   110018.07,    95123.62,          0.006719,     18.83,     13.92,              40.02, 1.0000,    True,    True, {"ff_name": "FF_UK0026_20210813_005105_190_0418816.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,  0.003236, 2459439.535477740224,  90.08604,  51.72367,               38.18963,  27.15599,        38.14647,       27.17344,     90.08604,     +51.72367,      90.11879,      +51.76066,  3413116.81, -1616390.62,  5258332.26,      54.493272,       +0.201590,  109907.54,  232908.39,       0.00,              146.44,    21.51,      0.00,           62202.45,     40.49,   -166.63,         151.86,  +2.83,  +0.99
  1,     UK000Z,       0,  0.043360, 2459439.535478204489,  90.43937,  51.63823,               38.04989,  26.95646,        38.03562,       26.96224,     90.43937,     +51.63823,      90.45045,      +51.65046,  3412294.94, -1617328.91,  5256416.83,      54.485897,       +0.183219,  108150.24,  230819.98,    2285.77,             2432.21,  -114.61,  56967.58,           62202.45,     13.22,    -54.72,          50.30,  +2.78,  +0.96
  2,     UK000Z,       0,  0.083504, 2459439.535478669219,  90.76982,  51.51813,               37.94507,  26.73773,        37.92296,       26.74668,     90.76982,     +51.51813,      90.78716,      +51.53706,  3411471.44, -1618269.08,  5254497.58,      54.478500,       +0.164807,  106389.76,  228731.32,    4576.09,             4722.53,  -247.39,  57052.67,           62202.45,     20.34,    -84.11,          78.03,  +1.66,  -0.14
  3,     UK000Z,       0,  0.123664, 2459439.535479133949,  91.25451,  51.40971,               37.74455,  26.47165,        37.77446,       26.45949,     91.25451,     +51.40971,      91.23186,      +51.38411,  3410398.65, -1619493.84,  5251997.35,      54.468854,       +0.140868,  104096.85,  226018.29,    7559.73,             7706.17,   312.19,  74293.74,           62202.45,    -27.02,    112.81,         105.86,  +0.95,  -0.82
  4,     UK000Z,       0,  0.163832, 2459439.535479598679,  91.56580,  51.26076,               37.66681,  26.23680,        37.66048,       26.23936,     91.56580,     +51.26076,      91.57143,      +51.26617,  3409593.02, -1620413.60,  5250119.77,      54.461603,       +0.122845,  102375.30,  223983.99,    9800.33,             9946.77,   128.24,  55780.77,           61955.16,      5.71,    -23.68,          22.43,  +1.19,  -0.56
  5,     UK000Z,       0,  0.203988, 2459439.535480063409,  91.90926,  51.12704,               37.55956,  26.00241,        37.54203,       26.00950,     91.90926,     +51.12704,      91.92391,      +51.14199,  3408767.52, -1621356.05,  5248195.87,      54.454166,       +0.104379,  100611.59,  221903.90,   12096.21,            12242.65,     0.30,  57174.11,           61201.41,     15.70,    -65.05,          62.20,  +1.00,  -0.73
  6,     UK000Z,       0,  0.244152, 2459439.535480528604,  92.28641,  50.99225,               37.43248,  25.75485,        37.41516,       25.76185,     92.28641,     +50.99225,      92.30116,      +51.00700,  3407895.66, -1622351.42,  5246163.92,      54.446304,       +0.084881,   98749.19,  219712.13,   14521.02,            14667.46,     0.81,  60372.69,           60843.45,     15.37,    -63.75,          61.56,  +0.88,  -0.83
  7,     UK000Z,       0,  0.284316, 2459439.535480993334,  92.71779,  50.86364,               37.26897,  25.49268,        37.27658,       25.48959,     92.71779,     +50.86364,      92.71291,      +50.85716,  3406957.45, -1623422.54,  5243977.34,      54.437835,       +0.063908,   96745.46,  217359.71,   17130.37,            17276.81,   185.85,  64967.28,           61038.07,     -6.67,     27.78,          27.11,  +0.77,  -0.92
  8,     UK000Z,       0,  0.324500, 2459439.535481458530,  93.05239,  50.69964,               37.18174,  25.23686,        37.15386,       25.24813,     93.05239,     +50.69964,      93.07618,      +50.72332,  3406141.97, -1624353.54,  5242076.80,      54.430467,       +0.045653,   95004.17,  215319.14,   19398.37,            19544.80,    28.34,  56440.37,           60822.13,     24.35,   -100.88,          99.41,  +1.38,  -0.29
  0,     UK0026,       0,  0.000000, 2459439.535477698781, 142.63937,  68.81956,                5.00191,  32.11374,         4.98934,       32.12638,    142.63937,     +68.81956,     142.66346,      +68.83361,  3413168.50, -1616331.61,  5258452.72,      54.493736,       +0.202750,  110018.07,  202602.64,       0.00,                2.68,    73.11,      0.00,           59185.53,    -34.74,    -47.00,          59.50,  +3.71,  +2.18
  1,     UK0026,       0,  0.040216, 2459439.535478164442, 143.69686,  68.59721,                4.58996,  31.84031,         4.58844,       31.84183,    143.69686,     +68.59721,     143.69997,      +68.59889,  3412300.67, -1617322.38,  5256430.17,      54.485948,       +0.183360,  108162.48,  200753.89,    2413.60,             2416.28,    59.27,  60015.96,           59185.53,     -4.14,     -5.60,           7.16,  +2.30,  +0.79
  2,     UK0026,       0,  0.080440, 2459439.535478629638, 144.70975,  68.35586,                4.19231,  31.55418,         4.19024,       31.55624,    144.70975,     +68.35586,     144.71417,      +68.35812,  3411449.11, -1618294.57,  5254445.54,      54.478299,       +0.164327,  106342.04,  198951.68,    4781.95,             4784.63,    -0.31,  58878.91,           59185.53,     -5.61,     -7.58,           9.77,  +1.77,  +0.28
  3,     UK0026,       0,  0.120672, 2459439.535479095299, 145.71328,  68.10224,                3.79260,  31.26012,         3.78799,       31.26470,    145.71328,     +68.10224,     145.72299,      +68.10722,  3410599.04, -1619265.06,  5252464.39,      54.470657,       +0.145323,  104525.11,  197164.71,    7146.15,             7148.83,   -64.52,  58764.25,           59185.53,    -12.38,    -16.73,          21.77,  +1.26,  -0.21
  4,     UK0026,       0,  0.160908, 2459439.535479560960, 146.76789,  67.83630,                3.36403,  30.95588,         3.36512,       30.95480,    146.76789,     +67.83630,     146.76635,      +67.83514,  3409715.81, -1620273.41,  5250405.94,      54.462708,       +0.125580,  102637.67,  195321.19,    9602.58,             9605.26,   -36.74,  61050.58,           59506.30,      2.91,      3.93,           5.16,  +1.22,  -0.23
  5,     UK0026,       0,  0.201160, 2459439.535480027087, 147.79644,  67.54632,                2.94070,  30.63295,         2.93644,       30.63715,    147.79644,     +67.54632,     147.80597,      +67.55080,  3408831.33, -1621283.20,  5248344.57,      54.454741,       +0.105806,  100747.90,  193488.84,   12062.51,            12065.19,    -6.43,  61113.10,           59827.62,    -11.19,    -15.13,          20.06,  +1.04,  -0.39
  6,     UK0026,       0,  0.241408, 2459439.535480492748, 148.84185,  67.25526,                2.50101,  30.31281,         2.50212,       30.31172,    148.84185,     +67.25526,     148.84058,      +67.25411,  3407946.08, -1622293.85,  5246281.45,      54.446759,       +0.086012,   98856.90,  191669.15,   14524.53,            14527.21,    26.22,  61171.36,           60086.38,      2.88,      3.89,           5.21,  +0.89,  -0.52
  7,     UK0026,       0,  0.281680, 2459439.535480958875, 149.95155,  66.92706,                2.02567,  29.95884,         2.03055,       29.95407,    149.95155,     +66.92706,     149.94261,      +66.92208,  3406996.42, -1623378.04,  5244068.18,      54.438187,       +0.064785,   96828.70,  189733.35,   17165.72,            17168.40,   236.58,  65583.72,           60652.76,     12.55,     16.95,          22.93,  +0.89,  -0.50
  8,     UK0026,       0,  0.321916, 2459439.535481424537, 150.86786,  66.63410,                1.62628,  29.64864,         1.62864,       29.64635,    150.86786,     +66.63410,     150.86429,      +66.63173,  3406197.91, -1624289.67,  5242207.18,      54.430972,       +0.046906,   95123.62,  188119.00,   19386.53,            19389.22,    28.75,  55194.71,           60553.11,      6.00,      8.11,          11.06,  +1.73,  +0.36

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.