Orbital Analysis for matched events on 20210810_225915.447_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 60.29° Bg 37.56° Vg 58.03km/s
mass 0.02621g, abs. mag -0.4
Path Details
------------
start -2.43° 52.08° 110.93km
end   -2.56° 51.99° 101.13km

Orbit Details
-------------
Semimajor axis 5.25A.U., eccentricity 0.82, inclination 113.79°, Period 12.02Y, LA Sun 138.23°, last Perihelion 2021-07-19

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: 2459437.457817674149
Time: 2021-08-10 22:59:15.479997 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000S and UK0027
 Convergence angle = 24.05489 deg
 R.A. =  44.32781  Dec = +56.22436 deg

Best intersection: Stations UK000S and UK0027 with Qconv = 24.05 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   2119196.81 +/- 12.97 m
 Y =  -3387430.83 +/- 10.28 m
 Z =   5097012.29 +/- 88.96 m
 Vx =    23068.18 +/- 231.62 m/s
 Vy =    22612.31 +/- 240.82 m/s
 Vz =    49471.06 +/- 338.53 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.717754e+02, +4.390584e+01, -2.084530e+02, +2.046651e+02, -4.321371e+02, +2.255566e+02
+4.390584e+01, +1.129118e+02, +1.988578e+02, +5.583337e+01, +3.271387e+02, -5.238604e+02
-2.084530e+02, +1.988578e+02, +9.154965e+03, -2.492011e+03, -8.334373e+02, +2.654105e+04
+2.046651e+02, +5.583337e+01, -2.492011e+03, +1.969282e+03, +6.461821e+02, -1.209085e+04
-4.321371e+02, +3.271387e+02, -8.334373e+02, +6.461821e+02, +4.254086e+03, -1.361553e+04
+2.255566e+02, -5.238604e+02, +2.654105e+04, -1.209085e+04, -1.361553e+04, +1.346897e+05

Timing offsets (from input data):
    UK000S: 0.000195 s
    UK0027: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-10 22:59:15.479997 UTC
  Lon     = +-2.421404 +/- 0.0002 deg
  Lat     = +52.089484 +/- 0.0005 deg
  Lat geo = +51.905988 +/- 0.0005 deg
  Ht      =  111595.38 +/- 68.69 m

  JD dynamic   = 2459437.458618796431 
  LST apparent = 302.0303416023 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  44.42823 +/- 0.0849 deg
  Dec       = +56.85710 +/- 0.2205 deg
  Azimuth   =  41.33445 +/- 0.1964 deg
  Elevation = +36.04993 +/- 0.1596 deg
  Vavg      =  58.68248 +/- 0.2305 km/s
  Vinit     =  59.08336 +/- 0.2538 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  44.31824 +/- 0.0849 deg
  Dec       = +56.62659 +/- 0.2205 deg
  Azimuth   =  41.59581 +/- 0.1964 deg
  Elevation = +35.94011 +/- 0.1596 deg
  Vavg      =  58.83858 +/- 0.2305 km/s
  Vinit     =  59.23946 +/- 0.2538 km/s
Radiant (geocentric, J2000):
  R.A.   =  44.73088 +/- 0.0850 deg
  Dec    = +56.41915 +/- 0.2258 deg
  Vg     =  58.03237 +/- 0.2585 km/s
  Vinf   =  59.08336 +/- 0.2538 km/s
  Zc     =  54.08795 +/- 0.1592 deg
  Zg     =  54.61290 +/- 0.1656 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  60.28634 +/- 0.1018 deg
  Bg     = +37.55603 +/- 0.2160 deg
  Vh     =  39.76660 +/- 0.3332 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  79.08215 +/- 0.1713 deg
  Bh     = +62.81483 +/- 0.1180 deg
  Vh_x   =  -3.44106 +/- 0.0367 km/s
  Vh_y   = -17.83923 +/- 0.1122 km/s
  Vh_z   = -35.37377 +/- 0.3261 km/s
Orbit:
  La Sun = 138.228175 +/- -0.0000 deg
  a      =   5.246541 +/- 0.4750 AU
  e      =   0.818592 +/- 0.0275
  i      = 113.793156 +/- 0.1289 deg
  peri   = 149.820768 +/- 0.6779 deg
  node   = 138.226727 +/- 0.0000 deg
  Pi     = 288.047495 +/- 0.6779 deg
  q      =   0.951764 +/- 0.0014 AU
  f      =  30.175084 +/- 0.6779 deg
  M      =   1.803993 +/- 0.6043 deg
  Q      =   9.541318 +/- 0.9488 AU
  n      =   0.082015 +/- 0.0220 deg/day
  T      =  12.017393 +/- 1.4572 years
  Last perihelion JD = 2459415.462785 (2021-07-19 23:06:24.603842) +/- 0.6550 days
  Tj     =   0.526617 +/- 0.1542
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +9.124092e-04, +3.976396e-05, +2.086770e-02, +5.218393e-09, +3.679974e-04, -6.573818e-05
q   , +3.976396e-05, +2.204856e-06, +9.988659e-04, +2.628867e-10, +1.827559e-05, -3.310078e-06
Tp  , +2.086770e-02, +9.988659e-04, +4.947530e-01, +1.259016e-07, +8.848785e-03, -1.585664e-03
node, +5.218393e-09, +2.628867e-10, +1.259016e-07, +3.714717e-14, +2.270369e-09, -4.678877e-10
peri, +3.679974e-04, +1.827559e-05, +8.848785e-03, +2.270369e-09, +1.591602e-04, -2.859215e-05
i   , -6.573818e-05, -3.310078e-06, -1.585664e-03, -4.678877e-10, -2.859215e-05, +5.893303e-06

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: UK0027
  Avg. res. = 3.285e-06 s
  Stddev    = 1.81e-03 s

Begin point on the trajectory:
  Lon =    -2.430073 +/- 0.0002 deg
  Lat =    52.083412 +/- 0.0003 deg
  Ht  = 110929.15 +/- 48.14 m
End point on the trajectory:
  Lon =    -2.558898 +/- 0.0001 deg
  Lat =    51.993750 +/- 0.0004 deg
  Ht  = 101129.50 +/- 63.09 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,   110929.15,   101201.14,          0.009565,     18.80,     22.94,              47.53, 1.0000,    True,    True, {"ff_name": "FF_UK000S_20210810_225911_167_0244736.fits"}
    UK0027,   False,    -2.374601,    51.371449,   48.00,   0.000000,   0.000000,   110689.28,   101129.50,          0.005104,      3.00,     10.98,              35.80, 1.0000,    True,    True, {"ff_name": "FF_UK0027_20210810_225907_550_0238336.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,  0.033151, 2459437.457818055525, 172.16123,  70.87867,              341.88932,  36.75980,       341.88513,       36.77080,    172.16123,     +70.87867,     172.18970,      +70.88546,  2118754.78, -3387864.13,  5096064.31,      52.083412,       -2.430073,  110929.15,  182521.29,       0.00,             1132.16,   -52.50,      0.00,           58799.84,    -28.33,    -23.22,          41.39,  +3.75,  +2.44
  1,     UK000S,       0,  0.073207, 2459437.457818519324, 173.26849,  70.38147,              341.15021,  36.58480,       341.14880,       36.58841,    173.26849,     +70.38147,     173.27802,      +70.38365,  2117720.69, -3388877.78,  5093846.65,      52.069201,       -2.450517,  109371.10,  180729.71,    2648.56,             3780.72,   229.41,  66121.37,           58799.84,     -9.24,     -7.57,          13.63,  +2.48,  +1.19
  2,     UK000S,       0,  0.113267, 2459437.457818982657, 174.09789,  69.95877,              340.55199,  36.42171,       340.54658,       36.43529,    174.09789,     +69.95877,     174.13270,      +69.96682,  2116887.41, -3389694.60,  5092059.62,      52.057742,       -2.467021,  108116.09,  179302.20,    4782.81,             5914.97,    -3.22,  53276.32,           58799.84,    -34.51,    -28.28,          51.33,  +1.75,  +0.48
  3,     UK000S,       0,  0.153323, 2459437.457819446456, 175.02679,  69.48868,              339.87759,  36.25008,       339.87362,       36.25983,    175.02679,     +69.48868,     175.05184,      +69.49434,  2115967.13, -3390596.69,  5090086.04,      52.045078,       -2.485229,  106730.59,  177741.96,    7139.86,             8272.02,   -12.81,  58843.87,           58799.84,    -24.61,    -20.17,          36.93,  +1.26,  +0.01
  4,     UK000S,       0,  0.193371, 2459437.457819909789, 175.95010,  69.00392,              339.18657,  36.07466,       339.18608,       36.07583,    175.95010,     +69.00392,     175.95381,      +69.00459,  2115038.94, -3391506.54,  5088095.48,      52.032298,       -2.503589,  105333.72,  176186.37,    9517.19,            10649.36,    -1.64,  59362.17,           58732.56,     -2.94,     -2.41,           4.45,  +1.26,  +0.03
  5,     UK000S,       0,  0.233419, 2459437.457820373587, 176.86352,  68.50650,              338.48193,  35.89614,       338.48714,       35.88385,    176.86352,     +68.50650,     176.83438,      +68.49964,  2114107.34, -3392419.72,  5086097.62,      52.019462,       -2.522013,  103932.29,  174643.84,   11903.24,            13035.40,    18.23,  59579.63,           58834.32,     30.65,     25.09,          46.78,  +1.34,  +0.13
  6,     UK000S,       0,  0.273487, 2459437.457820837386, 177.74008,  67.96661,              337.74993,  35.68510,       337.75347,       35.67693,    177.74008,     +67.96661,     177.72143,      +67.96214,  2113141.72, -3393366.26,  5084026.78,      52.006148,       -2.541102,  102480.26,  173065.23,   14376.44,            15508.60,   124.08,  61725.04,           59180.50,     20.25,     16.58,          31.20,  +1.49,  +0.30
  7,     UK000S,       0,  0.313555, 2459437.457821301185, 178.46897,  67.47325,              337.10088,  35.48230,       337.09855,       35.48757,    178.46897,     +67.47325,     178.48290,      +67.47608,  2112290.76, -3394200.41,  5082201.85,      51.994408,       -2.557941,  101201.14,  171692.15,   16555.96,            17688.12,   -63.75,  54395.55,           58925.85,    -12.99,    -10.64,          20.17,  +3.14,  +1.97
  0,     UK0027,       1,  0.000000, 2459437.457817674149, 272.10268,  87.26306,              357.68936,  53.72055,       357.70971,       53.77088,    272.10268,     +87.26306,     272.86211,      +87.22638,  2119199.11, -3387428.58,  5097017.20,      52.089515,       -2.421221,  111598.83,  137655.90,       0.00,                5.87,   779.90,      0.00,           54747.52,   -119.88,    -32.93,         186.29,  +5.45,  +4.76
  1,     UK0027,       0,  0.039868, 2459437.457818135619, 267.77947,  86.95062,              357.08684,  53.85609,       357.08692,       53.85630,    267.77947,     +86.95062,     267.78277,      +86.95048,  2118595.61, -3388020.16,  5095722.96,      52.081225,       -2.433223,  110689.28,  136393.53,    1545.72,             1539.84,   -41.66,  38770.88,           54747.52,     -0.50,     -0.14,           0.79,  +2.29,  +1.62
  2,     UK0027,       0,  0.079700, 2459437.457818596624, 260.72574,  86.39999,              355.95214,  54.00741,       355.95090,       54.00401,    260.72574,     +86.39999,     260.67967,      +86.40190,  2117522.54, -3389072.02,  5093421.70,      52.066476,       -2.454430,  109072.62,  134163.57,    4294.12,             4288.25,   353.33,  68999.86,           54747.52,      7.87,      2.15,          12.54,  +2.28,  +1.64
  3,     UK0027,       0,  0.119580, 2459437.457819058094, 256.48929,  85.95051,              355.06409,  54.10671,       355.06545,       54.11069,    256.48929,     +85.95051,     256.53990,      +85.94854,  2116716.89, -3389861.75,  5091693.94,      52.055396,       -2.470391,  107859.33,  132502.44,    6357.58,             6351.71,    60.55,  51741.80,           54747.52,     -9.04,     -2.47,          14.59,  +1.20,  +0.59
  4,     UK0027,       0,  0.159440, 2459437.457819519565, 252.93880,  85.43018,              354.08462,  54.21985,       354.08490,       54.22074,    252.93880,     +85.43018,     252.94979,      +85.42979,  2115851.51, -3390710.02,  5089838.09,      52.043487,       -2.487521,  106556.56,  130731.10,    8574.02,             8568.15,   -78.07,  55605.60,           55093.32,     -2.01,     -0.55,           3.28,  +0.92,  +0.34
  5,     UK0027,       0,  0.199272, 2459437.457819980569, 249.80195,  84.80652,              352.94404,  54.34860,       352.94110,       54.33856,    249.80195,     +84.80652,     249.69868,      +84.81040,  2114875.10, -3391667.14,  5087744.11,      52.030041,       -2.506826,  105087.21,  128749.16,   11074.87,            11068.99,    69.36,  62784.78,           56290.10,     22.08,      6.03,          36.67,  +0.81,  +0.26
  6,     UK0027,       0,  0.239136, 2459437.457820442040, 247.23855,  84.21646,              351.85700,  54.43543,       351.85807,       54.43946,    247.23855,     +84.21646,     247.27759,      +84.21507,  2113982.67, -3392541.94,  5085830.24,      52.017743,       -2.524481,  103744.77,  126954.00,   13360.61,            13354.73,    -0.20,  57338.51,           56829.99,     -8.72,     -2.38,          14.68,  +0.88,  +0.36
  7,     UK0027,       0,  0.278984, 2459437.457820903044, 245.25230,  83.59411,              350.73843,  54.53250,       350.73857,       54.53310,    245.25230,     +83.59411,     245.25859,      +83.59392,  2113090.05, -3393416.92,  5083915.96,      52.005436,       -2.542138,  102402.56,  125174.67,   15646.84,            15640.96,   -68.32,  57373.72,           57100.25,     -1.27,     -0.35,           2.16,  +1.24,  +0.75
  8,     UK0027,       0,  0.318844, 2459437.457821364515, 243.57171,  82.98372,              349.63991,  54.60681,       349.64151,       54.61439,    243.57171,     +82.98372,     243.63301,      +82.98158,  2112243.10, -3394247.13,  5082099.63,      51.993750,       -2.558898,  101129.50,  123502.08,   17816.08,            17810.21,  -254.14,  54421.64,           57047.78,    -15.87,     -4.34,          27.48,  +1.97,  +1.51

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.