Orbital Analysis for matched events on 20210813_223554.635_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 65.28° Bg 35.44° Vg 59.86km/s
mass 0.03209g, abs. mag -0.6
Path Details
------------
start -3.41° 49.80° 111.38km
end   -3.57° 49.65° 100.15km

Orbit Details
-------------
Semimajor axis 9.65A.U., eccentricity 0.90, inclination 117.25°, Period 29.98Y, LA Sun 141.09°, last Perihelion 2021-07-20

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: 2459440.441604571883
Time: 2021-08-13 22:35:54.635011 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000H and UK0021
 Convergence angle = 32.84998 deg
 R.A. =  51.59850  Dec = +56.43500 deg

Best intersection: Stations UK000H and UK0021 with Qconv = 32.85 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   1979654.29 +/- 21.10 m
 Y =  -3700894.98 +/- 116.62 m
 Z =   4933321.69 +/- 23.30 m
 Vx =    20604.20 +/- 276.31 m/s
 Vy =    26850.54 +/- 601.78 m/s
 Vz =    50599.05 +/- 471.54 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+4.790428e+02, +1.203393e+03, -1.321070e+02, +2.634261e+03, +4.606172e+03, -4.260112e+02
+1.203393e+03, +1.467775e+04, +1.017994e+03, +4.376299e+03, +6.961865e+04, +4.348535e+03
-1.321070e+02, +1.017994e+03, +5.859541e+02, -2.084310e+03, +7.332891e+03, +1.223464e+03
+2.634261e+03, +4.376299e+03, -2.084310e+03, +2.462135e+04, +1.157167e+04, +4.681919e+02
+4.606172e+03, +6.961865e+04, +7.332891e+03, +1.157167e+04, +3.793319e+05, +4.416354e+04
-4.260112e+02, +4.348535e+03, +1.223464e+03, +4.681919e+02, +4.416354e+04, +1.686674e+04

Timing offsets (from input data):
    UK000H: 0.000000 s
    UK0021: 0.000194 s

Reference point on the trajectory:
  Time: 2021-08-13 22:35:54.635011 UTC
  Lon     = +-3.412908 +/- 0.0009 deg
  Lat     = +49.796577 +/- 0.0007 deg
  Lat geo = +49.610004 +/- 0.0007 deg
  Ht      =  111381.29 +/- 58.81 m

  JD dynamic   = 2459440.442405312788 
  LST apparent = 298.1428749102 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  52.49858 +/- 0.6504 deg
  Dec       = +56.22198 +/- 0.3497 deg
  Azimuth   =  35.43992 +/- 0.1619 deg
  Elevation = +29.13240 +/- 0.4770 deg
  Vavg      =  59.24196 +/- 0.1576 km/s
  Vinit     =  60.87485 +/- 0.3233 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  52.28665 +/- 0.6504 deg
  Dec       = +56.00423 +/- 0.3497 deg
  Azimuth   =  35.70770 +/- 0.1619 deg
  Elevation = +29.05102 +/- 0.4770 deg
  Vavg      =  59.39755 +/- 0.1576 km/s
  Vinit     =  61.03044 +/- 0.3233 km/s
Radiant (geocentric, J2000):
  R.A.   =  52.76494 +/- 0.6385 deg
  Dec    = +55.72682 +/- 0.3517 deg
  Vg     =  59.85543 +/- 0.3289 km/s
  Vinf   =  60.87485 +/- 0.3233 km/s
  Zc     =  61.01967 +/- 0.4770 deg
  Zg     =  61.58984 +/- 0.4768 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  65.27663 +/- 0.3128 deg
  Bg     = +35.44000 +/- 0.4296 deg
  Vh     =  40.73650 +/- 0.1729 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  84.14234 +/- 0.4405 deg
  Bh     = +58.42972 +/- 0.8002 deg
  Vh_x   =  -2.17662 +/- 0.1503 km/s
  Vh_y   = -21.21599 +/- 0.5574 km/s
  Vh_z   = -34.70745 +/- 0.1983 km/s
Orbit:
  La Sun = 141.092730 +/- -0.0000 deg
  a      =   9.651336 +/- 0.9218 AU
  e      =   0.904044 +/- 0.0150
  i      = 117.250871 +/- 0.7066 deg
  peri   = 145.001969 +/- 0.8303 deg
  node   = 141.090852 +/- 0.0001 deg
  Pi     = 286.092821 +/- 0.8304 deg
  q      =   0.926103 +/- 0.0042 AU
  f      =  34.993832 +/- 0.8303 deg
  M      =   0.801184 +/- 0.1997 deg
  Q      =  18.376569 +/- 1.8460 AU
  n      =   0.032872 +/- 0.0085 deg/day
  T      =  29.983463 +/- 3.8577 years
  Last perihelion JD = 2459416.069377 (2021-07-20 13:39:54.170183) +/- 0.4658 days
  Tj     =   0.006167 +/- 0.0931
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.526897e-04, -4.548348e-05, -2.362586e-03, -1.310112e-08, -1.226771e-04, +1.623564e-04
q   , -4.548348e-05, +1.889756e-05, +1.866428e-03, +3.758504e-09, +6.312767e-05, -4.677703e-05
Tp  , -2.362586e-03, +1.866428e-03, +2.160211e-01, +3.113299e-07, +6.670235e-03, -3.885074e-03
node, -1.310112e-08, +3.758504e-09, +3.113299e-07, +1.111029e-12, +1.173647e-08, -1.380248e-08
peri, -1.226771e-04, +6.312767e-05, +6.670235e-03, +1.173647e-08, +2.168630e-04, -1.462106e-04
i   , +1.623564e-04, -4.677703e-05, -3.885074e-03, -1.380248e-08, -1.462106e-04, +1.714773e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.131745
 a2 = 21.211398

Mean time residuals from time vs. length:
  Station with reference time: UK000H
  Avg. res. = 8.793e-06 s
  Stddev    = 2.97e-03 s

Begin point on the trajectory:
  Lon =    -3.412938 +/- 0.0008 deg
  Lat =    49.796550 +/- 0.0006 deg
  Ht  = 111379.16 +/- 63.80 m
End point on the trajectory:
  Lon =    -3.574349 +/- 0.0005 deg
  Lat =    49.650709 +/- 0.0006 deg
  Ht  = 100147.41 +/- 79.57 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
    UK000H,   False,    -1.778230,    50.857470,   24.00,   0.000000,   0.000000,   111379.16,   104386.25,          0.006263,     10.27,     19.60,             115.37, 1.0000,    True,   False, {"ff_name": "FF_UK000H_20210813_223554_291_0221440.fits"}
    UK0021,   False,    -3.515726,    50.691998,   17.00,   0.045637,  23.926069,   109522.17,   100147.41,          0.020290,     46.91,     26.44,              94.19, 1.0000,    True,    True, {"ff_name": "FF_UK0021_20210813_223552_177_0211200.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,     UK000H,       0,  0.000000, 2459440.441604571883, 263.15239,   2.76757,              225.22408,  32.92030,       225.23735,       32.91868,    263.15239,      +2.76757,     263.14169,       +2.77112,  1979652.81, -3700896.91,  4933318.06,      49.796550,       -3.412938,  111379.16,  200881.71,       0.00,                4.37,   410.24,      0.00,           59474.40,     34.96,    -18.33,          40.54,  +4.95,  +3.44
  1,     UK000H,       0,  0.040440, 2459440.441605039872, 262.96752,   2.27228,              225.15645,  32.39478,       225.15029,       32.39553,    262.96752,      +2.27228,     262.97268,       +2.27063,  1978953.79, -3701807.83,  4931601.44,      49.783560,       -3.427385,  110373.96,  201801.10,    2065.23,             2069.60,    13.70,  51069.05,           59474.40,    -16.40,      8.59,          18.92,  +3.88,  +2.36
  2,     UK000H,       0,  0.080956, 2459440.441605508793, 262.76645,   1.68586,              225.05885,  31.78042,       225.04884,       31.78165,    262.76645,      +1.68586,     262.77495,       +1.68315,  1978125.02, -3702887.85,  4929566.17,      49.768151,       -3.444479,  109182.81,  202911.84,    4513.83,             4518.20,    -4.11,  60435.27,           59474.40,    -26.98,     14.13,          30.96,  +2.54,  +1.00
  3,     UK000H,       0,  0.121516, 2459440.441605978180, 262.56239,   1.04184,              224.93577,  31.11307,       224.93948,       31.11262,    262.56239,      +1.04184,     262.55985,       +1.04285,  1977211.16, -3704078.75,  4927321.96,      49.751151,       -3.463305,  107870.18,  204163.08,    7213.80,             7218.17,   226.78,  66567.38,           59474.40,     10.13,     -5.31,          11.56,  +1.93,  +0.38
  4,     UK000H,       0,  0.161952, 2459440.441606446169, 262.39062,   0.54568,              224.85734,  30.59236,       224.85620,       30.59250,    262.39062,      +0.54568,     262.39224,       +0.54537,  1976493.28, -3705014.26,  4925559.02,      49.737789,       -3.478125,  106839.62,  205167.20,    9334.77,             9339.14,  -113.79,  52452.51,           58814.35,     -3.13,      1.64,           3.55,  +2.18,  +0.62
  5,     UK000H,       0,  0.202416, 2459440.441606914625, 262.21424,   0.00821,              224.76334,  30.03254,       224.76721,       30.03207,    262.21424,      +0.00821,     262.21188,       +0.00927,  1975711.67, -3706032.83,  4923639.56,      49.723235,       -3.494243,  105718.16,  206279.20,   11644.03,            11648.41,  -267.77,  57069.59,           58376.63,     10.79,     -5.65,          12.18,  +1.49,  -0.08
  6,     UK000H,       0,  0.242964, 2459440.441607384011, 261.99495,  -0.61875,              224.66894,  29.37342,       224.66344,       29.37410,    261.99495,      -0.61875,     262.00056,       -0.62027,  1974782.81, -3707243.28,  4921358.51,      49.705929,       -3.513360,  104386.25,  207625.16,   14388.33,            14392.70,     8.18,  67680.16,           59218.47,    -15.54,      8.14,          17.43,  +2.00,  +0.41
  0,     UK0021,       1,  0.030585, 2459440.441604924388, 300.40586,   7.44047,              176.57814,  46.70372,       176.49101,       46.66431,    300.40586,      +7.44047,     300.46776,       +7.40340,  1978847.90, -3701945.83,  4931341.39,      49.781591,       -3.429506,  110221.73,  150385.83,       0.00,             2382.47,   926.50,      0.00,           53438.44,    -92.43,    163.63,         257.76,  +5.08,  +4.19
  1,     UK0021,       0,  0.071033, 2459440.441605392378, 300.14572,   6.95730,              176.97779,  46.23012,       176.93142,       46.20921,    300.14572,      +6.95730,     300.17903,       +6.93748,  1978361.19, -3702580.09,  4930146.15,      49.772543,       -3.439614,  109522.17,  150535.55,    1437.97,             3820.44,   -97.79,  35551.14,           53438.44,    -49.44,     87.64,         137.87,  +1.89,  +1.00
  2,     UK0021,       0,  0.111837, 2459440.441605864558, 299.66223,   6.10381,              177.70286,  45.39122,       177.69780,       45.38895,    299.66223,      +6.10381,     299.66633,       +6.10164,  1977485.89, -3703720.74,  4927996.63,      49.756262,       -3.457655,  108264.70,  150839.49,    4024.02,             6406.49,     4.33,  63377.40,           53438.44,     -5.44,      9.66,          15.16,  +1.14,  +0.25
  3,     UK0021,       0,  0.152565, 2459440.441606335808, 299.19559,   5.34566,              178.38287,  44.64333,       178.37514,       44.63988,    299.19559,      +5.34566,     299.20181,       +5.34231,  1976687.89, -3704760.66,  4926036.92,      49.741412,       -3.474114,  107118.93,  151154.77,    6381.72,             8764.19,  -117.29,  57888.83,           53438.44,     -8.41,     14.91,          23.36,  +0.99,  +0.09
  4,     UK0021,       0,  0.193401, 2459440.441606808454, 298.68196,   4.47351,              179.11366,  43.77837,       179.12386,       43.78289,    298.68196,      +4.47351,     298.67533,       +4.47797,  1975775.64, -3705949.47,  4923796.64,      49.724426,       -3.492900,  105809.92,  151559.56,    9076.96,            11459.42,    92.06,  66001.45,           56737.13,     11.23,    -19.93,          31.13,  +0.96,  +0.06
  5,     UK0021,       0,  0.234125, 2459440.441607280169, 298.22671,   3.72917,              179.74517,  43.03691,       179.75302,       43.04037,    298.22671,      +3.72917,     298.22193,       +3.73262,  1974985.16, -3706979.59,  4921855.41,      49.709699,       -3.509196,  104676.32,  151948.27,   11412.42,            13794.88,   -51.55,  57348.49,           57764.16,      8.72,    -15.48,          24.11,  +1.05,  +0.14
  6,     UK0021,       0,  0.274901, 2459440.441607751884, 297.74097,   2.92927,              180.40344,  42.23660,       180.41088,       42.23987,    297.74097,      +2.92927,     297.73662,       +2.93256,  1974132.19, -3708091.14,  4919760.74,      49.693800,       -3.526762,  103453.82,  152406.94,   13932.48,            16314.95,   -13.71,  61802.73,           58563.89,      8.37,    -14.85,          23.07,  +1.10,  +0.18
  7,     UK0021,       0,  0.315613, 2459440.441608223133, 297.32123,   2.19358,              180.95906,  41.49777,       180.99243,       41.51238,    297.32123,      +2.19358,     297.29769,       +2.20846,  1973355.77, -3709102.94,  4917854.03,      49.679321,       -3.542763,  102341.65,  152859.55,   16226.41,            18608.88,  -198.12,  56345.26,           58712.07,     37.90,    -67.30,         104.23,  +1.06,  +0.14
  8,     UK0021,       0,  0.356389, 2459440.441608695313, 296.84510,   1.39879,              181.57571,  40.69638,       181.61352,       40.71287,    296.84510,      +1.39879,     296.81821,       +1.41578,  1972500.45, -3710217.56,  4915753.56,      49.663361,       -3.560368,  101117.18,  153396.51,   18753.45,            21135.92,  -153.32,  61973.64,           58998.86,     43.44,    -77.14,         119.04,  +1.66,  +0.73
  9,     UK0021,       0,  0.396997, 2459440.441609165166, 296.43043,   0.79641,              182.10386,  40.08569,       182.09330,       40.08110,    296.43043,      +0.79641,     296.44006,       +0.79164,  1971822.69, -3711100.78,  4914089.15,      49.650709,       -3.574349,  100147.41,  153850.34,   20755.88,            23138.35,  -622.90,  49311.15,           58618.25,    -12.26,     21.73,          33.45,  +3.82,  +2.88

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.