Orbital Analysis for matched events on 20210813_003329.271_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 65.01° Bg 39.25° Vg 56.62km/s
mass 0.00713g, abs. mag 0.7
Path Details
------------
start -0.73° 51.05° 106.65km
end   -0.83° 51.00° 97.12km

Orbit Details
-------------
Semimajor axis 4.91A.U., eccentricity 0.81, inclination 109.94°, Period 10.88Y, LA Sun 140.21°, last Perihelion 2021-07-18

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: 2459439.523255456705
Time: 2021-08-13 00:33:29.271459 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK0001 and UK000F
 Convergence angle = 9.55999 deg
 R.A. =  55.64345  Dec = +60.00713 deg
Intersection 2 - Stations: UK0001 and UK002C
 Convergence angle = 2.74911 deg
 R.A. =  31.01707  Dec = +51.22889 deg
Intersection 3 - Stations: UK000F and UK002C
 Convergence angle = 12.22276 deg
 R.A. =  48.69703  Dec = +59.06036 deg

Best intersection: Stations UK000F and UK002C with Qconv = 12.22 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3512433.04 +/- 279.90 m
 Y =  -2084631.58 +/- 143.69 m
 Z =   5020202.56 +/- 383.94 m
 Vx =    18856.24 +/- 1581.89 m/s
 Vy =    22349.93 +/- 998.75 m/s
 Vz =    49736.32 +/- 1434.26 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+6.211257e+04, +3.044205e+04, +8.401376e+04, +2.148421e+05, +1.743810e+04, +1.182594e+05
+3.044205e+04, +1.924837e+04, +4.851249e+04, +6.976484e+04, +5.369244e+03, +3.134793e+04
+8.401376e+04, +4.851249e+04, +1.272506e+05, +2.361855e+05, +1.551599e+04, +1.211363e+05
+2.148421e+05, +6.976484e+04, +2.361855e+05, +1.554458e+06, +6.993809e+04, +9.251729e+05
+1.743810e+04, +5.369244e+03, +1.551599e+04, +6.993809e+04, +6.296891e+04, +1.217664e+05
+1.182594e+05, +3.134793e+04, +1.211363e+05, +9.251729e+05, +1.217664e+05, +7.163317e+05

Timing offsets (from input data):
    UK0001: 0.000000 s
    UK000F: -0.003330 s
    UK002B: 0.000000 s
    UK002C: -0.002376 s

Reference point on the trajectory:
  Time: 2021-08-13 00:33:29.271459 UTC
  Lon     = +-0.734111 +/- 0.0036 deg
  Lat     = +51.053161 +/- 0.0012 deg
  Lat geo = +50.867987 +/- 0.0012 deg
  Ht      =  106595.65 +/- 400.50 m

  JD dynamic   = 2459439.524056197610 
  LST apparent = 329.3108380312 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  49.84626 +/- 2.2669 deg
  Dec       = +59.54726 +/- 0.4127 deg
  Azimuth   =  46.34058 +/- 1.2578 deg
  Elevation = +46.28848 +/- 0.8376 deg
  Vavg      =  54.71217 +/- 1.4452 km/s
  Vinit     =  57.69557 +/- 1.4203 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  49.94127 +/- 2.2669 deg
  Dec       = +59.29636 +/- 0.4127 deg
  Azimuth   =  46.63448 +/- 1.2578 deg
  Elevation = +46.13383 +/- 0.8376 deg
  Vavg      =  54.86165 +/- 1.4452 km/s
  Vinit     =  57.84505 +/- 1.4203 km/s
Radiant (geocentric, J2000):
  R.A.   =  50.17947 +/- 2.3150 deg
  Dec    = +59.27773 +/- 0.3955 deg
  Vg     =  56.61805 +/- 1.4494 km/s
  Vinf   =  57.69557 +/- 1.4203 km/s
  Zc     =  43.83952 +/- 0.8405 deg
  Zg     =  44.27417 +/- 0.8714 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  65.01073 +/- 1.5922 deg
  Bg     = +39.24637 +/- 0.1144 deg
  Vh     =  39.62910 +/- 1.0397 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  90.17911 +/- 5.3760 deg
  Bh     = +64.67370 +/- 0.3747 deg
  Vh_x   =   0.05299 +/- 1.4972 km/s
  Vh_y   = -16.95216 +/- 0.6604 km/s
  Vh_z   = -35.82020 +/- 0.9266 km/s
Orbit:
  La Sun = 140.210830 +/- 0.0000 deg
  a      =   4.911452 +/- 1.0291 AU
  e      =   0.811104 +/- 0.0706
  i      = 109.935908 +/- 1.6143 deg
  peri   = 144.252625 +/- 6.9326 deg
  node   = 140.210418 +/- 0.0001 deg
  Pi     = 284.463042 +/- 6.9325 deg
  q      =   0.927756 +/- 0.0281 AU
  f      =  35.743618 +/- 6.9326 deg
  M      =   2.315095 +/- 3.4945 deg
  Q      =   8.895148 +/- 2.0313 AU
  n      =   0.090550 +/- 0.0765 deg/day
  T      =  10.884676 +/- 3.0247 years
  Last perihelion JD = 2459413.957063 (2021-07-18 10:58:10.208817) +/- 4.8171 days
  Tj     =   0.672135 +/- 0.5035
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +3.309402e-03, +1.213731e-03, +2.179818e-01, -8.476010e-08, +5.387976e-03, +1.239927e-03
q   , +1.213731e-03, +5.106882e-04, +8.738340e-02, -3.434066e-08, +2.201645e-03, +5.012172e-04
Tp  , +2.179818e-01, +8.738340e-02, +1.523118e+01, -5.970015e-06, +3.810259e-01, +8.720125e-02
node, -8.476010e-08, -3.434066e-08, -5.970015e-06, +2.407325e-12, -1.495307e-07, -3.514527e-08
peri, +5.387976e-03, +2.201645e-03, +3.810259e-01, -1.495307e-07, +9.558303e-03, +2.183515e-03
i   , +1.239927e-03, +5.012172e-04, +8.720125e-02, -3.514527e-08, +2.183515e-03, +5.131851e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 3.951999
 a2 = 21.089356

Mean time residuals from time vs. length:
  Station with reference time: UK0001
  Avg. res. = 1.552e-06 s
  Stddev    = 1.25e-03 s

Begin point on the trajectory:
  Lon =    -0.733543 +/- 0.0034 deg
  Lat =    51.053503 +/- 0.0007 deg
  Ht  = 106654.26 +/- 380.27 m
End point on the trajectory:
  Lon =    -0.827106 +/- 0.0031 deg
  Lat =    50.997732 +/- 0.0005 deg
  Ht  = 97122.26 +/- 366.97 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
    UK0001,   False,    -1.778230,    50.857470,   24.00,   1.662834,  24.364337,   106654.26,    97122.26,          0.036789,     76.87,     28.22,              19.61, 0.1126,    True,    True, {"ff_name": "FF_UK0001_20210813_003327_973_0395520.fits"}
    UK000F,   False,    -1.306160,    51.883100,   80.00,   0.000000,   0.000000,   105202.19,    98699.38,          0.004086,     10.21,      1.53,              69.27, 0.8747,    True,    True, {"ff_name": "FF_UK000F_20210813_003328_454_0370944.fits"}
    UK002B,    True,    -1.367130,    50.815550,   22.00,   0.000000,   0.000000,   106875.89,    98954.33,          0.046426,       nan,       nan,              19.84, 0.0000,    True,    True, {"ff_name": "FF_UK002B_20210813_003329_681_0398080.fits"}
    UK002C,   False,    -1.801980,    51.351940,  130.00,   0.000000,   0.000000,   105514.65,    99315.41,          0.013111,     27.57,     10.46,              43.41, 0.4723,    True,    True, {"ff_name": "FF_UK002C_20210813_003321_902_0390656.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,     UK0001,       0,  0.000000, 2459439.523255456705,  24.75094,  47.21782,               73.06482,  53.70428,        73.04764,       53.74627,     24.75094,     +47.21782,      24.70280,      +47.24607,  3512459.54, -2084600.17,  5020272.46,      51.053503,       -0.733543,  106654.26,  131648.46,       0.00,               81.09,   230.74,      0.00,           56790.54,    -34.25,    -93.17,         155.52,  +2.25,  +1.65
  1,     UK0001,       0,  0.039956, 2459439.523255919106,  24.43966,  46.98089,               73.58525,  53.78371,        73.56891,       53.82484,     24.43966,     +46.98089,      24.39280,      +47.00840,  3511743.89, -2085448.41,  5018384.82,      51.044265,       -0.749066,  105071.62,  129575.73,    2189.72,             2108.63,   -47.00,  54803.35,           56790.54,    -32.94,    -89.69,         152.10,  +2.11,  +1.55
  2,     UK0001,       0,  0.079920, 2459439.523256381508,  24.11691,  46.71317,               74.16029,  53.85561,        74.14030,       53.90779,     24.11691,     +46.71317,      24.05777,      +46.74781,  3510987.90, -2086344.48,  5016390.76,      51.034498,       -0.765457,  103400.12,  127390.99,    4502.89,             4421.80,   -39.58,  57881.29,           56790.54,    -41.04,   -111.63,         192.58,  +1.14,  +0.61
  3,     UK0001,       0,  0.119856, 2459439.523256843910,  23.75712,  46.45697,               74.74063,  53.95506,        74.72768,       53.98995,     23.75712,     +46.45697,      23.71801,      +46.48000,  3510239.71, -2087231.29,  5014417.30,      51.024825,       -0.781682,  101746.26,  125233.50,    6792.16,             6711.07,   -54.44,  57323.48,           56790.54,    -26.85,    -73.28,         128.54,  +1.21,  +0.72
  4,     UK0001,       0,  0.159804, 2459439.523257306311,  23.40281,  46.16987,               75.36730,  54.03639,        75.35392,       54.07392,     23.40281,     +46.16987,      23.36101,      +46.19447,  3509472.49, -2088140.66,  5012393.64,      51.014899,       -0.798317,  100050.71,  123026.46,    9139.66,             9058.57,   -11.76,  58763.96,           57274.82,    -28.31,    -77.30,         138.02,  +1.31,  +0.86
  5,     UK0001,       0,  0.199724, 2459439.523257768247,  23.04088,  45.93447,               75.92346,  54.14643,        75.92302,       54.14771,     23.04088,     +45.93447,      23.04028,      +45.93530,  3508800.53, -2088937.12,  5010621.24,      51.006199,       -0.812908,   98566.00,  121097.14,   11195.70,            11114.60,  -258.94,  51503.82,           56589.44,     -0.94,     -2.59,           4.70,  +2.57,  +2.15
  6,     UK0001,       0,  0.239660, 2459439.523258230649,  22.70410,  45.68374,               76.49129,  54.23357,        76.49610,       54.21919,     22.70410,     +45.68374,      22.72126,      +45.67440,  3508146.99, -2089711.75,  5008897.41,      50.997732,       -0.827106,   97122.26,  119224.75,   13195.39,            13114.29,  -563.38,  50072.40,           55646.52,     10.40,     28.67,          52.76,  +4.45,  +4.07
  0,     UK000F,       0,  0.036383, 2459439.523255914450, 344.73404,   9.30281,              157.18922,  45.45881,       157.18698,       45.45732,    344.73404,      +9.30281,     344.73612,       +9.30175,  3511802.94, -2085378.42,  5018540.57,      51.045027,       -0.747797,  105202.19,  146349.27,       0.00,             1927.95,   -21.53,      0.00,           57681.08,      0.82,      5.46,           7.79,  +3.30,  +2.47
  1,     UK000F,       0,  0.076871, 2459439.523256382905, 344.30465,   8.54117,              158.03031,  44.82001,       158.03609,       44.82381,    344.30465,      +8.54117,     344.30005,       +8.54391,  3511032.25, -2086291.91,  5016507.74,      51.035071,       -0.764506,  103498.17,  145537.95,    2358.14,             4286.10,     0.63,  58243.02,           57681.08,     -2.11,    -14.05,          20.14,  +2.07,  +1.26
  2,     UK000F,       0,  0.117335, 2459439.523256851360, 343.87996,   7.80712,              158.84005,  44.20185,       158.84238,       44.20337,    343.87996,      +7.80712,     343.87847,       +7.80822,  3510292.51, -2087168.71,  5014556.57,      51.025508,       -0.780552,  101862.96,  144791.13,    4621.56,             6549.51,   -70.55,  55936.44,           57681.08,     -0.85,     -5.65,           8.13,  +1.75,  +0.95
  3,     UK000F,       0,  0.157835, 2459439.523257319815, 343.42092,   7.02025,              159.69645,  43.53462,       159.68974,       43.53029,    343.42092,      +7.02025,     343.42732,       +7.01707,  3509505.70, -2088101.29,  5012481.24,      51.015329,       -0.797609,  100124.10,  144031.94,    7029.00,             8956.95,     0.22,  59443.07,           57681.08,      2.43,     16.18,          23.44,  +2.34,  +1.55
  4,     UK000F,       0,  0.198259, 2459439.523257787805, 343.05374,   6.36222,              160.37744,  42.96895,       160.37759,       42.96905,    343.05374,      +6.36222,     343.05445,       +6.36229,  3508860.90, -2088865.56,  5010780.48,      51.006981,       -0.811619,   98699.38,  143436.53,    9001.93,            10929.88,  -359.14,  48805.83,           56026.70,     -0.05,     -0.36,           0.53,  +5.55,  +4.77
  0,     UK002B,       1, -0.007486, 2459439.523255370092,  13.16679,  56.95594,               59.16504,  63.57506,        58.97707,       63.62107,     13.16679,     +56.95594,      13.09785,      +57.04367,  3512559.75, -2084481.39,  5020536.77,      51.054796,       -0.731361,  106875.89,  119031.96,       0.00,              387.70,   969.28,     -0.00,           54811.75,     57.79,   -189.61,         343.49,  +3.05,  +2.67
  1,     UK002B,       1,  0.032246, 2459439.523255829699,  12.53517,  56.86303,               59.45070,  63.90909,        59.35089,       63.93339,     12.53517,     +56.86303,      12.49864,      +56.90902,  3511848.90, -2085323.95,  5018661.79,      51.045621,       -0.746781,  105303.81,  116975.94,    2175.04,             1787.34,    76.57,  54742.69,           54811.75,     30.12,    -97.87,         180.57,  +1.78,  +1.44
  2,     UK002B,       1,  0.071986, 2459439.523256289773,  11.90602,  56.74121,               59.80231,  64.24057,        59.74517,       64.25446,     11.90602,     +56.74121,      11.88523,      +56.76721,  3511141.08, -2086162.92,  5016794.80,      51.036478,       -0.762137,  103738.77,  114933.23,    4340.79,             3953.09,   -50.50,  54498.04,           54811.75,     16.86,    -54.52,         102.42,  +1.43,  +1.13
  3,     UK002B,       1,  0.111718, 2459439.523256749846,  11.25780,  56.59928,               60.20444,  64.58238,        60.16982,       64.59080,     11.25780,     +56.59928,      11.24542,      +56.61483,  3510423.00, -2087014.04,  5014900.76,      51.027196,       -0.777714,  102151.39,  112865.88,    6537.94,             6150.24,  -145.72,  55299.19,           54811.75,      9.97,    -32.14,          61.49,  +1.42,  +1.16
  4,     UK002B,       1,  0.151410, 2459439.523257208988,  10.50795,  56.42677,               60.69284,  64.97939,        60.68120,       64.98223,     10.50795,     +56.42677,      10.50423,      +56.43192,  3509614.66, -2087972.14,  5012768.65,      51.016739,       -0.795230,  100364.89,  110545.50,    9011.25,             8623.55,    37.55,  62312.66,           56348.58,      3.26,    -10.47,          20.46,  +1.48,  +1.26
  5,     UK002B,       1,  0.191150, 2459439.523257669061,   9.88898,  56.29150,               61.08256,  65.30962,        61.11023,       65.30287,      9.88898,     +56.29150,       9.90016,      +56.27941,  3508976.30, -2088728.79,  5011084.85,      51.008475,       -0.809099,   98954.33,  108717.04,   10964.50,            10576.81,  -302.02,  49150.78,           55759.36,     -7.57,     24.25,          48.20,  +2.41,  +2.23
  0,     UK002C,       0,  0.024274, 2459439.523255763575,   7.56355,  27.03152,              114.25730,  51.74985,       114.25747,       51.75013,      7.56355,     +27.03152,       7.56337,      +27.03167,  3511944.24, -2085210.95,  5018913.26,      51.046852,       -0.744711,  105514.65,  133520.88,       0.00,             1495.62,   244.78,      0.00,           55598.86,     -0.25,     -0.66,           1.09,  +4.94,  +4.31
  1,     UK002C,       0,  0.064394, 2459439.523256227840,   7.19508,  26.46262,              115.24894,  51.51940,       115.24884,       51.51924,      7.19508,     +26.46262,       7.19552,      +26.46254,  3511226.15, -2086062.08,  5017019.19,      51.037577,       -0.760289,  103926.86,  131928.27,    2197.18,             3692.80,   127.21,  54765.14,           55598.86,      0.14,      0.37,           0.62,  +1.60,  +1.00
  2,     UK002C,       0,  0.104510, 2459439.523256692104,   6.80530,  25.89012,              116.26113,  51.29255,       116.24984,       51.27515,      6.80530,     +25.89012,       6.82393,      +25.88090,  3510510.84, -2086909.92,  5015132.45,      51.028332,       -0.775808,  102345.55,  130359.45,    4385.85,             5881.47,     1.36,  54558.57,           55598.86,     15.15,     39.95,          67.60,  +1.29,  +0.71
  3,     UK002C,       0,  0.144674, 2459439.523257157300,   6.43575,  25.24111,              117.31815,  50.98834,       117.32594,       50.99991,      6.43575,     +25.24111,       6.42424,      +25.24724,  3509751.91, -2087809.47,  5013130.66,      51.018515,       -0.792265,  100668.19,  128715.34,    6707.99,             8203.60,     6.21,  57816.37,           55598.86,    -10.03,    -26.39,          45.23,  +1.18,  +0.63
  4,     UK002C,       0,  0.184766, 2459439.523257621098,   6.07786,  24.73279,              118.21698,  50.78319,       118.20516,       50.76608,      6.07786,     +24.73279,       6.09661,      +24.72370,  3509139.72, -2088535.08,  5011515.91,      51.010591,       -0.805574,   99315.41,  127403.40,    8581.14,            10076.76,  -433.76,  46721.44,           54012.36,     14.72,     38.84,          67.24,  +3.66,  +3.13

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.