Orbital Analysis for matched events on 20210813_002253.947_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 63.84° Bg 38.76° Vg 59.42km/s
mass 0.06392g, abs. mag -1.6
Path Details
------------
start 0.35° 49.38° 107.24km
end   0.21° 49.30° 93.60km

Orbit Details
-------------
Semimajor axis 87.97A.U., eccentricity 0.99, inclination 112.79°, Period 825.10Y, LA Sun 140.20°, last Perihelion 2021-07-23

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: 2459439.515902174637
Time: 2021-08-13 00:22:53.947889 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002D and UK002N
 Convergence angle = 12.07024 deg
 R.A. =  48.96003  Dec = +58.52255 deg

Best intersection: Stations UK002D and UK002N with Qconv = 12.07 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3576907.68 +/- 397.99 m
 Y =  -2257926.40 +/- 90.67 m
 Z =   4899955.34 +/- 103.37 m
 Vx =    20753.59 +/- 1823.45 m/s
 Vy =    23488.46 +/- 588.48 m/s
 Vz =    51691.70 +/- 835.53 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+1.939518e+05, -4.267227e+04, -4.843301e+04, +7.516413e+05, -2.211139e+05, -2.887567e+05
-4.267227e+04, +1.016923e+04, +1.071131e+04, -1.606198e+05, +5.011982e+04, +6.058594e+04
-4.843301e+04, +1.071131e+04, +1.336425e+04, -1.847018e+05, +5.219360e+04, +7.215772e+04
+7.516413e+05, -1.606198e+05, -1.847018e+05, +3.331993e+06, -9.440264e+05, -1.255042e+06
-2.211139e+05, +5.011982e+04, +5.219360e+04, -9.440264e+05, +3.024079e+05, +3.805431e+05
-2.887567e+05, +6.058594e+04, +7.215772e+04, -1.255042e+06, +3.805431e+05, +5.409755e+05

Timing offsets (from input data):
    UK002D: -0.001202 s
    UK002N: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 00:22:53.947889 UTC
  Lon     = ++0.347271 +/- 0.0019 deg
  Lat     = +49.384271 +/- 0.0031 deg
  Lat geo = +49.197154 +/- 0.0031 deg
  Ht      =  107276.24 +/- 177.47 m

  JD dynamic   = 2459439.516702915542 
  LST apparent = 327.7377914230 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  48.53730 +/- 2.6926 deg
  Dec       = +58.76922 +/- 1.0270 deg
  Azimuth   =  46.03119 +/- 2.2060 deg
  Elevation = +44.67273 +/- 0.9100 deg
  Vavg      =  58.19014 +/- 0.2194 km/s
  Vinit     =  60.45206 +/- 0.2860 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  48.62658 +/- 2.6926 deg
  Dec       = +58.52307 +/- 1.0270 deg
  Azimuth   =  46.31514 +/- 2.2060 deg
  Elevation = +44.52483 +/- 0.9100 deg
  Vavg      =  58.34859 +/- 0.2194 km/s
  Vinit     =  60.61051 +/- 0.2860 km/s
Radiant (geocentric, J2000):
  R.A.   =  48.82619 +/- 2.7086 deg
  Dec    = +58.51340 +/- 1.0234 deg
  Vg     =  59.42474 +/- 0.2910 km/s
  Vinf   =  60.45206 +/- 0.2860 km/s
  Zc     =  45.45734 +/- 0.9153 deg
  Zg     =  45.86870 +/- 0.9232 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  63.83540 +/- 2.2102 deg
  Bg     = +38.75786 +/- 0.4448 deg
  Vh     =  41.72530 +/- 0.5572 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  84.36731 +/- 5.5052 deg
  Bh     = +63.07456 +/- 0.3229 deg
  Vh_x   =  -1.85451 +/- 1.6731 km/s
  Vh_y   = -18.80327 +/- 0.7460 km/s
  Vh_z   = -37.20213 +/- 0.4475 km/s
Orbit:
  La Sun = 140.203769 +/- 0.0000 deg
  a      =  87.970196 +/- 94.4650 AU
  e      =   0.989231 +/- 0.0508
  i      = 112.794198 +/- 0.9445 deg
  peri   = 150.376217 +/- 4.3284 deg
  node   = 140.203116 +/- 0.0001 deg
  Pi     = 290.579333 +/- 4.3283 deg
  q      =   0.947387 +/- 0.0156 AU
  f      =  29.619968 +/- 4.3284 deg
  M      =   0.024561 +/- 0.3339 deg
  Q      = 174.993004 +/- 188.9385 AU
  n      =   0.001195 +/- 0.0220 deg/day
  T      = 825.095036 +/- 2189.7061 years
  Last perihelion JD = 2459418.955546 (2021-07-23 10:55:59.197739) +/- 2.7246 days
  Tj     =  -0.407114 +/- 0.2566
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +2.826540e-03, -8.103515e-04, -1.262390e-01, +5.784717e-08, -3.680749e-03, -7.830815e-04
q   , -8.103515e-04, +2.894479e-04, +4.790537e-02, -2.158206e-08, +1.357941e-03, +2.918071e-04
Tp  , -1.262390e-01, +4.790537e-02, +8.474738e+00, -3.720607e-06, +2.353022e-01, +5.016061e-02
node, +5.784717e-08, -2.158206e-08, -3.720607e-06, +1.749024e-12, -1.040948e-07, -2.361685e-08
peri, -3.680749e-03, +1.357941e-03, +2.353022e-01, -1.040948e-07, +6.577016e-03, +1.404566e-03
i   , -7.830815e-04, +2.918071e-04, +5.016061e-02, -2.361685e-08, +1.404566e-03, +3.189384e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.000166
 a2 = 46.892929

Mean time residuals from time vs. length:
  Station with reference time: UK002N
  Avg. res. = 4.192e-06 s
  Stddev    = 2.05e-03 s

Begin point on the trajectory:
  Lon =     0.346948 +/- 0.0019 deg
  Lat =    49.384067 +/- 0.0031 deg
  Ht  = 107243.43 +/- 177.49 m
End point on the trajectory:
  Lon =     0.210855 +/- 0.0011 deg
  Lat =    49.298988 +/- 0.0021 deg
  Ht  = 93597.85 +/- 101.23 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
    UK002D,   False,    -1.801980,    51.351940,  129.00,   0.000000,   0.000000,   103337.59,    93793.19,          0.010157,     43.85,     26.05,              78.50, 1.0000,    True,    True, {"ff_name": "FF_UK002D_20210813_002248_920_0375552.fits"}
    UK002N,   False,    -0.727590,    51.263100,   57.00,   0.000759,  42.015636,   107243.43,    93597.85,          0.013477,     55.40,     18.66,              84.85, 1.0000,    True,    True, {"ff_name": "FF_UK002N_20210813_002245_159_0382976.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,     UK002D,       0,  0.075022, 2459439.515903056599, 359.11303, -12.60669,              145.06807,  19.73274,       145.06119,       19.72628,    359.11303,     -12.60669,     359.12195,      -12.61033,  3574983.87, -2260103.72,  4895163.65,      49.359785,       +0.308100,  103337.59,  288869.98,       0.00,             5603.75,   512.44,      0.00,           55314.78,     23.57,     39.68,          32.96,  +1.91,  -0.39
  1,     UK002D,       0,  0.115338, 2459439.515903523192, 358.95512, -12.98959,              145.36870,  19.43256,       145.37160,       19.43528,    358.95512,     -12.98959,     358.95198,      -12.98806,  3574265.09, -2260917.22,  4893373.36,      49.350626,       +0.293413,  101866.62,  288572.78,    2093.69,             7697.44,   168.94,  51931.97,           55314.78,     -9.93,    -16.70,          13.89,  +1.59,  -0.71
  2,     UK002D,       0,  0.155670, 2459439.515903989784, 358.77263, -13.39210,              145.69888,  19.12201,       145.70132,       19.12429,    358.77263,     -13.39210,     358.77023,      -13.39081,  3573500.01, -2261783.12,  4891467.75,      49.340870,       +0.277789,  100301.25,  288273.31,    4322.25,             9926.01,   -40.64,  55255.52,           55314.78,     -8.33,    -14.01,          11.66,  +1.00,  -1.30
  3,     UK002D,       0,  0.196026, 2459439.515904456843, 358.58385, -13.82391,              146.04443,  18.78538,       146.05145,       18.79195,    358.58385,     -13.82391,     358.57586,      -13.82018,  3572685.76, -2262704.68,  4889439.65,      49.330479,       +0.261170,   98635.68,  287973.67,    6694.06,            12297.81,  -108.44,  58772.08,           55314.78,    -23.98,    -40.35,          33.62,  +1.04,  -1.26
  4,     UK002D,       0,  0.236402, 2459439.515904924367, 358.34910, -14.28483,              146.44280,  18.43644,       146.43300,       18.42730,    358.34910,     -14.28483,     358.36242,      -14.29005,  3571796.18, -2263711.49,  4887223.94,      49.319119,       +0.243028,   96816.53,  287669.00,    9285.27,            14889.03,    41.96,  64177.06,           57432.95,     33.41,     56.26,          46.92,  +0.87,  -1.42
  5,     UK002D,       0,  0.276766, 2459439.515905391425, 358.18093, -14.72874,              146.76904,  18.07926,       146.78233,       18.09162,    358.18093,     -14.72874,     358.16535,      -14.72164,  3570980.39, -2264634.77,  4885192.04,      49.308692,       +0.226375,   95148.74,  287409.44,   11661.52,            17265.28,   -21.88,  58870.54,           58243.18,    -45.31,    -76.23,          63.64,  +0.74,  -1.55
  6,     UK002D,       0,  0.317046, 2459439.515905857552, 357.99636, -15.07035,              147.07115,  17.82252,       147.06620,       17.81792,    357.99636,     -15.07035,     358.00393,      -15.07300,  3570317.20, -2265385.36,  4883540.21,      49.300211,       +0.212805,   93793.19,  287211.68,   13593.30,            19197.05,  -525.11,  47958.64,           57432.49,     16.85,     28.38,          23.70,  +2.12,  -0.17
  0,     UK002N,       0,  0.000000, 2459439.515902174637, 345.71650, -12.09516,              159.46227,  24.51233,       159.47795,       24.52451,    345.71650,     -12.09516,     345.69949,      -12.08650,  3576891.66, -2257944.53,  4899915.43,      49.384067,       +0.346948,  107243.43,  248712.95,       0.00,               46.67,  -509.42,      0.00,           64541.42,    -26.01,    -77.16,          67.53,  +2.95,  +0.97
  1,     UK002N,       0,  0.040416, 2459439.515902642626, 345.39948, -12.70183,              159.94125,  23.98966,       159.96387,       24.00717,    345.39948,     -12.70183,     345.37504,      -12.68929,  3575878.00, -2259091.76,  4897390.69,      49.371171,       +0.326308,  105167.87,  248572.01,    2952.62,             2999.29,    -0.03,  73055.64,           64541.42,    -37.55,   -111.36,          97.52,  +2.06,  +0.08
  2,     UK002N,       0,  0.080756, 2459439.515903109219, 345.09012, -13.22040,              160.38622,  23.54924,       160.38840,       23.55092,    345.09012,     -13.22040,     345.08807,      -13.21918,  3574987.27, -2260099.88,  4895172.10,      49.359829,       +0.308149,  103344.53,  248476.75,    5547.20,             5593.87,   155.92,  64317.90,           64541.42,     -3.62,    -10.76,           9.42,  +1.42,  -0.56
  3,     UK002N,       0,  0.121064, 2459439.515903575812, 344.82701, -13.67854,              160.76526,  23.15645,       160.75787,       23.15076,    344.82701,     -13.67854,     344.83560,      -13.68266,  3574208.25, -2260981.55,  4893231.79,      49.349901,       +0.292245,  101750.30,  248415.27,    7816.34,             7863.01,   -11.64,  56295.11,           64541.42,     12.25,     36.42,          31.91,  +1.10,  -0.88
  4,     UK002N,       0,  0.161440, 2459439.515904043335, 344.55557, -14.22289,              161.16914,  22.67966,       161.18054,       22.68842,    344.55557,     -14.22289,     344.54375,      -14.21651,  3573310.76, -2261997.31,  4890996.38,      49.338456,       +0.273946,   99914.10,  248370.79,   10430.60,            10477.27,   161.80,  64747.70,           63751.17,    -18.94,    -56.24,          49.29,  +1.02,  -0.96
  5,     UK002N,       0,  0.201732, 2459439.515904509462, 344.29438, -14.66284,              161.53538,  22.30146,       161.53330,       22.29987,    344.29438,     -14.66284,     344.29750,      -14.66401,  3572558.23, -2262849.01,  4889122.01,      49.328851,       +0.258575,   98374.86,  248354.23,   12622.61,            12669.28,   -81.92,  54403.29,           62192.09,      3.45,     10.25,           8.98,  +0.98,  -1.00
  6,     UK002N,       0,  0.242080, 2459439.515904976521, 344.01565, -15.18000,              161.93324,  21.84973,       161.93618,       21.85198,    344.01565,     -15.18000,     344.01342,      -15.17835,  3571692.73, -2263828.56,  4886966.29,      49.317797,       +0.240919,   96605.03,  248359.74,   15143.68,            15190.35,     0.03,  62482.94,           61666.06,     -4.89,    -14.55,          12.75,  +0.66,  -1.32
  7,     UK002N,       0,  0.282396, 2459439.515905443113, 343.74430, -15.65016,              162.30983,  21.44113,       162.30577,       21.43803,    343.74430,     -15.65016,     343.74996,      -15.65246,  3570894.32, -2264732.19,  4884977.65,      49.307592,       +0.224617,   94972.78,  248387.37,   17469.34,            17516.00,  -111.50,  57685.75,           61115.39,      6.75,     20.06,          17.58,  +0.92,  -1.06
  8,     UK002N,       0,  0.322656, 2459439.515905909240, 343.51129, -16.04440,              162.62859,  21.09845,       162.61591,       21.08878,    343.51129,     -16.04440,     343.52667,      -16.05159,  3570221.62, -2265493.53,  4883302.14,      49.298988,       +0.210855,   93597.85,  248427.10,   19428.80,            19475.46,  -585.84,  48670.15,           60030.49,     21.11,     62.81,          55.02,  +1.75,  -0.23

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.