Orbital Analysis for matched events on 20210813_023732.997_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 61.11° Bg 37.34° Vg 59.54km/s
mass 0.01865g, abs. mag -0.3
Path Details
------------
start -1.95° 50.25° 108.24km
end   -2.01° 50.22° 98.05km

Orbit Details
-------------
Semimajor axis 10.89A.U., eccentricity 0.91, inclination 115.33°, Period 35.93Y, LA Sun 140.29°, last Perihelion 2021-07-25

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: 2459439.609409693163
Time: 2021-08-13 02:37:33.010163 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK000H and UK0038
 Convergence angle = 25.07294 deg
 R.A. =  48.84173  Dec = +56.86300 deg

Best intersection: Stations UK000H and UK0038 with Qconv = 25.07 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   4155977.73 +/- 140.96 m
 Y =    -57737.91 +/- 10.79 m
 Z =   4964989.29 +/- 46.77 m
 Vx =    23206.90 +/- 884.29 m/s
 Vy =    23982.25 +/- 458.91 m/s
 Vz =    50535.77 +/- 535.79 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.275858e+04, -6.945324e+02, +6.256041e+03, +1.290858e+05, -1.199059e+04, +2.314262e+04
-6.945324e+02, +1.153077e+02, -2.133691e+02, -4.686186e+03, +1.081430e+03, -1.212412e+03
+6.256041e+03, -2.133691e+02, +2.500622e+03, +3.639353e+04, -6.601758e+03, +7.966669e+03
+1.290858e+05, -4.686186e+03, +3.639353e+04, +8.520465e+05, -9.476436e+04, +1.536098e+05
-1.199059e+04, +1.081430e+03, -6.601758e+03, -9.476436e+04, +2.845382e+04, -2.525521e+04
+2.314262e+04, -1.212412e+03, +7.966669e+03, +1.536098e+05, -2.525521e+04, +3.192953e+04

Timing offsets (from input data):
    UK000H: 0.000000 s
    UK0038: 0.000216 s

Reference point on the trajectory:
  Time: 2021-08-13 02:37:33.010163 UTC
  Lon     = +-1.941387 +/- 0.0001 deg
  Lat     = +50.252147 +/- 0.0008 deg
  Lat geo = +50.066035 +/- 0.0008 deg
  Ht      =  109489.57 +/- 121.34 m

  JD dynamic   = 2459439.610210580751 
  LST apparent = 359.2040559599 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  45.94133 +/- 1.2644 deg
  Dec       = +56.56046 +/- 0.3431 deg
  Azimuth   =  58.78282 +/- 0.8705 deg
  Elevation = +62.01565 +/- 0.6392 deg
  Vavg      =  57.27042 +/- 0.4001 km/s
  Vinit     =  60.56049 +/- 0.4063 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  46.29561 +/- 1.2644 deg
  Dec       = +56.38605 +/- 0.3431 deg
  Azimuth   =  59.09668 +/- 0.8705 deg
  Elevation = +61.79917 +/- 0.6392 deg
  Vavg      =  57.39268 +/- 0.4001 km/s
  Vinit     =  60.68275 +/- 0.4063 km/s
Radiant (geocentric, J2000):
  R.A.   =  45.97374 +/- 1.2810 deg
  Dec    = +56.44755 +/- 0.3428 deg
  Vg     =  59.53535 +/- 0.4135 km/s
  Vinf   =  60.56049 +/- 0.4063 km/s
  Zc     =  28.08122 +/- 0.6414 deg
  Zg     =  28.32584 +/- 0.6510 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  61.10909 +/- 0.9592 deg
  Bg     = +37.34067 +/- 0.1553 deg
  Vh     =  40.86136 +/- 0.2241 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  76.92367 +/- 2.5981 deg
  Bh     = +62.09967 +/- 0.1952 deg
  Vh_x   =  -4.32598 +/- 0.8652 km/s
  Vh_y   = -18.62465 +/- 0.1000 km/s
  Vh_z   = -36.11176 +/- 0.2208 km/s
Orbit:
  La Sun = 140.293556 +/- 0.0000 deg
  a      =  10.888572 +/- 1.2849 AU
  e      =   0.911238 +/- 0.0180
  i      = 115.328772 +/- 0.6188 deg
  peri   = 154.589486 +/- 2.6579 deg
  node   = 140.293592 +/- 0.0000 deg
  Pi     = 294.883078 +/- 2.6578 deg
  q      =   0.966488 +/- 0.0104 AU
  f      =  25.406964 +/- 2.6579 deg
  M      =   0.501691 +/- 0.3248 deg
  Q      =  20.810655 +/- 2.5599 AU
  n      =   0.027431 +/- 0.0109 deg/day
  T      =  35.929982 +/- 5.5396 years
  Last perihelion JD = 2459421.321275 (2021-07-25 19:42:38.132923) +/- 1.8107 days
  Tj     =  -0.031795 +/- 0.1214
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +3.656657e-04, +2.069729e-04, +3.645574e-02, -1.311687e-08, +9.318680e-04, +1.943204e-04
q   , +2.069729e-04, +1.203771e-04, +2.107386e-02, -7.918752e-09, +5.398324e-04, +1.174024e-04
Tp  , +3.645574e-02, +2.107386e-02, +3.698056e+00, -1.385158e-06, +9.466977e-02, +2.053093e-02
node, -1.311687e-08, -7.918752e-09, -1.385158e-06, +5.999982e-13, -3.554285e-08, -8.900905e-09
peri, +9.318680e-04, +5.398324e-04, +9.466977e-02, -3.554285e-08, +2.424001e-03, +5.268582e-04
i   , +1.943204e-04, +1.174024e-04, +2.053093e-02, -8.900905e-09, +5.268582e-04, +1.320483e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.181637
 a2 = 35.689138

Mean time residuals from time vs. length:
  Station with reference time: UK000H
  Avg. res. = 3.017e-06 s
  Stddev    = 1.74e-03 s

Begin point on the trajectory:
  Lon =    -1.949241 +/- 0.0002 deg
  Lat =    50.249095 +/- 0.0007 deg
  Ht  = 108235.92 +/- 85.87 m
End point on the trajectory:
  Lon =    -2.014007 +/- 0.0003 deg
  Lat =    50.224220 +/- 0.0005 deg
  Ht  = 98047.70 +/- 58.44 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,   107184.73,    98898.90,          0.008377,     18.28,      2.13,              56.14, 1.0000,    True,    True, {"ff_name": "FF_UK000H_20210813_023731_744_0577024.fits"}
    UK0038,   False,    -2.379250,    51.361350,  169.00,   0.000000,   0.000000,   108235.92,    98047.70,          0.025230,     62.47,     39.03,              63.54, 1.0000,    True,    True, {"ff_name": "FF_UK0038_20210813_023733_517_0574720.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,       1,  0.000000, 2459439.609409693163, 353.83991,  18.63371,              189.77438,  57.47862,       189.81495,       57.48926,    353.83991,     +18.63371,     353.81831,      +18.64674,  4155961.99,   -57754.18,  4964955.01,      50.252059,       -1.941562,  109453.29,  129323.25,       0.00,               41.09,  -132.94,      0.00,           62759.14,     -6.38,    -54.39,          87.35,  +4.67,  +4.11
  1,     UK000H,       0,  0.040808, 2459439.609410165343, 353.27963,  17.86397,              190.58004,  56.65172,       190.56768,       56.64849,    353.27963,     +17.86397,     353.28648,      +17.85995,  4154977.54,   -58771.52,  4962811.26,      50.246534,       -1.955947,  107184.73,  127832.39,    2569.00,             2610.09,   -35.29,  62953.35,           62759.14,      1.94,     16.67,          27.08,  +2.14,  +1.61
  2,     UK000H,       0,  0.081632, 2459439.609410637990, 352.76153,  17.05434,              191.27922,  55.78646,       191.29766,       55.79124,    352.76153,     +17.05434,     352.75176,      +17.06042,  4154001.65,   -59780.01,  4960686.14,      50.241052,       -1.970215,  104936.10,  126388.86,    5115.68,             5156.77,    39.07,  62381.92,           62759.14,     -2.92,    -25.01,          41.09,  +1.16,  +0.65
  3,     UK000H,       0,  0.122484, 2459439.609411110636, 352.19182,  16.23808,              192.03946,  54.90478,       192.01985,       54.89972,    352.19182,     +16.23808,     352.20325,      +16.23152,  4153014.35,   -60800.30,  4958536.18,      50.235500,       -1.984655,  102661.39,  124964.48,    7692.12,             7733.21,   141.50,  63067.73,           62759.14,      3.11,     26.78,          44.50,  +0.77,  +0.29
  4,     UK000H,       0,  0.163276, 2459439.609411582816, 351.69608,  15.46373,              192.66520,  54.07115,       192.66161,       54.07023,    351.69608,     +15.46373,     351.69879,      +15.46251,  4152119.31,   -61725.25,  4956587.11,      50.230462,       -1.997766,  100599.40,  123705.70,   10027.82,            10068.91,     6.81,  57258.74,           61678.33,      0.57,      4.93,           8.28,  +0.67,  +0.21
  5,     UK000H,       0,  0.203944, 2459439.609412053600, 351.27396,  14.81690,              193.18651,  53.37167,       193.18279,       53.37072,    351.27396,     +14.81690,     351.27694,      +14.81562,  4151381.12,   -62488.10,  4954979.62,      50.226303,       -2.008614,   98898.90,  122691.67,   11954.19,            11995.27,  -529.70,  47368.09,           59333.30,      0.60,      5.14,           8.71,  +1.83,  +1.39
  0,     UK0038,       0,  0.012888, 2459439.609409839846,   9.52829,   1.64882,              166.00797,  39.46782,       166.06853,       39.49522,      9.52829,      +1.64882,       9.47798,       +1.66887,  4155433.72,   -58300.10,  4963804.64,      50.249095,       -1.949241,  108235.92,  167875.45,       0.00,             1419.65,   465.11,      0.00,           57096.60,    -84.15,   -134.62,         195.06,  +3.59,  +2.47
  1,     UK0038,       0,  0.053280, 2459439.609410307370,   9.27009,   1.10281,              166.44224,  38.96626,       166.46506,       38.97656,      9.27009,      +1.10281,       9.25126,       +1.11040,  4154674.35,   -59084.84,  4962151.02,      50.244831,       -1.960377,  106486.10,  166956.48,    1981.64,             3401.29,     0.60,  49060.28,           57096.60,    -31.64,    -50.70,          73.84,  +1.30,  +0.19
  2,     UK0038,       0,  0.093788, 2459439.609410776291,   8.97356,   0.40870,              166.94566,  38.32198,       166.95232,       38.32498,      8.97356,      +0.40870,       8.96836,       +0.41093,  4153734.81,   -60055.78,  4960105.05,      50.239552,       -1.974121,  104321.27,  165845.83,    4433.47,             5853.13,    -0.75,  60527.10,           57096.60,     -9.22,    -14.79,          21.68,  +0.63,  -0.47
  3,     UK0038,       0,  0.134312, 2459439.609411245212,   8.69153,  -0.30231,              167.42500,  37.65688,       167.43738,       37.66243,      8.69153,      -0.30231,       8.68163,       -0.29813,  4152794.88,   -61027.10,  4958058.26,      50.234265,       -1.987876,  102155.76,  164763.90,    6886.29,             8305.94,    -2.10,  60527.37,           57096.60,    -17.15,    -27.50,          40.57,  +0.17,  -0.91
  4,     UK0038,       0,  0.174824, 2459439.609411714133,   8.38413,  -1.00931,              167.92662,  36.99715,       167.91738,       36.99301,      8.38413,      -1.00931,       8.39271,       -1.01244,  4151860.15,   -61993.06,  4956022.77,      50.229002,       -2.001562,  100002.39,  163717.41,    9325.55,            10745.20,   -16.26,  60210.98,           58177.54,     12.78,     20.51,          30.44,  +0.17,  -0.90
  5,     UK0038,       0,  0.215304, 2459439.609412182588,   8.11185,  -1.66313,              168.36787,  36.38365,       168.35147,       36.37633,      8.11185,      -1.66313,       8.12677,       -1.66873,  4151011.60,   -62869.97,  4954174.93,      50.224220,       -2.014007,   98047.70,  162793.17,   11539.94,            12959.59,  -253.36,  54703.22,           57989.89,     22.68,     36.42,          54.36,  +2.17,  +1.11

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.