I'm trying to calculate the perigee and apogee of a given satellite based on its TLE
from skyfield.api import Topos, EarthSatellite
ts = load.timescale()
# latest TLE as of this morning, epoch is epoch=2020-08-24T12:30:01Z
line=['0 ISS (ZARYA)',
'1 25544U 98067A 20237.52084486 .00016717 00000-0 10270-3 0 9031',
'2 25544 51.6430 10.2947 0001353 63.6269 296.5020 15.49179055 2606']
satellite = EarthSatellite(line[1], line[2], line[0], ts)
t = ts.utc(2020, 8, 24, 12, range(30,123)) #epoch + a full orbit
geocentric = satellite.at(t)
subpoint = geocentric.subpoint()
print(f"max {max(subpoint.elevation.km)}")
print(f"min {min(subpoint.elevation.km)}")
This produces an apogee of 437.7 and perigee of 418.5. The perigee looks right, but apogee looks about 17km too high.
Thinking I was reading the docs wrong, I've also tried calculating the topocentric distance along the way and got identical results (to 7 places)
difference = satellite - bluffton
topocentric = difference.at(t)
alt, az, distance = topocentric.altaz()
print(f"max {max(distance.km)}")
print(f"min {min(distance.km)}")
Which produces identical results within 7 decimals.
Doing this more by hand, at the the TLE's epoch:
revs_per_day = 15.49179055
eccentricity = 0.0001353
earth_equatorial_radius = 6378.14
period_hrs = 24.0 / revs_per_day
range = (6028.9 * (period_hrs * 60))** (2 / 3)
perigee = range * (1 + eccentricity) - earth_equatorial_radius
produces an apogee of 420.02 km and perigee of 418.18 km, which is more in line with what I expected.
What am I doing wrong? Am I not understanding what Skyfield's distances represent?
Correct, you have a slight misconception about the distance you are asking for; and then there’s some other discrepancy that I am less sure of.
subpoint.elevation.km which measures against that rising and falling surface as the ISS crosses from high to low latitude, try just geocentric.distance().km. You can always then subtract the Earth’s mean radius from that if you are less interested in the full shape of the orbit from the Earth’s center, than in just that component that’s above ground.geocentric.distance().km with, say, NASA HORIZONS output for comparison. I attach some of its output below: it shows the ISS rising and falling from 6788 km to 6803 km over an orbit, almost the same distances as the 6789–6802 km range returned from Skyfield — suggesting that the range in altitude is indeed more than 2 km for the current orbit.*******************************************************************************
Ephemeris / WWW_USER Mon Aug 24 17:36:17 2020 Pasadena, USA / Horizons
*******************************************************************************
Target body name: International Space Station (spacecraft) (-125544) {source: iss}
Center body name: Earth (399) {source: DE431mx}
Center-site name: GEOCENTRIC
*******************************************************************************
Start time : A.D. 2020-Aug-25 00:00:00.0000 UT
Stop time : A.D. 2020-Aug-25 03:00:00.0000 UT
Step-size : 1 minutes
*******************************************************************************
...
Center pole/equ : High-precision EOP model {East-longitude positive}
Center radii : 6378.1 x 6378.1 x 6356.8 km {Equator, meridian, pole}
Target primary : Earth
Vis. interferer : MOON (R_eq= 1737.400) km {source: DE431mx}
Rel. light bend : Sun, EARTH {source: DE431mx}
Rel. lght bnd GM: 1.3271E+11, 3.9860E+05 km^3/s^2
Atmos refraction: NO (AIRLESS)
RA format : HMS
Time format : CAL
EOP file : eop.200824.p201115
EOP coverage : DATA-BASED 1962-JAN-20 TO 2020-AUG-24. PREDICTS-> 2020-NOV-14
Units conversion: 1 au= 149597870.700 km, c= 299792.458 km/s, 1 day= 86400.0 s
Table cut-offs 1: Elevation (-90.0deg=NO ),Airmass (>38.000=NO), Daylight (NO )
Table cut-offs 2: Solar elongation ( 0.0,180.0=NO ),Local Hour Angle( 0.0=NO )
Table cut-offs 3: RA/DEC angular rate ( 0.0=NO )
****************************************************************************************************************
Date__(UT)__HR:MN R.A._____(ICRF)_____DEC APmag S-brt delta deldot S-O-T /r S-T-O
****************************************************************************************************************
$$SOE
2020-Aug-25 00:00 11 24 02.95 +19 59 34.2 n.a. n.a. 0.00004542337255 0.0095997 18.8151 /T 161.1844
...
2020-Aug-25 00:25 16 34 19.41 -47 50 11.1 n.a. n.a. 0.00004547799868 0.0003566 101.0263 /T 78.9709
2020-Aug-25 00:26 16 56 12.33 -49 10 57.0 n.a. n.a. 0.00004547808220 0.0000571 104.6886 /T 75.3086
2020-Aug-25 00:27 17 19 10.96 -50 15 22.9 n.a. n.a. 0.00004547804847 -0.0002273 108.3437 /T 71.6534
2020-Aug-25 00:28 17 43 04.17 -51 02 05.5 n.a. n.a. 0.00004547790303 -0.0004991 111.9896 /T 68.0075
...
2020-Aug-25 01:13 05 07 59.71 +49 48 30.6 n.a. n.a. 0.00004538023740 -0.0018603 73.4466 /L 106.5505
2020-Aug-25 01:14 05 31 35.95 +50 43 36.4 n.a. n.a. 0.00004537965836 -0.0010181 69.7785 /L 110.2186
2020-Aug-25 01:15 05 55 59.08 +51 20 10.6 n.a. n.a. 0.00004537942066 -0.0001615 66.1208 /L 113.8763
2020-Aug-25 01:16 06 20 51.01 +51 37 19.0 n.a. n.a. 0.00004537952843 0.0007013 62.4763 /L 117.5208
2020-Aug-25 01:17 06 45 50.83 +51 34 35.0 n.a. n.a. 0.00004537998258 0.0015622 58.8484 /L 121.1487
2020-Aug-25 01:18 07 10 36.81 +51 12 03.0 n.a. n.a. 0.00004538078075 0.0024132 55.2411 /L 124.7560