I know there are a lot of geostationary satellites out there, but I'm wondering - are there any geosynchronous satellites that are not geostationary (ie - have a notable inclination to their orbit)?
3$\begingroup$ relevant: Why do the geosynchronous TDRS satellites have this distribution of inclinations? and also Is TDRS-M (TDRS-13) where it's supposed to be? $\endgroup$– uhohJul 18, 2019 at 23:02
2$\begingroup$ I read somewhere IRNSS use such orbits. $\endgroup$– Manu HJul 19, 2019 at 4:56
$\begingroup$ @ManuH yep, they're on my list! Hopefully someone will ask *Why do some satellites use such high inclination geosynchronous orbits?" $\endgroup$– uhohJul 19, 2019 at 6:28
$\begingroup$ @uhoh I think this file answers that question in a visual way $\endgroup$– Manu HJul 19, 2019 at 7:49
$\begingroup$ @ManuH that's a special case though and easy to explain. Most of these orbits are circular, so the top and bottom half of the pattern are symmetrical. QZSS is in a substantially elliptical Molniya-like orbit so that they spend most of their time in the upper half, over Japan. I'm pretty sure these three are QZSS i.stack.imgur.com/XyW0F.png None of the other orbits look like that, so they will need a different explanation. $\endgroup$– uhohJul 19, 2019 at 8:34
Are there any satellites in geosynchronous but not geostationary orbits?
Apparently there are various advantages to being synchronous even when oscillating wildly in position above/below the Earth's equator (up to +/- 60 degrees!)
After seeing the figures below in A New Look at the GEO and Near-GEO Regimes: Operations, Disposals,and Debris (found in this comment) I decided to go satellite hunting myself
left: "Fig. 3. The number and complexity of geosynchronous orbits for operational spacecraft increased significantly from 1999 to 2011. Only spacecraft whose orbital parameters are available at www.spacetrack.org are shown above." right: "Fig. 7. Highly-inclined geosynchronous communications and navigations systems (Sirius, Beidou, and Michibiki) have been deployed since 2000"
I went to Celestrak's NORAD Two-Line Element Sets; Current Data and downloaded https://celestrak.org/NORAD/elements/geo.txt I then propagated them all in Python using Skyfield (script below) and started plotting.
There are 513 TLEs in the list. Here are their current inclinations versus year of launch:
There are 18 satellites with an inclination greater than 19 degrees:
AMC-14 2008 20.4237 SDO 2010 29.7791 QZS-1 (MICHIBIKI-1) 2010 41.3507 BEIDOU 8 2011 58.8155 BEIDOU 9 2011 54.4339 BEIDOU 10 2011 52.1119 IRNSS-1A 2013 30.184 IRNSS-1B 2014 29.253 IRNSS-1D 2015 29.1615 BEIDOU 17 2015 53.522 BEIDOU 20 2015 53.1176 IRNSS-1E 2016 29.3272 BEIDOU IGSO-6 2016 56.5705 QZS-2 (MICHIBIKI-2) 2017 43.5483 QZS-4 (MICHIBIKI-4) 2017 40.7615 IRNSS-1I 2018 29.3069 BEIDOU IGSO-7 2018 55.0396 BEIDOU-3 IGSO-1 2019 55.0177
Here are some gratuitous 3D plots of the 18 with inclinations greater than 19 degrees:
Python 3 script:
class Object(object): def __init__(self, name, L1, L2): self.name = name.strip() self.L1 = L1 self.L2 = L2 year = int(L1[9:11]) + 1900 if year < 1957: year += 100 self.year = year self.inc = float(L2[8:16]) import numpy as np import matplotlib.pyplot as plt from skyfield.api import Topos, Loader, EarthSatellite from mpl_toolkits.mplot3d import Axes3D fname = 'Celestrak satellites in GEO.txt' # https://celestrak.org/NORAD/elements/geo.txt with open(fname, 'r') as infile: lines = infile.readlines() TLEs = zip(*[[line for line in lines[n::3]] for n in range(3)]) load = Loader('~/Documents/fishing/SkyData') # single instance for big files ts = load.timescale() de421 = load('de421.bsp') earth = de421['earth'] zero = Topos(0.0, 0.0) minutes = np.arange(0, 24*60, 4) # last one is 23h 56m times = ts.utc(2019, 7, 19, 0, minutes) # Doing a quick ugly de-rotate to imitate earth-fixed coordinates. zeropos = zero.at(times).position.km theta = np.arctan2(zeropos, zeropos) cth, sth, zth, oth = [f(-theta) for f in (np.cos, np.sin, np.zeros_like, np.ones_like)] R = np.array([[cth, -sth, zth], [sth, cth, zth], [zth, zth, oth]]) objects =  for i, (name, L1, L2) in enumerate(TLEs): o = Object(name, L1, L2) objects.append(o) o.orbit = EarthSatellite(L1, L2).at(times).position.km if not i%20: print (i,) data = [(o.year, o.inc) for o in objects] plt.figure() year, inc = zip(*data) plt.plot(year, inc, '.k', markersize=8) plt.xlabel('launch year', fontsize=16) plt.ylabel('current inclination (degs)', fontsize=16) plt.title('Geosynchronous TLEs from Celestrak', fontsize=16) plt.show() high_incs = [o for o in objects if o.inc > 19] fig = plt.figure(figsize=[10, 8]) # [12, 10] ax = fig.add_subplot(1, 1, 1, projection='3d') for o in high_incs: orbit = (R * o.orbit).sum(axis=1) x, y, z = orbit ax.plot(x, y, z) ax.plot(x[:1], y[:1], z[:1], 'ok') ax.set_xlim(-40000, 40000) ax.set_ylim(-40000, 40000) ax.set_zlim(-40000, 40000) plt.show() fig = plt.figure(figsize=[10, 8]) # [12, 10] ax = fig.add_subplot(1, 1, 1, projection='3d') for o in objects: orbit = (R * o.orbit).sum(axis=1) x, y, z = orbit ax.plot(x, y, z) # ax.plot(x[:1], y[:1], z[:1], 'ok') ax.set_xlim(-40000, 40000) ax.set_ylim(-40000, 40000) ax.set_zlim(-40000, 40000) plt.show() for o in high_incs: print(o.name, o.year, o.inc)
13$\begingroup$ OUTSTANDING work! :D $\endgroup$ Jul 19, 2019 at 7:21
23$\begingroup$ @ThePiachu thanks! As usual, I'll go to any length to avoid doing what I should have been doing today ;-) bbc.co.uk/programmes/w3csy9k0 $\endgroup$– uhohJul 19, 2019 at 8:34
2$\begingroup$ Are they all navigation satellites? I can see how it makes sense for regional satellite navigation. IRNSS (Indian), BEIDOU (Chinese) and QZS (Japanese) are, at least. $\endgroup$– gerritJul 19, 2019 at 8:53
3$\begingroup$ Re You can still communicate with them continuously using a single ground station, if it is somewhat near the equator. The highly inclined (63.4°) and somewhat elliptical (0.2 to 0.3) geosynchronous satellites follow Tundra orbits. Such orbits aren't of much use at equatorial sites because tracking antennae are needed to communicate with such satellites and the satellites are rarely in view at a given equatorial site. Where they are of use is the extreme latitudes, typically 60+°N, where the satellites appear to dwell at apogee. $\endgroup$ Jul 19, 2019 at 9:13
9$\begingroup$ @gerrit, the second on that list, SDO, is a solar observatory. It produces images at a very high cadence, so rather than using the DSN where it would saturate the bandwidth, it has a dedicated ground station, thus the need for being geosynchronous. It can't be geostationary because that would mean having the earth occult the sun once every day, where the inclined orbit means the earth only occults the sun once a day for a week every 6 months.. $\endgroup$ Jul 19, 2019 at 16:08