Are there any satellites in geosynchronous but not geostationary orbits?

Question

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)?

Answer 1

Are there any satellites in geosynchronous but not geostationary orbits?

Yep, lots!

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:

Side view:

Top view:

"Family portrait"

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[1], zeropos[0])
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)