# Are there any satellites in geosynchronous orbits that are neither geostationary nor 'wobbly geostastionary' (figure of eight geostationary)?

None of the examples in this question: Are there any satellites in geosynchronous but not geostationary orbits? are nothing like geostationary. They still stay above the one side of the earth. What about satellites that go around the earth exactly twice per 23h 56m 04s? Or some other whole number of times? They are also geosynchronous because after one revolution of the earth they are back above the one point on the earth's surface. Or in the other case, after exactly two revolution. This is an unusual sense of the word 'geosynchronous', but a valid one. It is this type of geosynchronous satellite that I am asking about.

Similar to this question except for the additional constraint to not be a figure of eight geostationary orbit i.e. a geostationary orbit with a (dramatic) wobble: Are there any satellites in geosynchronous but not geostationary orbits?

• Geostationary orbits are essentially circular orbits with a period of essentially one sidereal day and an inclination of essentially zero.

• What you term "wobbly geosynchronous orbits" have the first two qualifications but inclinations substantially different than zero.

The obvious choice for a geosynchronous orbit having a period of essentially one sidereal day that was neither a $$e=0, \ i=0$$ orbit nor a $$e=0, \ i \ne 0$$ orbit would be a $$e \ne 0$$ orbit, i.e. an elliptical orbit with a period of one sidereal day!

I went to https://celestrak.com/satcat/search.php and downloaded the CSV version then sorted it with the scrappy script at the end. I kept data where the periods were between 1434.0 and 1437.5 minutes because there was a pronounced peak there.

Geosynchronous satellites are always jiggling around due to imperfect station keeping or being caught in the middle of a slow, electric propulsion induced station-keeping or longitude-changing maneuver.

Note also that when folks want to "park" two or three (or more?) satellites in the same longitude slot, they use slight offsets in both eccentricity and inclination to create a "special kind of wobble" that is very small, but reliably keeps them from hitting each other for a while. How does the "eccentricity-inclination vector separation" technique work for colocated GEO satellites?

But I found about 10 geosynchronous satellites with moderate eccentricities between about 0.06 and 0.14, and a few very high-fliers with larger eccentricities.

### So:

Are there any satellites in geosynchronous orbits that are neither geostationary nor 'wobbly geostastionary' (figure of eight geostationary)?

### Yes!

Wobbly and not-wobbly geosynchronous orbits that the OP has described:

From here.

Python script for plot, uses CSV SATCAT data downloaded from Celestrak as described above.

import numpy as np
import matplotlib.pyplot as plt

fname = 'satcat oo102.csv'
with open(fname, 'r') as infile:

datal = []
for line in lines[1:]:
try:
datal.append([float(x) for x in line.split(',')[9:13]])
except:
pass
data = np.array(list(zip(*datal)))
period = data[0]

fig, (ax1, ax2, ax3) = plt.subplots(3, 1)
a, b = np.histogram(period, bins=np.arange(1400, 1500, 0.2))
ax1.plot(b[1:], a, '-k')

keep = (period >= 1434) * (period <= 1437.5)

period = data[0]
period, inclination, apo, peri = data[:, keep]

a, b = np.histogram(period, bins=np.arange(1400, 1500, 0.2))
ax1.plot(b[1:], a, '-r')
ax1.set_yscale('log')

eccentricity = (apo - peri) / (apo + peri + 2 * 6378.137)

for ax in (ax2, ax3):
ax.plot(inclination, eccentricity, '.k')
ax.set_xlabel('inclination (deg)')
ax.set_ylabel('eccentricity')
ax2.set_ylim(0, 0.15)
plt.show()

"""
0 OBJECT_NAME
1 OBJECT_ID
3 OBJECT_TYPE
4 OPS_STATUS_CODE
5 OWNER
6 LAUNCH_DATE
7 LAUNCH_SITE
8 DECAY_DATE
9 PERIOD
10 INCLINATION
11 APOGEE
12 PERIGEE
13 RCS
14 DATA_STATUS_CODE
15 ORBIT_CENTER
16 ORBIT_TYPE
"""

• I have just started reading your answer. 'What you term "wobbly geosynchronous orbits" have the first two qualifications but inclinations substantially different than zero.' You have misquoted me here. I took so long to comment because I didn't get a notification in my inbox that you had answered my question. Jun 15 '21 at 12:22
• 1. 'Geosynchronous satellites are always jiggling around due to imperfect station keeping or being caught in the middle of a slow, electric propulsion induced station-keeping or longitude-changing maneuver.' Don't you mean 'Geostationary satellites'? 2. The one labelled 'not wobbly' are surely at least slightly wobbly, even if it's a just by a few millimeters, because every geostationary must wobble slightly and it's always a question of how wobbly, surely? 3. How come your 3D diagram doesn't show any satellites wobbling away and towards the earth as well as north, south, east, and west? Jun 15 '21 at 13:18
• @Matthew I'll take a look in the morning, thanks for your reply! I occasionally also seem to not get a notification it seems I should have, I know the feeling. Sorry if I've misunderstood or misquoted, Briefly, an orbit who's period is a rational number times one sidereal day is called a repeat ground track orbit.
– uhoh
Jun 15 '21 at 13:23
• @Matthew Are there terms for Earth orbits with rational number multiples of 1 sidereal day? So two orbits or one-half orbit or 3/2 or even 1/14 of an orbit per 23h 56m 4.09s, any rational number (perhaps except 1) GPS and other GNSS satellites are all in repeat ground track orbits in MEO.
– uhoh
Jun 15 '21 at 13:28
• @MatthewChristopherBartsh Does the “17” really mean anything with respect to GNSS orbits being rational factions of a sidereal day? Periods of GNSS satellites (sidereal days): GPS: 1/2, Glonass: 8/17, BeiDou: 9/17, Galileo: 10/17
– uhoh
Jun 15 '21 at 13:56

Satellites that orbit twice per day are called semi-sychronous and geosynchronous is explicitly only one orbit per Earth sidereal day. Molniya orbits are semi-synchronous, but I don't know if they are 'not wobbly'.