# Are there terms for Earth orbits with rational number multiples of 1 sidereal day?

An Earth orbit with a period of 1 sidereal day (and zero inclination) is a geosynchronous orbit, orbits slightly above and below that are supersynchronous and subsynchronous orbits, and a Molniya orbit (or the MEO of the GPS satellites) designed with a half-day period is a semi-synchronous orbit.

I am guessing that an orbit with a period of 2 sidereal days might be called a bisynchronous orbit if it turned out to be useful. Right now I don't see that term outside of KSP.

What would an Earth orbit designed to have a period of a rational fraction of a sidereal day be called. For example a ~16 hour orbit designed to pass over the same location on earth every ~48 hours having a period of 2/3 (2:3) of a sidereal day?

I thought that would fall under a general category of synchronous orbits, but it seems synchronous refers specifically to 1:1. Is there a different term for the group of orbits synchronized to rational numbers of sidereal days?

• Resonant orbits seem to be a popular topic. Plutinos wrt Neptune. Hildas wrt Jupiter. Usually the name I see is the numbers, E. G. 3:2, 2:3 orbital resonance, etc. You also see resonances mentioned in discussions of Kirkwood gaps in The Main Asteroid Belt. Gaps in Saturn's rings seem to correspond to resonances with some of the moons. Sep 5 '16 at 21:13
• The whole point of a synchronous orbit is that it stays over some particular part (for a sun-synchronous orbit it's the point with the desired light angle) of the world. A two-day orbit doesn't stay put, it would have no reason to have a special term. Sep 6 '16 at 2:20
• @LorenPechtel apparently there are a lot of people using repeat-groundtrack orbits that haven't realized their orbits are pointless: 1, 2, 3, 4, 5.
– uhoh
Sep 6 '16 at 2:46
• @uhoh The two-day orbit is a small subclass of the type of orbit you're talking about. Sep 6 '16 at 2:53
• @LorenPechtel OK so I said that I only found the term for a 2-sidereal-day orbit within Kerbal Space Program and not elsewhere as an example of an apparent lack of terms for rational fraction but non 1:1 orbits as background information for the question only. It's all I could find at the time of the asking of the question. I guess we don't have much disagreement that some things in KSP might not be so important in the real world.
– uhoh
Sep 6 '16 at 3:29

I don't know if there's a term that applies just to the (rational-fraction-of-day-period) satellite, but such a satellite could be said to be in a resonant or harmonic orbit with a second, synchronous satellite.

You could say your 16-hour satellite was in 2:3 resonance with Earth's day, for example.

• Resonance is a term on dynamic, usually meaning an stable or unstable orbit. I don't see why any arbitrary ratio should be called a resonance.
– Pere
Sep 4 '16 at 22:05
• I think @Pere is right. I think it only applies when a body is in an orbit with a period close enough to a rational number times the period of a perturbing force so that it is at least temporarily "locked in" some how. For example I've asked "Is there a good working definition of orbital resonance, and is 2016 OH3's orbit in 1:1 resonance with Earth's orbit?" in this question. In the current question, if the satellite used a perturbation from a "bump" in Earth's gravity or magnetic field as the planet rotates, that could be a resonance perhaps.
– uhoh
Sep 4 '16 at 23:27
• It seem's I am wrong - just found a resonant repeat-gorundtrack orbit. Now to figure out if there are both resonant and non-resonant repeat-groundtrack orbits, and if resonant implies some sort of locking or not. In physics and engineering, the term "resonance" is generally used with systems that are coupled, even if very weakly. I'm curious if there is any coupling with the rotation of the earth in this case.
– uhoh
Sep 6 '16 at 2:51
• I found this review and a ton of other stuff. Indeed - resonance with a lumpy, rotating geopotential.
– uhoh
Sep 6 '16 at 3:16

This is a total coincidence, but I just ran across this introduction to the paper New Synchronous Orbits Using the Geomagnetic Lorentz Force (Brett Streetman and Mason A. Peck: Journal of Guidance, Control, and dynamics, Vol. 30, No. 6, November–December 2007):

In a repeat-groundtrack orbit, the subsatellite point traces out a recurring pattern in some integer number of orbital periods. Traditionally, these orbits are achieved by adjusting the period of a satellite such that it completes an integer number of revolutions in exactly an integer number of sidereal Earth days.

So it seems that the term "repeat-groundtrack orbit" might be a suitably all-encompassing term for Earth orbits with rational number multiples of 1 sidereal day.

Here is a bit more of the first paragraph in case someone is interested...

Geostationary and geosynchronous Earth orbits (GEOs) are perhaps the most familiar and useful examples. These orbits have a mean motion equal to the spin rate of the Earth. We shall refer to orbits that repeat their groundtrack every orbital period as GT-1 orbits. Thus, all trajectories in GEO are in the GT-1 class. A more general class, the GT-x orbit, repeats its groundtrack every x revolutions. For example, satellites in the GPS constellation are in 12 sidereal hour orbits and can thus be considered GT-2 satellites. Many low-Earth-orbit (LEO) imaging satellites designed for full-Earth coverage also use repeat-track orbits. Every 16 days, over the course of 233 orbits, Landsat 7 covers the full Earth, making it a GT-233 satellite...

• "Every 16 days, over the course of 233 orbits, Landsat 7 covers the full Earth, making it a GT-233 satellite...". Every sixteen sidereal days? Jun 15 at 13:40
• @MatthewChristopherBartsh It's a quote from a source, not my words, but in order to repeat a ground track the kind of days that the author is referring to would be sidereal.
– uhoh
Jun 15 at 13:50
• Of course I knew they were not your words. Jun 15 at 13:52
• @MatthewChristopherBartsh I reply to comments from hundreds of users; I don't know who know what and who doesn't so I just aim for maximum accuracy in a response. Don't take any offense please!
– uhoh
Jun 15 at 13:55
• It probably clarifies matters for many readers, and I knew that, so I wasn't blaming you. Some people read the comments very hastily indeed. Jun 15 at 14:14

Molniya is called semisynchronous because it can work as a sort-of geosynchronous satellite for part of its orbit, not because its period is 12h.

I've never seen specific names for orbits other than geosynchronous and sun-synchronous.

• Wouldn't that be pseudo-synchronous? But then again, it could be hemi-synchronous too. Can you help me find a reference to it not being because of the half-day orbit? The Wikipedia article does say "For Earth, a semi-synchronous orbit is considered a medium Earth orbit, with a period of just under 12 hours." but there's no citation for that, so it could be an assumption.
– uhoh
Sep 4 '16 at 11:37
• 11.96 hours give or take, not twelve hours. Half a sidereal day is not twelve hours. The earth's period is one sidereal day, not twenty-four hours. Who said anything about twelve hours, anyway? Jun 15 at 13:48