# How much is a geostationary satellite expected to deviate from the geostationary orbit?

I've read this already and some Wikipedia articles, but found no real estimates on how much does a satellite deviate from its standard location. Say that the standard sub-satellite point (SSP) is (0°N,0°E) at a satellite height of 42164km. While the satellite is still fully operational, how much is the SSP expected to deviate from this point on these two directions:

• perpendicular to the equatorial plane (N-S)
• tangent to the circular orbit (E-W)?

What about the satellite height? Obviously, it cannot increase by more than 300km (since this is approximately where the graveyard orbit is).

I've also read about the 8-like figure described by the satellite motion on a daily basis after corrections are stopped being performed on the N-S direction. What is the amplitude of this 8-like figure in terms of the SSP?

I really do not need very precise figures (I am just guessing they are mission specific anyway), but rather some estimates.

• I thought there was a good, clear explanation of the increase in inclination in some answer here in SXSE, but when I look I find it mentioned but not really discussed well. This section of Wikipedia briefly mentions the tendency of inclination to steadily increase over a few decades (N-S), and to drift in longitude (E-W) but a good answer here would be really nice. This answer about perturbations on orbital elements other than inclination is also helpful to read. – uhoh Dec 24 '16 at 11:40

Regulatory limits

The deviations depend upon the radio frequency licensing agreement applicable to each satellite. This is a feature of the International Telecommunications Union, ITU.

Limits in terms of degrees can be typically +- 0.05deg in both longitude and latitude or, especially for some older registrations possibly +-0.1 deg longitude and unlimited in latitude.
In terms of km this becomes

+-0.05 deg = +-37km

+-0.1 deg = +-74km

Inclined orbits

That said, operating a satellite with a latitude other than 0.0 deg largely means in an inclined orbit, and this means that the North-South excusions are equal and opposite over a 24 hour cycle. To do so also introduces an East-West excusion naturally (this follows geometrically). From the Earth looking up at a satellite with a slight inclined orbit at geosynchronous altitude the satellites motion appears circular for very small inclinations less than half a degree or so but becomes the "figure of 8" motion for larger inclinations.

Eccentricity

The eccentricity of the orbit will affect firstly the orbital height and then as a consequence its velocity at apogee and perigee and thus its longitude and also the shape of the figure-of-8. An example eccentricity is 0.0003, which would lead to a ~12km excursion in height from the Geostationary radius.

Natural perturbations

A non manouvering object left exactly at GEO will drift firstly in longitude because the Earth is not exactly spherical. Correcting this is called East-West Station-keeping and is usually done every couple of weeks, depending on the type of propulsion system, and this is roughly sufficient for the +-0.05 deg limit.

The effects of gravity of the Sun and the Moon, "luni-solar" perturbations, cause the satellite's inclination to change. It also causes the Right Ascension of the Ascending Node, RAAN, to change though we can come back to that. If left uncorrected this will cause a North South drift of roughly 1 deg in the first year. North South Station Keeping, NSSK, is also often performed once every week or two but is far more costly in energetic terms and has driven the development of more efficient propulsion to keep propellent requirements down.

Many satellites are actually operated without NSSK towards the end of their working lives to save propellant though this depends on the ground users still being able to obtain a good signal from the displaced satellite. Interestingly, objects left to drift indefinitely reach a maximum inclination of ~15deg before their inclination drifts down again over several decades.

The physical size of the satellite, its Area/Mass ratio and reflective properties, also make the satellite subject to Solar Radiation Pressure. This can cause the eccentricity to grow, which increases the daily East-West drift, and thus reduces the time before an East West manouevre is needed. Hence Eccentricity correction, reducing the eccentricity and making the orbit more circular is usually performed at the same time as the East-West manoeuvres themselves.

Collision avoidance

There are also international guidelines for debris mitigation which suggest that the operational zone for GEO in height terms is 42164.5 +- 50km and that the rest of the way up to +-200km is a "manoeuvre corridor" for satellites undergoing a change of station. This isn't mandatory but is, I believe, followed by a large fraction of operators.