Station keeping

Draft

An orbit left alone does not stay where it was put. Station keeping is the continuous expenditure of propellant to hold an orbit against the perturbations catalogued in Orbital perturbations, and for a long-lived satellite it is often the largest single line in the delta-v budget.

Geostationary orbit

GEO has two independent station keeping problems with very different costs, and the asymmetry between them drives satellite design and end-of-life practice.

North-south: inclination control

Lunar and solar gravity torque the orbital plane, driving inclination away from zero at a rate that varies between about 0.75° and 0.95° per year over the 18.6-year cycle of the lunar node, averaging roughly 0.85°.

Correcting it is a plane change at GEO speed, and from Plane changes and inclination:

\Delta v = 2v\sin\frac{\Delta i}{2} = 2(3.075)\sin(0.425°) = 45.6\ \text{m/s per year}

This single term dominates the GEO budget. Over a 15-year design life it is about 685 m/s, comparable to the entire GTO-to-GEO circularisation burn.

Because it is so expensive, many operators stop paying it near end of life. Abandoning north-south control lets inclination grow at 0.85° per year, turning the ground track into a figure-eight. The satellite remains useful for applications with steerable ground antennas, and the extension buys several extra years from the propellant that would have gone on inclination.

East-west: longitude control

Earth’s equatorial cross-section is slightly elliptical, described by the tesseral harmonic $J_{22}$ . This creates two stable longitudes, near 75.3° E and 105.3° W, and two unstable ones, near 11.5° W and 161.9° E. A satellite drifts toward the nearest stable point like a marble in a shallow bowl.

Correcting the drift costs 2 to 6 m/s per year depending on longitude, with the worst case at the unstable points. Solar radiation pressure also pumps eccentricity, which appears as a daily east-west oscillation in the ground track, and controlling it is folded into the same manoeuvre cycle.

Term	Annual delta-v	Driver
North-south, inclination	45 to 55 m/s	Lunisolar gravity
East-west, longitude	2 to 6 m/s	Earth triaxiality, $J_{22}$
Eccentricity control	1 to 3 m/s	Solar radiation pressure
Total	50 to 60 m/s

The station keeping box is typically specified as ±0.05° in both latitude and longitude, which at GEO range is about ±37 km. Tighter boxes cost more propellant and are used where satellites are co-located in the same slot.

Low Earth orbit

In LEO the dominant perturbation is atmospheric drag, and unlike every other perturbation it removes energy irreversibly. For a near-circular orbit the semi-major axis decays at

Drag decay rate

\frac{\mathrm{d}a}{\mathrm{d}t} = -C_D\frac{A}{m}\rho\sqrt{\mu a}

Everything hard about this is in $\rho$ . Thermospheric density at a given altitude varies by more than an order of magnitude over the solar cycle, and by factors of two or three within a single geomagnetic storm. Predicting decay more than a few weeks ahead is therefore predicting solar activity, which is not currently possible with useful accuracy.

The grouping $m/(C_D A)$ is the ballistic coefficient. High values decay slowly. This is why a dense, compact satellite outlives a large, light one at the same altitude, and why deployable drag sails work as a disposal device.

Altitude	Approximate natural lifetime
300 km	Weeks to a few months
400 km	Months to about a year
600 km	Years to a decade
800 km	Roughly a century
Above 1000 km	Effectively indefinite

The ISS at about 400 km loses roughly 2 km per month under moderate solar activity and is reboosted periodically by visiting vehicles. The reboost also serves phasing, since raising the orbit changes the period and shifts the station’s along-track position for an upcoming arrival.

Low-altitude constellations must budget continuous drag makeup, which is a major reason large LEO constellations fly electric propulsion: the total delta-v over a five-year life is modest but continuous, which suits a low-thrust system.

Frozen orbits

Some orbits can be chosen so the perturbations cancel rather than being fought.

The $J_2$ term drives the argument of perigee, and the smaller $J_3$ term, which represents the slight pear shape of the Earth, drives eccentricity. Choosing $\omega = 90°$ and a specific small eccentricity makes the two effects balance:

e_{\text{frozen}} \approx -\frac{J_3}{2J_2}\cdot\frac{R_\oplus}{a}\sin i

For a sun-synchronous orbit at 800 km this gives $e \approx 0.001$ , with perigee locked over the north pole. The orbit is not circular, but its shape and orientation are stationary, so altitude over any given latitude repeats exactly from orbit to orbit.

For an imaging mission this is worth a great deal: consistent altitude means consistent ground sample distance, and no propellant is spent maintaining it. Most operational Earth observation satellites fly frozen orbits.

Repeat ground track orbits are a related choice, tuning the semi-major axis so that an integer number of orbits fits an integer number of days. Holding the repeat requires a small amount of propellant to counter drag, but it guarantees the satellite revisits the same ground points with the same geometry. See Ground tracks and coverage.

Disposal

Disposal is a mandatory line item, and the rules have recently tightened.

LEO: Deorbit within 5 years of mission end for US-licensed spacecraft, under the FCC rule effective September 2024. The long-standing international guideline remains 25 years.
LEO cost: Below about 600 km, natural decay may suffice. Above it, a deorbit burn or a drag device is required.
GEO: Raise into a graveyard orbit at least 235 km above GEO, plus a term for area-to-mass ratio, per the IADC formula.
GEO cost: Roughly 11 m/s for a 300 km raise, plus passivation: venting tanks and discharging batteries so the derelict cannot explode.

The GEO graveyard manoeuvre is cheap, about the cost of three months of north-south station keeping, but it must be planned. A satellite that runs its tanks dry holding station cannot then perform disposal, and propellant gauging in zero gravity is imprecise enough that the reserve is a real design decision. The consequence of getting it wrong is a derelict drifting through the operational belt indefinitely.

References

Soop, E. M. Handbook of Geostationary Orbits, Kluwer, 1994.
Vallado, D. A. Fundamentals of Astrodynamics and Applications, 5th ed., Microcosm Press, 2022, chapters 9 and 11.
IADC-02-01, IADC Space Debris Mitigation Guidelines, revision 3, 2021.
FCC Report and Order 22-74, Mitigation of Orbital Debris in the New Space Age, adopted September 2022, effective for most licensees September 2024.
Vallado, D. A. and Finkleman, D. “A critical assessment of satellite drag and atmospheric density modeling”, Acta Astronautica, 95:141, 2014.