Orbit types and regimes

Orbit selection is the first irreversible decision in a mission, and almost everything downstream follows from it: link budget, radiation dose, coverage, launch cost and disposal obligation. This page covers the standard regimes and the two special orbits that exist only because the Earth is not a sphere.

Altitude regimes

The trade-offs run in opposite directions and none of them can be optimised simultaneously.

Latency

Round-trip through GEO is about 240 ms, through LEO about 5 ms. Fixed by geometry, not by technology.

Coverage per satellite

One GEO satellite sees roughly a third of the globe. A 400 km LEO satellite sees a footprint about 2700 km across.

Link budget

Path loss scales as the square of range. GEO is about 60 times further than LEO, costing roughly 36 dB.

Radiation

MEO is the worst regime, sitting inside the outer belt. LEO below the belts is the mildest.

Debris and disposal

LEO decays naturally and is regulated on a schedule. GEO never decays and requires a graveyard manoeuvre.

Sun-synchronous orbits

A sun-synchronous orbit holds a constant angle between its orbital plane and the Sun, so every pass over a given latitude happens at the same local solar time. For imaging that means consistent illumination and consistent shadow geometry, which is what makes multi-date comparison possible at all.

The mechanism is $J_2$. Earth’s equatorial bulge exerts a torque that precesses the line of nodes at

Sun-synchronicity requires this to match Earth’s mean motion about the Sun, $360°/365.2422\ \text{d} = 0.9856°$ per day. Since that is positive and the leading sign is negative, $\cos i$ must be negative, so every sun-synchronous orbit is retrograde. That is a consequence of the algebra, not a design choice.

Solving for inclination at several altitudes:

Altitude and inclination are therefore not independent. Choosing one fixes the other, which removes a degree of freedom from the design and means an orbit raise on a sun-synchronous satellite is not simply a matter of adding energy.

The local time of the descending node is the remaining choice. Mid-morning, typically 10:30, is the most common for optical imaging: it gives enough shadow for terrain relief while keeping cloud development lower than in the afternoon. Dawn-dusk orbits, at 06:00 or 18:00, keep the satellite in near-continuous sunlight, which suits power-hungry payloads such as synthetic aperture radar and largely removes the eclipse thermal cycle.

Highly elliptical orbits

Kepler’s second law says a satellite lingers near apogee. An orbit with apogee over a high latitude therefore dwells where a geostationary satellite cannot usefully see at all, because from above 70° latitude a GEO satellite sits too close to the horizon.

Molniya orbits have a 12-hour period, $e \approx 0.74$ and apogee near 40 000 km. A satellite spends roughly eight of its twelve hours usefully positioned, so three satellites give continuous coverage.

Tundra orbits use a 24-hour period with lower eccentricity, and two satellites suffice.

Both depend on a second $J_2$ result. The argument of perigee normally drifts:

Unchecked, this rotates the ellipse within its plane and walks apogee away from the intended latitude within months. But the bracket vanishes when $\cos^2 i = 1/5$:

At that inclination apogee stays put with no propellant at all. The 63.4° figure appearing in every Molniya and Tundra design is this root, and the prograde solution at 116.565° is its retrograde counterpart.

Geostationary orbit

A circular equatorial orbit whose period equals one sidereal day (86 164.09 s, not 86 400 s) holds a fixed longitude:

which is 35 786 km altitude, at 3.075 km/s.

Geostationary is the special case of geosynchronous with zero inclination and zero eccentricity. Inclined geosynchronous orbits trace a figure-eight ground track, and satellites near end of life are often allowed to drift into one, because abandoning north-south station keeping saves the dominant propellant cost. See Station keeping.

GEO is a finite resource. Satellites must be separated in longitude to avoid radio interference, slots are coordinated through the ITU, and the ring is already congested over the major markets.

GTO, the geostationary transfer orbit, is the elliptical parking orbit that launchers deliver to: perigee 185 to 250 km, apogee at or near GEO altitude, inclination set by the launch site. Circularising and removing the inclination is the satellite’s own job, and doing both in one apogee burn is one of the most valuable optimisations in the field. See Plane changes and inclination.

Cislunar orbits

Beyond GEO the two-body model stops being adequate and the Earth-Moon system must be treated as a restricted three-body problem. See Lagrange points.

Low lunar orbits are unusually hostile. The Moon’s gravity field is strongly non-uniform, dominated by mass concentrations under the maria, and most low circular orbits are unstable on a timescale of months. The frozen inclinations above are the exceptions where the perturbations average out.

The Gateway NRHO is chosen for a 9:2 synodic resonance, which keeps the spacecraft out of eclipse, requires only a few metres per second per year of station keeping, and never loses line of sight to Earth.

Selecting a regime

References

• Vallado, D. A. Fundamentals of Astrodynamics and Applications, 5th ed., Microcosm Press, 2022, chapters 8 and 11.
• Wertz, J. R., Everett, D. F. and Puschell, J. J. (eds.) Space Mission Engineering: The New SMAD, Microcosm Press, 2011, chapter 9.
• Capdevila, L. R. and Howell, K. C. “A transfer network linking Earth, Moon and the triangular libration point regions”, Advances in Space Research, 62:1826, 2018.
• Whitley, R. and Martinez, R. “Options for Staging Orbits in Cis-Lunar Space”, IEEE Aerospace Conference, 2016.