Why orbits change—and what missions do about it.

1. What changes—and when does it matter?

Reaching the intended orbit establishes a starting point. The next question is how the spacecraft’s trajectory will evolve—and whether that evolution preserves the observation timing, coverage or relative geometry the mission needs.

In the ideal two-body model, a bound Earth orbit is an ellipse with fixed size, shape and orientation in nonrotating axes. The spacecraft advances along it, but the ellipse itself does not rotate or shrink. Real orbital motion includes additional effects. NASA: orbital geometry and perturbations, pp. 35–36 and 42–43

To describe orientation, we first need a reference frame. Here the axes originate at Earth’s center and retain the directions of its mean equator and equinox at a chosen reference epoch. +Z points toward that epoch’s north celestial pole, +X toward its vernal equinox, and +Y completes the right-handed frame. These axes do not rotate with Earth; Earth-fixed longitude uses a different, rotating reference. NASA/JPL: reference frames

For an unpowered spacecraft, a simplified Newtonian model organizes the additional effects as:

Here, r is the position measured from Earth’s center in nonrotating axes, r its magnitude, and μ_E Earth’s gravitational parameter. The first term represents spherical-Earth gravity. The remaining terms represent departures from that gravity field, atmospheric drag, radiation forces, and the differential gravitational influence of other bodies, particularly the Sun and Moon. Their importance depends on the orbit and spacecraft. NASA: force-model considerations, Appendix P.3

This is an explanatory force budget, not a complete precision model.

Some perturbations produce sustained drift; others produce oscillations. Either can change the conditions needed for observations, communications or other operations. NASA: secular and periodic changes, pp. 42–43

The engineering question is which quantity must remain within limits, over what interval, and with what confidence in its predicted evolution. The following cases show why that can lead to exploiting natural motion, accepting it, improving its prediction or actively correcting it.

2. Earth’s nonspherical gravity can create useful motion

Earth’s equatorial bulge and uneven mass distribution make its gravity field more complex than that of a sphere. Engineers represent this structure using spherical harmonics: spatial patterns indexed by degree ℓ and order m.

The familiar J₂ coefficient represents the leading nonspherical term, associated with Earth’s equatorial bulge. NASA: gravitational harmonics, pp. 31–34

Using precession

One consequence is rotation of the orbital plane around Earth’s polar axis. The first-order, orbit-averaged J₂ nodal rate is approximately

Here, Ω is the right ascension of the ascending node: the northbound equator crossing’s angular direction from a fixed equatorial reference, not Earth-fixed longitude. The mean elements a, e and i describe semimajor axis, eccentricity and inclination; R_E is Earth’s equatorial radius; and n is mean motion. NASA: GDC Orbit Primer, slides 3–4

For a Sun-synchronous orbit, designers select geometry giving approximately 0.986° of eastward precession per day, following the Sun’s mean apparent annual motion. This keeps equator crossings near the selected local mean solar time. In this first-order averaged model, the plane turns while its inclination remains constant; other perturbations can change that inclination. NASA: GDC Orbit Primer, slides 4 and 11

Choosing how much drift to accept

EUMETSAT’s 2017 account of Metop-A illustrates the spacecraft-level consequences. Its equator-crossing time supported consistent observations and influenced solar-array geometry, radiator placement and instrument accommodation. Inclination adjustments maintained the required precession rate. Later, EUMETSAT planned to stop those adjustments and accept local-time drift, preserving propellant for end-of-life orbit lowering.

Whether that was workable depended on more than orbital mechanics. Engineers assessed the changing illumination, eclipses, power balance and temperatures. An initial thermal analysis missed solar-array shading of a battery radiator because its tools had been developed for the original orbital conditions. Examining the changed geometry exposed the missing effect. EUMETSAT: extending Metop-A’s working lifetime

Accepting orbital drift therefore changed the spacecraft’s thermal and power assessment—not just its orbit-maintenance plan.

3. Atmospheric drag connects the environment to spacecraft design

In low Earth orbit (LEO), the residual atmosphere can gradually remove orbital energy and reduce semimajor axis, changing orbital period and along-track timing as well as altitude. NASA: aerodynamic drag, pp. 38–39

A simplified drag-acceleration model is

Here, ρ is atmospheric density, A the projected area facing the flow, m_sc spacecraft mass, and C_D the drag coefficient for that area and the applicable flow conditions. The velocity v_rel is relative to the local atmosphere; drag acts opposite that relative motion. This lumped model describes drag acceleration, not aerodynamic torques. NASA: drag equation and reference-area convention · NASA: spacecraft drag modeling, Appendix P.3

Changing attitude or deploying a structure can change the spacecraft’s exposed area and aerodynamic response. Atmospheric density varies with location, time and solar activity; solar and geomagnetic disturbances can heat and expand the upper atmosphere, increasing density at a given altitude. NASA: orbital-drag dependencies · NASA: space weather and satellite drag

NASA’s conjunction-assessment handbook treats density-forecast error and uncertain spacecraft frontal area as contributors to trajectory uncertainty. NASA: density and area uncertainty, Appendix N The planning implication is to evaluate the expected configurations and environmental range, rather than rely on one nominal drag estimate.

GOCE: compensation in service of the measurement

ESA’s GOCE gravity mission illustrates a particularly demanding response. Its low orbit strengthened the gravity signal available for measurement, but also exposed it to atmospheric disturbances. A slender, symmetric spacecraft reduced aerodynamic forces and torques. An ion thruster, controlled using gradiometer feedback, compensated drag along the flight direction. ESA: GOCE spacecraft and control design, pp. 16–18

ESA reported successful operation of the combined system during commissioning in May 2009. This “drag-free” operation used active compensation to support the gravity instrument’s quiet measurement conditions. The payload needed control of along-flight nongravitational acceleration, not merely periodic restoration of orbital altitude. ESA: GOCE commissioning results

4. Radiation and third-body gravity change the prediction problem

The Sun influences a spacecraft through both light and gravity. These are distinct mechanisms: solar radiation pressure comes from the momentum exchanged when photons interact with spacecraft surfaces. It is not the pressure of the solar wind, which is a flow of charged particles. NASA: light pressure and solar wind

Spacecraft surfaces belong in the orbit model

Radiation forces depend on illuminated area, surface orientation and optical properties; the resulting acceleration also depends on spacecraft mass. Body attitude and solar-array motion therefore connect the spacecraft’s operating configuration to its trajectory. Eclipse transitions change the direct sunlight available, but sunlight is not the only radiation contribution: Earth-reflected light, terrestrial infrared and unequal thermal emission in different directions from the spacecraft can also produce forces. ESA: GNSS radiation-force modeling, slides 2–4 · ESA: satellite eclipses

ESA’s 2020 report on orbit-prediction development for Galileo’s medium Earth orbit (MEO) navigation satellites shows why these details matter. The work modeled radiation incident on and emitted by the satellites, including a refined thermal model for the navigation antenna. Its final model performed better than the alternatives evaluated on most criteria, although uncertainties remained. ESA: long-term orbit prediction

This illustrates a separate engineering task from control: representing spacecraft-specific forces well enough to predict motion, whether or not those forces warrant a corrective maneuver.

The Sun and Moon accelerate Earth, too

Earth and its satellites both accelerate toward the Sun and Moon. In an Earth-centered description, each body’s contribution is the difference between its acceleration of the spacecraft and of Earth’s center.

For a third body represented as a point mass,

Here, r points from Earth’s center to the spacecraft, R points from Earth’s center to the third body, and μ₃ is that body’s gravitational parameter. Both vectors use the same nonrotating axes. The first term is the body’s attraction of the spacecraft; the second subtracts its attraction of Earth’s center. This is a differential gravitational effect, dependent on their relative geometry. University of Tokyo: third-body gravity model, §2.1.3

Near geostationary orbit (GEO), these forces contribute to several simultaneous behaviors. Sun–Moon gravity and Earth’s oblateness affect the orbital plane, radiation pressure can change eccentricity, and longitude-dependent Earth gravity affects longitude evolution. ESA: characteristics of geostationary orbits, p. 93 The longitude dynamics provide a useful example of why bounded motion and an acceptable operating orbit are different questions.

5. GEO: stable does not mean motionless

In the ideal spherical-Earth model, a prograde, circular, equatorial orbit with a period of one sidereal day remains above a fixed longitude. No longitude is preferred: rotating that ideal orbit around Earth’s axis produces an equivalent solution.

Earth’s longitude-dependent gravity breaks this symmetry. Its tesseral and sectoral components create east–west forcing that depends on longitude. Zonal terms alone cannot select a longitude because they are axisymmetric. The resulting dynamics include regions of bounded longitude oscillation and regions of circulation around Earth. Gkolias and Colombo: geosynchronous resonance

How longitude and orbital size interact

To isolate the slow coupling near circular, equatorial GEO, we can construct a leading-order model relating mean Earth-fixed longitude λ and semimajor-axis offset Δa = a − a₀:

Here, a₀ is the Keplerian GEO reference radius, n₀ equals Earth’s rotation rate, and A_T is the longitude-dependent tangential gravitational acceleration evaluated near the reference orbit, positive eastward. Longitude is also positive eastward.

The first relation follows by expanding n(a) − n₀, with n(a) = √(μ_E / a³), about a₀. The second is the circular-orbit limit of Gauss’s semimajor-axis equation, with its coefficient evaluated at that reference. This is an explanatory reduction derived from standard orbital mechanics. Fitzpatrick: Keplerian mean motion · Fitzpatrick: Gauss planetary equations, Eq. I.53

A larger semimajor axis produces slower mean orbital motion and westward drift relative to Earth; a smaller one produces eastward drift. Tangential gravity changes semimajor axis, altering the subsequent drift. The model retains a stationary Earth-gravity contribution and omits Sun–Moon and radiation forcing. It describes the slow longitude–size interaction, not the full perturbed motion or exact equilibrium radius.

Bounded motion can still violate a mission limit

Near a stable center in the conservative local approximation, sufficiently small departures produce libration: longitude oscillates around the equilibrium. Without damping, it does not converge to that point. The broader nonlinear resonance also admits circulation, with longitude passing through successive revolutions rather than remaining around one center. Gkolias and Colombo: resonance structure, §3.1

For an operating spacecraft, the amplitude matters. A bounded trajectory may still travel outside the longitude range needed for its coverage or ground-antenna geometry. Its desired operating longitude may not coincide with a natural equilibrium at all. Meanwhile, inclination and eccentricity can evolve under the other perturbations discussed earlier. ESA: GEO operating geometry and perturbations, p. 93

Dynamical stability describes how motion behaves near a reference state. Mission suitability asks whether that motion remains within useful operating limits. The first can inform stationkeeping strategy; it cannot replace the second.

6. From natural motion to operating limits

The examples above connect orbital physics to different engineering decisions:

Across these cases, the assessment must identify the quantity to preserve, its acceptable range and the interval over which it must remain there.

A nominal trajectory inside a boundary is not sufficient evidence that the spacecraft will remain inside it. Uncertainty in the estimated orbit, environmental forces and spacecraft configuration affects the prediction. NASA: uncertainty considerations, Appendix N That uncertainty belongs in the assessment of how much margin remains for a response.

Where a correction is needed, the next step is to specify the required change in motion, the time available and the acceptable execution error.

The next article develops those maneuver requirements, including repetition, interruptions to other activities and recovery before useful operations resume. They provide the basis for comparing propulsion and control approaches.

This article is an educational synthesis of public sources and original illustrative models. It does not report Aeterna hardware performance, qualification or flight results. Aeterna’s propulsion and fluid-control programs are in development.

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