Semimajor Axis Decay Research Articles

Gaseous Dynamical Friction on Elliptical Keplerian Orbits

We compute the gaseous dynamical friction force experienced by massive perturbers on elliptical Keplerian orbits. Using linear perturbation theory, we investigate the density wake morphology, dynamical friction force, and secular orbital evolution for massive single perturbers as well as equal-mass binaries embedded in a homogeneous, static medium. In all cases, the rate of change in the semimajor axis is found to be negative (as expected), whereas the rate of change in eccentricity is negative for strictly subsonic trajectories and positive for strictly supersonic trajectories. Transonic orbits can experience both positive and negative torques during the course of an orbit, with some growing in eccentricity and others circularizing. We observe all initial orbits becoming highly supersonic and eccentric (over sufficiently long timescales) due to a relentless semimajor axis decay increasing the Mach number and subsequent eccentricity driving. We compare our findings to previous studies for rectilinear and circular motion while also making our data for the evolution of Keplerian orbits available.

Retrieval and analysis of thermospheric mass densities below 200 km altitude based on precise orbit data of the re-entry objects SZ-10 MODULE and TIANGONG 1

Atmospheric mass densities in the lower thermosphere below 200 km have not been adequately determined, but they are crucial for re-entry prediction of space objects. In this paper, based on precise orbit data of the re-entry objects SZ-10 MODULE and TIANGONG 1 (COSPAR identifiers 2013-029H and 2011-053A, respectively; NORAD catalog numbers 39193 and 37820, respectively), the semi-major axis decay numerical method and the improved energy balance method are adopted to retrieve thermospheric mass densities below 200 km altitude, and a total of 7044 and 4698 points of valid densities data with one-minute temporal resolution are obtained, respectively. Then the retrieved densities after preprocessing are compared with the NRLMSISE-00 empirical model of the atmosphere. It shows that there is an excellent consistency between these two methods with the Pearson correlation coefficients around 1.00, the retrieved densities of which are also in good agreement with the model with the Pearson correlation coefficients above 0.97 (their systematic biases are about 1.1% and 4.5% with standard deviations of about 14% and 20% for these two objects respectively), but the retrieved densities of the semi-major axis decay numerical method have a smaller systematic bias from the model than the results of the improved energy balance method which is computationally more efficient. In addition, the corresponding retrieved densities and their ratios to the model are further analyzed in terms of latitude and local solar time, and the retrieved densities of these two methods are also in good consistency within about 97%. The maximum mean deviations from the model in both dimensions reach about 12%. It reveals the variations of the thermospheric mass densities below 200 km altitude with latitude and local solar time due to solar activity. Additionally, it also indicates that the NRLMSISE-00 model underestimates the thermospheric densities at high solar activity and overestimates the densities at low solar activity, as compared to the retrieved densities that are regarded as true values.

Sounding the Atmospheric Density at the Altitude of LARES and Ajisai during Solar Cycle 24

During Solar Cycle 24, the passive spherical satellites LARES and Ajisai, placed in nearly circular orbits with mean geodetic altitudes between 1450 and 1500 km, were used as powerful tools to probe the neutral atmosphere density and the performances of six thermospheric models in orbital regimes for which the role of dominant atomic species is contended by hydrogen and helium, and accurate satellite measurements are scarce. The starting point of the analysis was the accurate determination of the secular semi-major axis decay rate and the corresponding neutral drag acceleration in a satellite- centered orbital system. Then, for each satellite, thermospheric model and solar activity level, the drag coefficients capable of reproducing the orbital decay observed were found. These coefficients were finally compared with the physical drag coefficients computed for both satellites in order to assess the biases affecting the thermospheric density models. None of them could be considered unconditionally the best; the specific outcome depending on solar activity and the regions of the atmosphere crossed by the satellites. During solar maximum conditions, an additional density bias linked to the satellite orbit inclination was detected.

On the secular decay of the LARES semi-major axis

The laser-ranged satellite LARES is expected to provide new refined measurements of relativistic physics, as well as significant contributions to space geodesy and geophysics. The very low area-to-mass ratio of this passive and extremely dense satellite was chosen to reduce as much as possible the disturbing effects of non-gravitational perturbations. However, because of its height, about 1450 km compared with about 5800–5900 km for the two LAGEOS satellites, LARES is exposed to a much stronger drag due to neutral atmosphere.From a precise orbit determination, analyzing the laser ranging normal points of LARES over a time span of about 3.7 years with the GEODYN II (NASA/GSFC) code, it was found an average semi-major axis decay rate of −0.999 m per year, corresponding to a non-conservative net force acting nearly opposite to the velocity vector of the satellite and with a mean along-track acceleration of −1.444 × 10−11 m/s2.By means of a modified version of the SATRAP (ISTI/CNR) code, the neutral drag perturbation acting on LARES was evaluated over the same time span, taking into account the real evolution of solar and geomagnetic activities, with five thermospheric density models (JR-71, MSIS-86, MSISE-90, NRLMSISE-00 and GOST-2004). All of them provided consistent results, well within their acknowledged uncertainties. Moreover, when the same models (JR-71 and MSIS-86) were used within GEODYN II in a least-square fit of the tracking data, the differences between the average drag coefficients estimated with SATRAP and GEODYN were of the order of 1% or less.Unlike what happened for the two LAGEOS, where Yarkovsky thermal drag and charged particle drag were the leading causes, it was found that neutral atmosphere drag alone was able to explain most (≈98.6%) of the observed semi-major axis decay of LARES. The remaining ≈1.4%, corresponding to an average along-track acceleration of about −2 × 10−13 m/s2 (i.e. ≈1/70 of neutral drag), was probably linked to thermal thrust effects. It was 50%, or less, of the value previously reported in the literature, but further and more detailed investigations, including the detection of the signature of the periodic terms, will be needed in order to characterize such smaller non-gravitational perturbation.

Thermospheric mass density derived from CHAMP satellite precise orbit determination data based on energy balance method

In this article, the energy balance method is used to retrieve thermospheric mass density from CHAMP satellite precise orbit determination (POD) data during 2007–2009. The retrieved thermospheric mass densities are compared with those from accelerometer data and an empirical model. The main conclusions are as follows: (1) Thermospheric mass density can be retrieved from POD data by the energy balance and semi-major axis decay methods, whose results are consistent. (2) The accuracy of the retrieved densities depends on the integration time period, and the optimal period for CHAMP density retrieval from POD data is about 20 minutes. (3) The energy balance method can be used to calibrate accelerometer data. (4) The accuracy of retrieving thermospheric density from POD data varies with satellite altitude and local time.

High-precision repeat-groundtrack orbit design and maintenance for Earth observation missions

The focus of this paper is the design and station keeping of repeat-groundtrack orbits for Sun-synchronous satellites. A method to compute the semimajor axis of the orbit is presented together with a station-keeping strategy to compensate for the perturbation due to the atmospheric drag. The results show that the nodal period converges gradually with the increase of the order used in the zonal perturbations up to $$J_{15}$$ . A differential correction algorithm is performed to obtain the nominal semimajor axis of the reference orbit from the inputs of the desired nodal period, eccentricity, inclination and argument of perigee. To keep the satellite in the proximity of the repeat-groundtrack condition, a practical orbit maintenance strategy is proposed in the presence of errors in the orbital measurements and control, as well as in the estimation of the semimajor axis decay rate. The performance of the maintenance strategy is assessed via the Monte Carlo simulation and the validation in a high fidelity model. Numerical simulations substantiate the validity of proposed mean-elements-based orbit maintenance strategy for repeat-groundtrack orbits.

Coevolution of binaries and circumbinary gaseous discs

The recent discoveries of circumbinary planets by $\it Kepler$ raise questions for contemporary planet formation models. Understanding how these planets form requires characterizing their formation environment, the circumbinary protoplanetary disc, and how the disc and binary interact and change as a result. The central binary excites resonances in the surrounding protoplanetary disc that drive evolution in both the binary orbital elements and in the disc. To probe how these interactions impact binary eccentricity and disc structure evolution, N-body smooth particle hydrodynamics (SPH) simulations of gaseous protoplanetary discs surrounding binaries based on Kepler 38 were run for $10^4$ binary periods for several initial binary eccentricities. We find that nearly circular binaries weakly couple to the disc via a parametric instability and excite disc eccentricity growth. Eccentric binaries strongly couple to the disc causing eccentricity growth for both the disc and binary. Discs around sufficiently eccentric binaries that strongly couple to the disc develop an $m = 1$ spiral wave launched from the 1:3 eccentric outer Lindblad resonance (EOLR) that corresponds to an alignment of gas particle longitude of periastrons. All systems display binary semimajor axis decay due to dissipation from the viscous disc.

Evolution of binary black holes in self gravitating discs

We study the interplay between gas accretion and gravity torques in changing a binary elements and its total angular momentum (L) budget. Especially, we analyse the physical origin of the gravity torques (T_g) and their location within the disc. We analyse 3D SPH simulations of the evolution of initially quasi-circular massive black hole binaries (BHBs) residing in the central hollow of massive self-gravitating circumbinary discs. We use different thermodynamics within the cavity and for the numerical size of the black holes to show that (i) the BHB eccentricity growth found previously is a general result, independent of the accretion and the adopted thermodynamics; (ii) the semi-major axis decay depends both on the T_g and on the interplay with the disc-binary L-transfer due to accretion; (iii) the spectral structure of the T_g is predominately caused by disc edge overdensities and spiral arms developing in the body of the disc and, in general, does not reflect directly the period of the binary; (iv) the net T_g changes sign across the BHB corotation radius. We quantify the relative importance of the two, which appear to depend on the thermodynamical properties of the instreaming gas, and which is crucial in assessing the disc-binary L-transfer; (v) the net torque manifests as a purely kinematic (non-resonant) effect as it stems from the cavity, where the material flows in and out in highly eccentric orbits. Both accretion onto the black holes and the interaction with gas streams inside the cavity must be taken into account to assess the fate of the BHB. Moreover, the total torque exerted by the disc affects L(BHB) by changing all the elements (mass, mass ratio, eccentricity, semimajor axis) of the BHB. Common prescriptions equating tidal torque to semi-major axis shrinking might therefore be poor approximations for real astrophysical systems.

KCTF evolution of trans-neptunian binaries: Connecting formation to observation

Recent observational surveys of trans-neptunian binary (TNB) systems have dramatically increased the number of known mutual orbits. Our Kozai Cycle Tidal Friction (KCTF) simulations of synthetic trans-neptunian binaries show that tidal dissipation in these systems can completely reshape their original orbits. Specifically, solar torques should have dramatically accelerated the semimajor axis decay and circularization timescales of primordial (or recently excited) TNBs. As a result, our initially random distribution of TNBs in our simulations evolved to have a large population of tight circular orbits. This tight circular population appears for a range of TNO physical properties, though a strong gravitational quadrupole can prevent some from fully circularizing. We introduce a stability parameter to predict the effectiveness of KCTF on a TNB orbit, and show that a number of known TNBs must have a large gravitational quadrupole to be stable.

Thermospheric density model biases at the 23rd sunspot maximum

Uncertainties in the neutral density estimation are the major source of aerodynamic drag errors and one of the main limiting factors in the accuracy of the orbit prediction and determination process at low altitudes. Massive efforts have been made over the years to constantly improve the existing operational density models, or to create even more precise and sophisticated tools. Special attention has also been paid to research more appropriate solar and geomagnetic indices. However, the operational models still suffer from weakness. Even if a number of studies have been carried out in the last few years to define the performance improvements, further critical assessments are necessary to evaluate and compare the models at different altitudes and solar activity conditions.Taking advantage of the results of a previous study, an investigation of thermospheric density model biases during the last sunspot maximum (October 1999—December 2002) was carried out by analyzing the semi-major axis decay of four satellites: Cosmos 2265, Cosmos 2332, SNOE and Clementine. Six thermospheric density models, widely used in spacecraft operations, were analyzed: JR-71, MSISE-90, NRLMSISE-00, GOST-2004, JB2006 and JB2008. During the time span considered, for each satellite and atmospheric density model, a fitted drag coefficient was solved for and then compared with the calculated physical drag coefficient. It was therefore possible to derive the average density biases of the thermospheric models during the maximum of the 23rd solar cycle.Below 500km, all the models overestimated the average atmospheric density by amounts varying between +7% and +20%. This was an inevitable consequence of constructing thermospheric models from density data obtained by assuming a fixed drag coefficient, independent of altitude. Because the uncertainty affecting the drag coefficient measurements was about 3% at both 200km and 480km of altitude, the calculated air density biases below 500km were statistically significant. The minimum average biases were obtained with JB2008, NRLMSISE-00 and GOST-2004.Above 500km, where only one satellite was analyzed (at 630km), and errors tend to increase with altitude, it cannot be asserted that the calculated biases are significant. Nevertheless, they are presented to show how the various models diverge at higher altitudes. Around 630km, NRLMSISE-00 had a negligible average bias, while the other models underestimated (GOST-2004) or overestimated the average density, by amounts varying between 6% and 16%. However, in terms of semi-major axis root mean square residuals, JB2006 and JB2008 were the best in any case.Below 500km, the short-term behavior of the models was also investigated by fitting the semi-major axis decay over 30-day arcs. The resulting fitted drag coefficients displayed a significant variability, probably associated with mismodeled density variations, but JB2008, followed by JB2006, provided the smallest semi-major axis residuals and a reduced short-term variability of the density bias at just a few frequencies, having been probably successful in removing a significant fraction of the mismodeling sources.

Measuring Absolute Thermospheric Densities And Accommodation Coefficients Using Paddlewheel Satellites: Past Findings, Present Uses, And Future Mission Concepts

The first absolute measurement of thermospheric density was made by combining simultaneous observations of spin and semimajor axis decay of Explorer VI. Providing two independent measures of the interaction with the airstream enabled the determination of both air density and drag coefficient. Then by using a realistic model of the gas-surface interaction, the energy accommodation coefficient was determined. Only four such measurements were made prior to the time of writing. In this paper, we review the history of paddlewheel measurements and explain their importance to ongoing work in satellite drag. Next, a novel concept for paddlewheel satellites based on the CubeSat platform is discussed along with the relevant design parameters. A rudimentary error analysis for paddlewheel measurements evaluated the feasibility of these designs and it was found that the drag torques generated on a three-kilogram paddlewheel are within the measurement capabilities of today’s technologies. For certain types of paddlewheel configurations, the use of direct simulation methods is important for accurately analyzing the data. This is because a paddlewheel with the spin axis oriented in the orbit normal direction undergoes significant flow-shadowing and this is not easily represented by analytical methods. Increasing the availability of accommodation measurements via the paddlewheel method represents an improvement in the accuracy of Earth’s total density models as well as the understanding of gas-surface interactions in low Earth orbit. This is of profound importance in the prediction of satellite orbits as well as the understanding of atmospheric phenomena.

CoRoT-7b: SUPER-EARTH OR SUPER-Io?

CoRoT-7 b, a planet about 70% larger than the Earth orbiting a Sun-like star, is the first-discovered rocky exoplanet, and hence has been dubbed a "super-Earth". Some initial studies suggested that since the planet is so close to its host star, it receives enough insolation to partially melt its surface. However, these past studies failed to take into consideration the role that tides may play in this system. Even if the planet's eccentricity has always been zero, we show that tidal decay of semi-major axis could have been large enough that the planet formed on a wider orbit which received less insolation. Moreover, CoRoT-7 b could be tidally heated at a rate that dominates its geophysics and drives extreme volcanism. In this case, CoRoT-7 b is a "super-Io" that, like Jupiter's volcanic moon, is dominated by volcanism and rapid resurfacing. Such heating could occur with an eccentricity of just 10^-5. This small value could be driven by CoRoT-7 c if its own eccentricity is larger than ~10^-4. CoRoT-7 b may be the first of a class of planetary super-Ios likely to be revealed by the CoRoT and Kepler spacecraft.

Drag and energy accommodation coefficients during sunspot maximum

Conditions appropriate to gas-surface interactions on satellite surfaces in orbit have not been successfully duplicated in the laboratory. However, measurements by pressure gauges and mass spectrometers in orbit have revealed enough of the basic physical chemistry that realistic theoretical models of the gas-surface interaction can now be used to calculate physical drag coefficients. The dependence of these drag coefficients on conditions in space can be inferred by comparing the physical drag coefficient of a satellite with a drag coefficient fitted to its observed orbital decay. This study takes advantage of recent data on spheres and attitude stabilized satellites to compare physical drag coefficients with the histories of the orbital decay of several satellites during the recent sunspot maximum. The orbital decay was obtained by fitting, in a least squares sense, the semi-major axis decay inferred from the historical two-line elements acquired by the US Space Surveillance Network. All the principal orbital perturbations were included, namely geopotential harmonics up to the 16th degree and order, third body attraction of the Moon and the Sun, direct solar radiation pressure (with eclipses), and aerodynamic drag, using the Jacchia-Bowman 2006 (JB2006) model to describe the atmospheric density. After adjusting for density model bias, a comparison of the fitted drag coefficient with the physical drag coefficient has yielded values for the energy accommodation coefficient as well as for the physical drag coefficient as a function of altitude during solar maximum conditions. The results are consistent with the altitude and solar cycle variation of atomic oxygen, which is known to be adsorbed on satellite surfaces, affecting both the energy accommodation and angular distribution of the reemitted molecules.

Analysis of the orbital decay of spherical satellites using different solar flux proxies and atmospheric density models

In order to highlight the performances of the JR-71 and MSISE-90 atmospheric density models and also to investigate whether the use of the E 10.7 index, instead of the F 10.7 cm solar radio flux, improves the trajectory modeling of low Earth objects, the orbital decay of 11 spherical satellites was analyzed. The data were distributed over a full solar activity cycle and covered altitudes in between 150 and 1500 km. The observed evolution of the mean semi-major axis was obtained by processing the historical two-line elements record. For each satellite, environmental condition, atmospheric model and solar flux proxy, a drag coefficient was computed by fitting the observed semi-major axis decay, comparing the results with the theoretical estimates. Below 400 km, both models overestimated the atmosphere density, independently on the solar flux proxy and environmental conditions. MSISE-90, with F 10.7, proved to be the best model to compute the air density, in low solar activity conditions. JR-71, with F 10.7, was generally more accurate over the maximum of the 23rd solar cycle, while MSISE-90 revealed to be the best model in the increasing phase of the solar flux, when using E 10.7. Between 750 and 850 km, the average accuracy of the models was generally better than 15% and the choice of the atmospheric density model was relatively inconsequential, both in conditions of low and high solar activity. A quite large uncertainty was instead observed in moderate conditions, when using E 10.7 in both models. At 1500 km, both models underestimated the air density by more than 35%, in low solar activity conditions. For high solar fluxes, the density was well represented by JR-71, both using F 10.7 and E 10.7, while it resulted to be underestimated, by about 25%, when using MSISE-90, both with E 10.7 and F 10.7. In general, more accurate orbital decay fits were obtained with E 10.7, which seems able to better describe the atmosphere density changes induced by a varying solar activity. In conclusion, none of the models analyzed was able to accurately describe the atmosphere density in all orbital regimes and environmental conditions, independently on the solar flux proxy.

An Analytical and Numerical Study of Plane Change Maneuvers Using Aerodynamic Force

The goal of the present work is to analyze space missions that use the terrestrial atmosphere to accomplish orbital maneuvers that involve a plane change. A set of analytical solutions is presented for the variation of the orbital elements due to a single passage through the atmosphere, assuming that the interval the spacecraft travels through the atmosphere is not too large. The study considers both the lift influence on the spacecraft orbit as well as drag. The final equations are tested with numerical integration and can be considered in accordance with the numerical results whenever the perigee height is larger than a critical value. Next, a numerical study of the ratio between the velocity increment required to correct the semimajor axis decay due to the atmospheric passage and the velocity variation required to obtain the change in the inclination is also presented. This analysis can be used to decide if a maneuver passing through the atmosphere can decrease the fuel consumption of the mission and, in the cases where this technique can be used, if a multiple passage is more efficient than a single passage.

The Yarkovsky Seasonal Effect on Asteroidal Fragments: A Nonlinearized Theory for Spherical Bodies

The long-term orbital evolution of meteoroids and small asteroids in the size range up to several kilo- meters is aUected by the ii seasonal ˇˇ Yarkovsky force, caused by radiation pressure recoil on spinning bodies heated by solar radiation to diUerent temperatures at diUerent latitudes on their surfaces. This eUect leads to a draglike, secular semimajor-axis decay, which may inject the bodies into chaotic zones associated with mean motion and secular resonances and eventually deliver them to near-Earth space. To model the Yarkovsky force, two kinds of simplifying assumptions have been frequently made: (1) a linearization in the ratio between temperature variation and average temperature and in the orbital eccentricity and (2) a plane-parallel geometry, that is, body sizes larger than the penetration depth of the seasonal thermal wave (typically, several meters). In a previous paper, we developed a new nonlinearized theory, and here we also remove the assumption of plane-parallel geometry and extend our theory to the more general spherical case, valid for all body sizes, by means of a new numerical approach. We also revise the linear theory, obtaining a fully analytical literal solution, which is well suited to develop ana- lytical and semianalytical secular perturbation theories and allows us to perform a detailed comparison with the results of the more accurate numerical model. We —nd that the accuracy of the linear theory is relatively good (20% or better) for near-circular orbits. Although the temperature variations grow with the orbital eccentricity, we show that the linear theory can still predict the averaged drift rates of the mean orbital elements up to eccentricities of 0.4¨0.5.

The Yarkovsky Seasonal Effect on Asteroidal Fragments: A Nonlinearized Theory for the Plane-parallel Case

The "seasonal" Yarkovsky force is due to radiation pressure recoil, which acts on anisotropically emitting rotating bodies, heated by sunlight to different temperatures at different latitudes on their surfaces. This force gives rise to a significant draglike effect on rapidly spinning asteroid fragments ≈1–100 m in size. Here we present a new treatment of this effect, based on the numerical solution of the heat transfer equation with no linearization in the ratio between the peak temperature difference and the average temperature on the body's surface. Our treatment is restricted to the large-body (plane-parallel) case, valid for radii larger than the penetration depth of the seasonal thermal wave (≈1–20 m depending on the conductivity of the surface layer). Also, we solve numerically the Gaussian perturbation equations for the evolution of the orbital eccentricity, as well of the semimajor axis under the seasonal Yarkovsky force. We find the results to be in broad agreement with the linearized model of D. P. Rubincam, with two main discrepancies: (i) for the same thermal and optical parameters and near-circular orbits, the semimajor axis decay rate predicted by the improved, nonlinearized theory is some 15% lower, and (ii) for some directions of the spin axis relative to the perihelion direction, the Yarkovsky force can cause a secular growth of the eccentricity. When gravitationally induced perihelion precession, spin axis precession, and collisional reorientations are accounted for, however, the eccentricity on average is found to decrease. We also show that the theory can be easily generalized to bodies of spheroidal shapes, with typical discrepancies of a factor of 2 in the semimajor axis decay rate with respect to the spherical case.

Strategies for Maximizing a Satellite Lifetime by Tether-Mediated Orbital Injection

The tether slingshot technique, which is based on the exchange of angular momentum between a satellite and a platform, is analyzed here with the goal of maximizing the satellite lifetime after release. Once the tether is deployed and the system librates about the local vertical, the tether is cut twice: the first time at the platform end in order to increase the apogee height of the satellite-tether system and later on at the satellite end in order to increase the perigee height of the satellite. The goal is to define the conditions at the end of deployment and the timing and parameters of the two cuts in order to maximize the satellite lifetime. Two separate strategies are followed: (a) the first tether cut occurs when the libration angle reaches a critical value for which the tether crosses the local vertical (with prograde libration) at the second apogee passage, i.e., when the second cut provides the maximum increase of perigee altitude; and (b) the first cut takes place when the tether crosses the local vertical and the true anomaly at the second tether cut is taken as an additional free parameter of the optimization process. In both strategies we assume, at first, that the maximum lifetime corresponds to the minimum semi-major axis decay rate or, conversely, to the maximum increase of the satellite perigee. Since increasing perigee height means sacrificing apogee height, the assumption above is tested by directly computing the satellite lifetime as a function of the free parameters in order to refine the estimate of the optimal cut parameters. The orbital-parameters-oriented approaches (a) and (b), together with the direct computation of the lifetime, allow us to select the end-of-deployment and cut parameters which maximize the satellite lifetime.

Thermal force effects on slowly rotating, spherical artificial satellites—II. Earth infrared heating

The theory developed in Farinella and Vokrouhlický ( Planet. Space Sci. 44, 1551–1561, 1996) is applied for the thermal force effects affecting the motion of LAGEOS-type artificial satellites to the specific case of the so-called Yarkovsky-Rubincam effect, due to anisotropic heating of the satellite's surface by the Earth's infrared radiation. This theory allows the usual assumption of a fast rotational motion of the satellite to be removed, so as to allow for a misalignment between the direction of the thermal force and the spin axis. When applied to the LAGEOS satellite, which has been strongly despun by magnetic torques since its launch in 1976, the theory shows that in the next decade the orbital perturbations associated with the Yarkovsky-Rubincam effect, will become much different than those predicted by the simple rapid-rotation approach. This is the case both for the drag-like effect causing a semimajor axis decay, and for the inclination changes.

The rotation of LAGEOS and its long‐term semimajor axis decay: A self‐consistent solution

We develop a self‐consistent model for the evolution of the spin axis of LAGEOS and the related long‐term semimajor axis perturbations, due to asymmetric emission/reflection of radiation from the satellite's surface. We show that the theory developed by Bertotti and Iess [1991] for the evolution of LAGEOS's rotation under magnetic and gravitational torques, which we have somewhat generalized here, can lead to a successful fit of the observed semimajor axis residuals, provided the correct initial conditions for the direction of the spin axis are chosen. The remaining residuals have an rms dispersion of 0.50 × 10−12 m/s2, comparable to that of previous solutions, based on purely empirical fits of the spin axis direction as a function of time. The spectrum of the residuals indicates that they are probably due to unmodeled radiation forces (e.g., from Earth albedo and/or penumbra passages). Our solution allows us to predict the future evolution of LAGEOS's rotation for about another decade in the future, until the spin rate will become so slow that some basic assumptions of the theory will fail. A similar model can also be used to model/predict the coupled spin‐orbit evolution of the LAGEOS II satellite, launched in late 1992, although the available data still cover a span of time too short for reaching significant quantitative conclusions concerning this satellite.