Effect Of Solar Radiation Pressure Research Articles

Comparison of the SRP spherical model between LEO and GEO satellites

Solar Radiation Pressure (SRP) is a phenomenon caused by the pressure exerted by solar photons on a satellite’s surface when it is exposed to sunlight. It is a form of radiation force and can significantly impact the motion and behaviour of satellites in space. SRP influences a satellite’s orbit by causing changes in its semimajor axis, eccentricity, inclination, argument of perigee, right ascension of the ascending node, and mean anomaly. SRP models are used to simulate the effects of solar radiation pressure on satellites. These models are essential for accurately predicting satellite trajectories and orbital behaviour. There are several types of SRP models, such as spherical model, flat model, box-wing model, faceted model, and analytical SRP models. This research focuses on Telkom 1 and LAPAN A1 satellites, both belonging to Indonesia and positioned in Geostationary Earth Orbit (GEO) and Low Earth Orbit (LEO) orbits, respectively. The study aims to find a comparison of the effects of SRP spherical model on LEO and GEO satellites. Our modelling shows that the semimajor axis and eccentricity are sensitive to SRP, while the inclination and right ascension of the ascending node are not significantly affected. Comparing the effects of SRP on LEO and GEO satellites, we concluded that both LEO and GEO orbit experience the most significant fluctuations in January (perihelion), likely due to the influence of solar radiation pressure.

Quantifying Solar Radiation Pressure Effects on Dust at Small Heliocentric Distances

The dynamics of dust grains has traditionally been modeled under the assumption that the ratio of the opposing solar radiation pressure and gravitational forces is fixed for an individual, unchanging grain. However, at small heliocentric distances, this assumption is inaccurate, as the variation in radiation pressure force with heliocentric distance does not follow an inverse square law there, as the Sun cannot be approximated as a point source of light. To correct for this, we have calculated the required correction to assumed radiation pressure force values, taking into account the decrease in both the visible solar area and in the radial solar radiation force components. We present here an empirical fit to this correction, for heliocentric distances 0.028–1.00 au. This correction may be used to more accurately simulate dust motion near the Sun.

Mission Concept and Development of the First Interstellar CubeSat Powered by Solar Sailing Technology

Project Svarog is a student-led initiative aiming to reach the heliopause using a solar sail. Orbital models have proven the feasibility of the mission given the mass-to-area ratio of about 9 grams per square meter of the sail for a satellite launched on a piggyback mission to Mars. Solar sailing increases the flexibility of missions to the outer Solar System, as unique planet alignment, which was crucial for gravity assists is no longer required. Long-term missions require a better understanding of thin membrane behaviour since buckling of sail material under solar radiation pressure might cause the spacecraft to tumble unpredictably. Reduced order model of membrane deflection is thus coupled with orbital simulation, resulting in the determination of the operation regime, for which the mission escapes the Solar System. Additionally, vacuum chamber experiments designed to investigate the effects of solar radiation pressure and heating on the transient and steady-state behaviour of the sail have been devised. The system is designed to be built as a 6U CubeSat, being one of the first missions to utilise small-scale platforms for deep space missions. Granted that the first mission is successful, the Svarog system could also serve as a low-cost testbed for new technologies and research opportunities in deep space. Keywords: Satellite, Deep Space, CubeSat, Solar Sail, Orbital Mechanics, Structural Design

Analytical and numerical estimates for solar radiation pressure semi-secular resonances

The aim of this work is to provide new insights on the dynamics associated to the resonances which arise as a consequence of the coupling of the effect due to the oblateness of the Earth and the Solar Radiation Pressure (SRP) effect for an uncontrolled object with moderate to high area-to-mass ratio. Analytical estimates for the location of the resulting resonant equilibrium points are provided, together with formulas to compute the maximum amplitude of the corresponding variation in the eccentricity, as a function of the initial conditions of the object and of its area-to-mass ratio. The period of the variations of the eccentricity and inclination due to such resonances is estimated using classical formulas. A classification based on the strength of the SRP resonances is provided. The estimates presented in the paper are validated using numerical tools, including the use of Fast Lyapunov Indicators to draw phase portraits and bifurcation diagrams. Many FLI maps depicting the location and overlapping of SRP resonances are presented. The results from this paper suggest that SRP resonances could be modeled in the context of either the Extended Fundamental Model by Breiter (1999) or the Second Fundamental Model by Henrard and Lemaitre (1983).

Balancing the effects of solar radiation pressure on the orbital elements of a spacecraft using Lorentz force

In this work, orbits of Lorentz spacecrafts and satellites are investigated under the perturbation of solar radiation pressure. An attempt is made to control the perturbation of the solar radiation pressure using the effect of Lorentz force that affects an electrically charged spacecraft. The charge per unit mass is the controlling parameter in this process. The redial, transverse and normal components of the mentioned forces are constructed. The Lagrange planetary equations for perturbations in the Keplerian orbital elements are formulated. The formula describing the charge per unit mass, as function of the physical parameter of the problem as well as the orbital elements, were derived. The effects of the combined forces are analytically and numerically studied.

Performance analysis of impulsive station-keeping strategies for cis-lunar orbits with the ephemeris model

Future long-term lunar missions, such as cis-lunar space stations and communication/navigation constellations, have been proposed by different space agencies. For such long-term missions, reliable station-keeping strategies are of great importance to counteract unfavourable effects of perturbations, navigation errors, etc. In this study, representative cis-lunar orbits with favourable characteristics, including near rectilinear halo orbits (NRHOs), distant retrograde orbits (DROs), and halo orbits, are considered as nominal orbits of long-term lunar missions for station-keeping analysis. Both the target point method and the discrete linear quadrant regulator (DLQR) control are applied to these nominal orbits in the ephemeris model. Under some practical constraints caused by the navigation and orbital control systems, Monte-Carlo simulations are carried out to evaluate performances of the station-keeping strategies. Then, effects of solar radiation pressure (SRP) and nonspherical lunar gravity on the station-keeping performances are demonstrated by Monte-Carlo simulations with low-fidelity nominal orbits constructed in ephemeris models without SRP or nonspherical lunar gravity. Finally, comparisons between different impulse intervals are made to find the balance between the station-keeping cost and position deviation. It is found that the stability index of the nominal orbit has no direct effect on the station-keeping cost, but plays an important role in the selection of the impulse interval. The DROs and NRHOs allow a much longer impulse interval than the unstable halo orbits. The results can provide useful references for selections of the nominal orbit and station-keeping strategy in future long-term lunar missions.

Evolution of the dust trail of comet 17P/Holmes

ABSTRACT The massive outburst of the comet 17P/Holmes in 2007 October is the largest known outburst by a comet thus far. We present a new comprehensive model describing the evolution of the dust trail produced in this phenomenon. The model comprises of multiparticle Monte Carlo simulation including the solar radiation pressure effects, gravitational disturbance caused by Venus, Earth and Moon, Mars, Jupiter and Saturn, and gravitational interaction of the dust particles with the parent comet itself. Good accuracy of computations is achieved by its implementation in Orekit, which executes Dormad-Prince numerical integration methods with higher precision. We demonstrate performance of the model by simulating particle populations with sizes from 0.001 to 1 mm with corresponding spherically symmetric ejection speed distribution, and towards the Sun outburst modelling. The model is supplemented with and validated against the observations of the dust trail in common nodes for 0.5 and 1 revolutions. In all cases, the predicted trail position showed a good match to the observations. Additionally, the hourglass pattern of the trail was observed for the first time within this work. By using variations of the outburst model in our simulations, we determine that the assumption of the spherical symmetry of the ejected particles leads to the scenario compatible with the observed hourglass pattern. Using these data, we make predictions for the two-revolution dust trail behaviour near the outburst point that should be detectable by using ground-based telescopes in 2022.

A Hybrid ECOM Model for Solar Radiation Pressure Effect on GPS Reference Orbit Derived by Orbit Fitting Technique

A hybrid ECOM (Empirical CODE Orbit Model) solar radiation pressure (SRP) model, which is termed ECOMC in this work, is proposed for global navigation satellite system (GNSS) orbit modeling. The ECOMC is mainly parameterized by both ECOM1 and ECOM2 models. The GNSS orbit mainly serves as a reference datum not only for its ranging measurement but also for the so-called precise point positioning (PPP) technique. Compared to a complex procedure of orbit determination with real tracking data, the so-called orbit fitting technique simply uses satellite positions from GNSS ephemeris as pseudo-observations to estimate the initial state vector and SRP parameters. The accuracy of the reference orbit is mainly dominated by the SRP, which is usually handled by either ECOM1 or ECOM2. However, the reference orbit derived by ECOM1 produces periodic variations on orbit differences with respect to International GNSS Service (IGS) final orbit for GPS IIR satellites. Such periodic variations are removed from a reference orbit formed using the ECOM2 model, which, however, yields large cross-track orbit errors for the IIR and IIF satellites. Such large errors are attributed to the fact that the ECOM2 intrinsically lacks 1 cycle per revolution (CPR) terms, which stabilize the estimations of the even-order CPR terms in the satellite-Sun direction when the orbit fitting is used. In comparison, a reference orbit constructed with the ECOMC model is free of both the periodic variations from the ECOM1 and the large cross-track orbit errors from the ECOM2. The above improvements from the ECOMC are associated with (1) the even CPR terms removing the periodic variations and (2) the 1 CPR terms compensating for the force mismodeling at ∆u = 90° and 270°, where the ∆u is the argument of the latitude of the satellite with respect to the Sun. The parameter correlation analysis also presents that the direct SRP estimation is sensitive to the 1 and 2 CPR terms in the ECOMC case. In addition, the root-mean-square (RMS) of orbit difference with respect to IGS orbit is improved by ~40%, ~10%, and ~50% in the radial, along-track, and cross-track directions, respectively, when the SRP model is changed from the ECOM2 to the ECOMC. The orbit accuracy is assessed through orbit overlaps at day boundaries. The accuracy improvements of the ECOMC-derived orbit over the ECOM2-derived orbit in the radial, along-track, and cross-track directions are 13.2%, 14.8%, and 42.6% for the IIF satellites and 7.4%, 7.7%, and 35.0% for the IIR satellites. The impact of the reference orbit using the three models on the PPP is assessed. The positioning accuracy derived from the ECOMC is better than that derived from the ECOM1 and ECOM2 by approximately 13% and 20%, respectively. This work may serve as a reference for forming the GNSS reference orbit using the orbit fitting technique with the ECOMC SRP model.

ON THE EFFECTS OF SOLAR RADIATION PRESSURE ON THE DEVIATION OF ASTEROIDS

In this work, we study the effects of solar radiation pressure (SRP) on the problem of changing the orbit of an asteroid to support planetary defense, scientific research, or exploitation of materials. This alternative considers a tethered reflective balloon (or a set of reflective balloons) attached to the asteroid, with a high area-to-mass ratio, to use the SRP to deflect a potentially hazardous asteroid (PHA) or to approximate the target asteroid to Earth. The tether is assumed to be inextensible and massless, and the motion is described only in the orbital plane of the asteroid around the Sun. The model is then used to study the effects that the tether length, the reflectivity coefficient, and the area-to-mass ratio have on the deviation of the trajectory of the asteroid.

Effects of solar radiation pressure on asteroid surface hopping transfers for high area/mass ratio rovers

The high area/mass ratio hopping rovers have potential applications in future asteroid surface exploration. This paper systematically investigates the effects of solar radiation pressure (SRP) on ballistic surface hopping transfers for the asteroid 101955 Bennu. Effects of SRP on the traveled distance and the trajectory design of hopping transfers are analyzed and summarized. The simulation results indicate that it is necessary to take SRP into account to ensure the success of hopping transfers and the proper use of SRP can help design the trajectories of hopping transfers with low initial impulses and short transfer times. It also reveals the potential possibility in using SRP to control the post-hopping transfers with specific control policies in the future surface exploration of asteroids.

Dependencies of Mantle Shock Heating in Pairwise Accretion

Abstract The final assembly of planets involves mutual collisions of large similar-sized protoplanets (“giant impacts”), setting the stage for modern geologic and atmospheric processes. However, thermodynamic consequences of impacts in diverse (exo)planetary systems/models are poorly understood. Impact velocity in “self-stirred” systems is proportional to the mass of the colliding bodies (v imp ∝ M 1/3), providing a predictable transition to supersonic collisions in roughly Mars-sized bodies. In contrast, nearby larger planets, or migrating gas giants, stir impact velocities, producing supersonic collisions between smaller protoplanets and shifting outcomes to disruption and nonaccretion. Our particle hydrocode simulations suggest that thermodynamic processing can be enhanced in merging collisions more common to calmer dynamical systems due to post-impact processes that scale with the mass of the accreting remnant. Thus, impact heating can involve some contribution from energy scaling, a departure from pure velocity-scaling in cratering scenarios. Consequently, planetary thermal history depends intimately on the initial mass distribution assumptions and dynamical conditions of formation scenarios. In even the gentlest pairwise accretions, sufficiently large bodies feature debris fields dominated by melt and vapor. This likely plays a critical role in the observed diversity of exoplanet systems and certain debris disks. Furthermore, we suggest solar system formation models that involve self-stirred dynamics or only one to a few giant impacts between larger-than-Mars-sized bodies (e.g., “pebble accretion”) are more congruent with the “missing mantle problem” for the main belt, as we demonstrate debris would be predominantly vapor and thus less efficiently retained due to solar radiation pressure effects.

Diagnostic Simulations of the Lunar Sodium Tail and Bright Spot

AbstractNumerical simulations of the lunar sodium tail and its bright sodium spot are presented. As an attempt to do reverse engineering to understand the lunar sodium exosphere, we simulated velocity distributions of the sodium tail and its bright spot that emerges in the night sky around new Moon phases. In this work, three physical sodium sources (i.e., photon‐stimulated desorption [PSD], solar‐wind ion sputtering [SIS], meteor impact vaporization [MIV]), the dust anisotropy effect reported by Lunar Atmosphere and Dust Environment Explorer (LADEE), three gravitational sources (i.e., the Moon, the Earth, and the Sun), and variable solar radiation pressure effects are considered. We simulated velocity distributions of the lunar bright spot considering different source contribution ratios and their temperatures in order to find the best initial parameters which can account for the important observed recessional velocity of 12.4 km/s by Mierkiewicz et al. (2006, https://doi.org/10.1029/2006GL027650). We found that the upper limits of Maxwellian temperatures of 1,800 K for the PSD and 2,500 K for the MIV and that the best contribution ratio of the three major sodium sources (i.e., PSD: SIS: MIV) is found at the case of 2: 1: 3 (i.e., MIV dominant). Based on the previous brightness observations of the bright spot, the total production rate of the lunar sodium is estimated to usually vary between 0.4 and 1.3 × 1022/s. We introduce an interesting event in the lunar sodium tail, the Sodium Ring phenomena, which can occur transiently during the total solar eclipse due to the umbra and penumbra effects of the Earth.

Controlling the Perturbations of Solar Radiation Pressure on the Lorentz Spacecraft

The aim of the present paper is to analyze the viability of using Lorentz Force (LF) acting on a charged spacecraft to neutralize the effects of Solar Radiation Pressure (SRP) on the longitude of the ascending node and the argument of perigee of the spacecraft’s orbit. In this setting, the Gauss planetary equations for LF and SRP are presented and averaged over the true anomaly. The averaged variations for the longitude of the ascending node (h) and the argument of perigee (g) are invariant under the symmetry (i,g)⟶(−i,−g) due to Lorentz Force. The sum of change rates due to both perturbing forces of LF and SRP is assigned by zero to estimate the charge amount to balance the variation for the argument of perigee and longitude of ascending. Numerical investigations have been developed to show the evolution of the charge quantity for different orbital parameters at both Low Earth and Geosynchronous Orbits.

Adopting the empirical CODE orbit model to Galileo satellites

In 2012 the Center for Orbit Determination in Europe (CODE) joined the Multi-GNSS-EXtension project (MGEX) of the International GNSS Service (IGS). Since the end of 2013 the CODE MGEX contributions were based on combined solutions of five already established and emerging GNSS: GPS, GLONASS, Galileo, BeiDou and QZSS. This undertaking was made possible thanks to the continuous development of new models and approaches and their introduction in our processing schemes in order to ensure the delivery of products of the highest quality.The European Galileo system with a total number of active satellites reaching the level of a nominal constellation is currently complete. Because of their relatively high area-to-mass ratio the Galileo spacecraft are more sensitive to non-gravitational forces than other GNSS satellites. The introduction of the extended empirical CODE orbit model (ECOM2) to the CODE MGEX solutions in early 2015 resulted in a significant improvement of the Galileo products. The use of the Galileo satellites metadata, which were made publicly available in the course of 2016 and 2017, has further enhanced the quality of the produced solutions. However, they still show significant degradations during eclipse seasons in particular for long-arc solutions (e.g., over three days), which are similarly observed in solutions of other IGS MGEX analysis centers to different extents. In particular this is reflected in elevated orbit misclosures, deterioration of the estimated satellite clock corrections and excessive satellite laser ranging (SLR) residuals during these periods. Since the ECOM2 parameters are designed to absorb the effect of solar radiation pressure, they are switched off during eclipses. Hence, there is no empirical force parameter left that can absorb any unmodelled perturbations (e.g., due to thermal radiation (TR)) during an eclipse period.In this study we take advantage of the satellites’ metadata to address the Galileo TR-induced accelerations and, therefore, to advance our orbit model further. By adjusting existing and introducing additional empirical parameters, as well as adopting a priori accelerations to account for unmodelled perturbations we achieve a significant improvement of our solutions. In particular, the use of a once-per-revolution sine term in the ECOM E3 direction (satellite-Sun), activation of the constant term in the ECOM E2 direction (along the solar panels) during the Earth’s shadow transitions as well as the use of a priori acceleration in the body-fixed +X direction substantially improve our solutions. The introduced modifications to the orbit model allow for an efficient adjustment of satellite velocity along the orbit that is necessary due to the apparent presence of unmodelled thermal radiation. The refinements lead to a substantial reduction of orbit misclosures and improvement of the radial orbital component accuracy during eclipse seasons up to 14% w.r.t. the solutions using ECOM2.

Frozen Orbits Construction for a Lunar Solar Sail

Frozen orbit is an attractive option for orbital design owing to its characteristics (its argument of pericenter and eccentricity are kept constant on an average). Solar sails are attractive solutions for massive and expensive missions. However, the solar radiation pressure effect represents an additional force on the solar sail that may greatly affect its orbital behavior in the long run. Thus, this force must be included as a perturbation force in the dynamical model for more accuracy. This study shows the calculations of initial conditions for a lunar solar sail frozen orbit. The disturbing function of the problem was developed to include the lunar gravitational field that is characterized by uneven mass distribution, third body perturbation, and the effect of solar radiation. An averaging technique was used to reduce the dynamical problem to a long period system. Lagrange planetary equations were utilized to formulate the rate of change of the argument of pericenter and eccentricity. Using the reduced system, frozen orbits for the Moon sail orbiter were constructed. The resulting frozen orbits are shown by two 3Dsurface (semimajor, eccentricity, inclination) figures. To simplify the analysis, we showed inclination–eccentricity contours for different values of semi-major axis, argument of pericenter, and values of sail lightness number.

On the stabilizing effect of Solar Radiation Pressure in the Earth-Moon system

Solar sails change the natural dynamics of systems: Trajectories that are driven by gravitational forces can be displaced and changed because of the effect of Solar Radiation Pressure (SRP). Moreover, if the lightness number of the sail is large enough, the instability of certain orbits can be diminished and even removed. In this paper we modify two models for the motion of a probe in the Earth-Moon system that include the effect of Sun’s gravity to take also into account the effect of SRP. These models, the Bicircular Problem (BCP) and the Quasi-Bicircular Problem (QBCP), are periodic perturbations of the Earth-Moon Restricted Three Body Problem (RTBP). The models are modified to consider the effect of the SRP upon a solar sail. We provide examples of periodic orbits that are stabilized (or made less unstable) due to the effect of SRP.

Simulation of long-term rotational dynamics of large space debris: A TOPEX/Poseidon case study

Accurate knowledge of the rotational dynamics of a large space debris is crucial for space situational awareness (SSA), whether it be for accurate orbital predictions needed for satellite conjunction analyses or for the success of an eventual active debris removal mission charged with stabilization, capture and removal of debris from orbit. In this light, the attitude dynamics of an inoperative satellite of great interest to the space debris community, the joint French and American spacecraft TOPEX/Poseidon, is explored. A comparison of simulation results with observations obtained from high-frequency satellite range measurements is made, showing that the spacecraft is currently spinning about its minor principal axis in a stable manner. Predictions of the evolution of its attitude motion to 2030 are presented, emphasizing the uncertainty on those estimates due to internal energy dissipation, which could cause a change of its spin state in the future. The effect of solar radiation pressure and the eddy-current torque are investigated in detail, and insights into some of the satellite’s missing properties are provided. These results are obtained using a novel, open-source, coupled orbit-attitude propagation software, the Debris SPin/Orbit Simulation Environment (D-SPOSE), whose primary goal is the study of the long-term evolution of the attitude dynamics of large space debris.

Sun-synchronous solar reflector orbits designed to warm Mars

Although the Martian environment is very cold (averaging about $-60^{\circ }$ C), highly oxidizing and desiccated, several studies have proposed human colonization of Mars. To carry out this ambitious goal, terraforming schemes have been designed to warm Mars and implant Earth-like life. Mars climate engineering includes the use of orbiting solar reflectors to increase the total solar insolation. In this study, Sun-synchronous solar reflectors orbits with inclination equal or less than $90^{\circ }$ with respect to the orbital plane of Mars are considered to intervene with the Mars’ climate system. With different inclinations, a family of Sun-synchronous solar reflectors orbits distributes azimuthally the energy intercepted by the reflector. The two-body problem is considered, and the Gauss’s form of the variational equations is used to find the conditions to achieve a Sun-synchronous frozen orbit with inclination equal or less than $90^{\circ }$ , taking into account the effects of solar radiation pressure for a perfectly reflecting space mirror and Mars’ $J_{2}$ oblateness perturbation.

On merging of resonant periodic orbits 4:3; 3:2 and 2:1 in Sun-Jupiter photo gravitational restricted three-body problem

We explore the merging of resonant periodic orbits in the frame work of planar circular restricted three body problem with the help of Poincaré surface of section. We have studied the effect of solar radiation pressure on 4:3, 3:2 and 2:1 periodic orbits. It is found that radiation pressure helps in merging these orbits (4:3 and 3.2 into 1:1 resonance and 2:1 into 1:1 resonance). At the time of merging these orbits become near-circular. The period and size of these orbits reduce with the increase in radiation pressure. Â

Linear Models for Spacecraft Relative Motion Perturbed by Solar Radiation Pressure

Many scientific applications require the implementation of spacecraft formation-flying around Earth and other celestial bodies. The control of these formations calls for simple relative dynamics models able to accurately and efficiently incorporate secular and long-periodic effects of relevant perturbations. This paper presents novel linear analytical models of the effect of solar radiation pressure (SRP) on the relative motion of two spacecraft in arbitrary eccentric orbit for two state definitions based on relative orbital elements. The new models are valid both around Earth and around other celestial bodies such as near-Earth asteroids. The linear models are derived by augmenting the state with force model parameters and Taylor expanding the differential equations of relative motion, including the secular and long-periodic effects of SRP. New state transition matrices including and SRP are formalized and validated through comparison with a high-fidelity orbit propagator around Earth and around a near-Earth asteroid. In addition, the dominant trends caused by SRP on the relative orbital elements are captured in closed-form. The new models have accuracy in the range of meter to few tens of meters in all orbit scenarios considered and can be leveraged for formation guidance, control, and design.