Global searches of frozen orbits around an oblate Earth-like planet

A frozen orbit is beneficial for observation owing to its stationary apsidal line.The traditional gravitational field model of frozen orbits only considers the main zonal harmonic terms J_(2) and limited high-order terms,which cannot meet the stringent demands of all missions.In this study,the gravitational field is expanded to J_(15) terms and the Hamiltonian canonical form described by the Delaunay variables is used.The zonal harmonic coefficients of the Earth are chosen as the sample.Short-periodic terms are eliminated based on the Hori-Lie transformation.An algorithm is developed to solve all equilibrium points of the Hamiltonian function.A stable frozen orbit with an argument of perigee that equals neither 90°nor 270°is first reported in this paper.The local stability and topology of the equilibrium points are obtained from their eigenvalues.The bifurcations of the equilibrium points are presented by drawing their global long-term evolution of frozen orbits and their orbital periods.The relationship between the terms of the gravitational field and number of frozen points is addressed to explain why only limited frozen orbits are found in the low-order term case.The analytical results can be applied to other Earth-like planets and asteroids.

Artificial Sun synchronous frozen orbit control scheme design based on J_2 perturbation

Sun synchronous orbit and frozen orbit formed due to J 2 perturbation have very strict constraints on orbital parameters,which have restricted the application a lot.In this paper,several control strategies were illustrated to realize Sun synchronous frozen orbit with arbitrary orbital elements using continuous low-thrust.Firstly,according to mean element method,the averaged rate of change of the orbital elements,originating from disturbing constant accelerations over one orbital period,was derived from Gauss＇ variation of parameters equations.Then,we proposed that binormal acceleration could be used to realize Sun synchronous orbit,and radial or transverse acceleration could be adopted to eliminate the rotation of the argument of the perigee.Finally,amending methods on the control strategies mentioned above were presented to eliminate the residual secular growth.Simulation results showed that the control strategies illustrated in this paper could realize Sun synchronous frozen orbit with arbitrary orbital elements,and can save much more energy than the schemes presented in previous studies,and have no side effect on other orbital parameters＇ secular motion.

Lunar orbits for telecommunication and navigation services

Orbits that are frozen in an averaged model,including the effect of a disturbing body laying on the equatorial plane of the primary body and the influence of the oblateness of the primary body,have been applied to probes orbiting the Moon.In this scenario,the main disturbing body is represented by the Earth,which is characterized by a certain obliquity with respect to the equatorial plane of the Moon.As a consequence of this,and of the perturbing effects that are not included in the averaged model,such solutions are not perfectly frozen.However,the orbit eccentricity,inclination,and argument of pericenter present limited variations and can be set to guarantee the fulfillment of requirements useful for lunar telecommunication missions and navigation services.Taking advantage of this,a practical case of a Moon-based mission was investigated to propose useful solutions for potential near-future applications.

Artificial frozen orbit control scheme based on J_2 perturbation

Since the inclination of frozen orbit with non-rotation of the perigee that occurs due to J2 perturbation must be equal to the critical inclination, this regulation has restricted the application of frozen orbit a lot. In this paper, we propose two control strategies to eliminate the secular growth of the argument of the perigee for orbits that are not at the critical inclination. One control strategy is using transverse continuous low-thrust, and the other is using both the transverse and the radial continuous low-thrusts. Fuel optimization in the second control strategy is addressed to make sure that the fuel consumption is the minimum. Both strategies have no effect on other orbital parameters’ secular motion. It is proved that the strategy with transverse control could save more energy than the one with radial control. Simulations show that the second control strategy could save 54.6% and 86% of energy, respectively, compared with the two methods presented in the references.

A new solar sail orbit

Solar sail is used to achieve a geocentric sun-synchronous frozen orbit.This kind of orbit combines the characteristics of both sun-synchronous orbits and frozen orbits.Furthermore,the impossible orbits for a typical spacecraft such as sun-synchronous orbits whose inclination is less than 90° are also possible for solar sail.To achieve a sun-synchronous frozen orbit,the characteristic acceleration of the sail is chosen properly.In addition,the attitude of the sail is adjusted to keep the sun-synchronous and frozen characteristics.The perturbations including atmosphere drag,third-body gravitational forces and shaded regions are discussed,where the atmosphere drag is cancelled by solar radiation pressure force,third-body gravitational forces have negligible effects on the orbit and the shaded region can be avoided by choosing the classical orbit elements of the sail.At last,a numerical example is employed to validate the sun-synchronous frozen characteristics of the sail.