Explicit VG Guidance Algorithm for a Solid Powered Closed Loop Guidance Mission

Optimal explicit guidance for three-dimensional launch trajectory

Ascent trajectory optimization and explicit guidance problems for a satellite launch vehicle with yaw maneuver in a 3-dimension are considered. The trajectory optimization problem with boundary conditions is formulated as a nonlinear programming problem by parameterizing the inertial pitch and yaw attitude control variables, and is solved by using the SQP algorithm. The flight constraints such as gravity-turn and range safety conditions are imposed. An explicit inertial guidance algorithm in the exoatmospheric phase is also presented. The guidance algorithm provides steering command and time-to-go value directly using the current states of the vehicle and the desired orbit insertion conditions. The liquid propelled Delta 2910 launch vehicle is used as a numerical model.

Aims. We investigate the long-term evolution of inclined test particles representing a small Earth-like body with negligible gravitational effects (hereafter called massless test-planets) in the restricted three-body problem, and consisting of a star, a gas giant, and a massless test-planet. The test-planet is initially on a circular orbit and moves around the star at distances closer than the gas giant. The aim is to show the influences of the eccentricity and the mass of the gas giant on the dynamics, for various inclinations of the test-planet, and to investigate in more detail the Kozai mechanism in the elliptic problem.Methods. We performed a parametric study, integrating the orbital evolution of test particles whose initial conditions were distributed on the semi-major axis – inclination plane. The gas giant’s initial eccentricity was varied. For the calculations, we used the Lie integration method and in some cases the Bulirsch-Stoer algorithm. To analyze the results, the maximum eccentricity and the Lyapunov characteristic indicator were used. All integrations were performed for 105 periods of the gas giant.Results. Our calculations show that inclined massless test-planets can be in stable configurations with gas giants on either circular or elliptic orbits. The higher the eccentricity of the gas giant, the smaller the possible range in semi-major axis for the test-planet. For gas giants on circular orbits, our results illustrate the well-known results associated with the Kozai mechanism, which do not allow stable orbits above a critical inclination of approximately 40°. For gas giants on eccentric orbits, the dynamics is quite similar, and the massless companion exhibits limited variations in eccentricity. In addition, we identify a region around 35° consisting of long-time stable, low eccentric orbits. We show that these results are also valid for Earth-mass companions, therefore they can be applied to extrasolar systems: for instance, the extrasolar planetary system HD 154345 can possess a 35° degree inclined, nearly circular, Earth-mass companion in the habitable zone.

The motion of two planets around a Sun-like star under the combined effects of mutual interaction and tidal dissipation is investigated. The secular behaviour of the system is analyzed using two different approaches. First, we solve the exact equations of motion through the numerical simulation of the system evolution. In addition to the orbital decay and circularization, we show that the final configuration of the system is affected by the shrink of the inner orbit. Our second approach consist in the analysis of the stationary solutions of mean equations of motion based on a Hamiltonian formalism. We consider the case of a hot super-Earth planet with a more massive outer companion. As a real example, the CoRoT-7 system is analyzed solving the exact and mean equations of motion. The star-planet tidal interaction produces orbital decay and circularization of the orbit of CoRoT-7b. In addition, the long-term tidal evolution is such that the eccentricity of CoRoT-7c is also circularized and a pair of final circular orbits is obtained. A curve in the space of eccentricities can be constructed through the computation of stationary solutions of mean equations including dissipation. The application to CoRoT-7 system shows that the stationary curve agrees with the result of numerical simulations of exact equations. A similar investigation performed in a super-Earth-Jupiter two-planet system shows that the doubly circular state is accelerated when there is a significant orbital migration of the inner planet, in comparison with previous results were migration is neglected.

This work is based on our published letter, where we developed the analytical expression of the coordinate time in terms of the eccentric anomaly at the second post-Newtonian (PN) order in general relativity (GR) for a compact binary system moving on eccentric orbits. The aim of this paper is to provide more details about the performed calculations and to produce other new results. More specifically, we focus on deriving the analytical expression of the coordinate time at the second PN order for circular orbits, and then discuss two astrophysical applications involving binary neutron star and black hole systems.

M dwarfs are prime targets in the search for exoplanets due to their prevalence and the enhanced radial velocity (RV) detectability of low-mass planets. Recent advancements in instrumentation have extended RV observations from the optical to the near-infrared (nIR) domain, enabling more effective study of M dwarfs, which frequently host rocky planets. The nIR range offers increased RV sensitivity and potentially reduced stellar activity signals, making it particularly well suited for these stars. We analyzed spectropolarimetric data of the M4.5V star GJ,4274, acquired using the nIR spectropolarimeter SPIRou, to characterize its stellar activity and to search for planetary signals. We additionally examined TESS photometric data to search for transits corresponding to the potential signals in the RV data. In this study, we employed a line-by-line framework to derive and analyze the RV signal of GJ,4274 acquired with SPIRou. From the SPIRou spectra, we also derived and analyzed the longitudinal large scale magnetic field, B_ and the surface temperature variations, dTemp. We combined the SPIRou RV data with RV measurements from CARMENES, to model possible planetary signals with both circular and eccentric orbits. We modeled the activity with a quasiperiodic Gaussian process. We also performed injection-recovery tests on the photometric TESS data to assess transit detectability. We report the discovery of two exoplanets around the nearby M dwarf star GJ,4274. Both planets are in a circular orbit with respective periods of P_b = 1.6339 ± 0.0001 and P_c = 69.6^ d, the latter located beyond the habitable zone. From their RV semi-amplitude signals (K_b = 5.10^ m/s and K_c = 4.11±0.64,m/s), we derive minimum masses of m_b i M_⊕ and m_c i = 8.4 ± 1.3, M_⊕, respectively. Photometric observations from TESS rule out most transit scenarios, including for the inner planet, yielding a maximum inclination of i_b łeq 83^ ̧irc for planet b. We do not detect RV variations related to stellar magnetic activity in the SPIRou time series, despite a prominent large-scale magnetic field with an amplitude of up to ±206^ G. From the activity indicators, we derive a rotation period for the star of $4.600^ $,d. The two reported planets belong to the sub-Neptune class. GJ 4274 b has one of the shortest orbital periods among planets orbiting < 0.2 M_⊙ M dwarfs within 15 pc, while GJ 4274 c lies in a sparsely populated region of the mass–period diagram. Their discovery adds to the census of nearby planetary systems and provides promising targets for future surveys.

Accretion of ornamental equatorial ridges on Pan, Atlas and Daphnis

The general energy requirement measured in terms of a characteristic velocity for the ascent from an initial circular parking orbit to any outer co-planar elliptic orbit by a two-instantaneous-impulse, cotangential transfer is determined as a function of the location of the second impulse on the final orbit. Of the infinity of such transfers to any particular final orbit, it is demonstrated generally that injection into the final orbit apogee is the most economical whereas injection at final orbit perigee the least economical. For the special case of final orbit perigee located on the initial parking orbit, the most economical transfer requires a single impulse applied at perigee.

PurposeHill equations have definite limitation in the design of multiple spacecraft formation flying in eccentric orbits. To solve the problem, the design method of spacecraft formation flying in a circular reference orbit based on Hill equation can be generalized and applied to spacecraft formation flying in eccentric orbits.Design/methodology/approachIn this paper, T‐H equation is expressed as the explicit function form of reference orbit true anomaly, and the state transition matrix of relative motion of spacecraft formation flying in eccentric orbits is derived. According to the requirement that relative dynamics equation of spacecraft formation flying in eccentric orbits has periodicity solution, the paper theoretically gives the initial condition needed by the long‐term close‐distance spacecraft formation flying including the relationship between relative position and relative velocity. Without perturbation the spacecraft formation, which satisfies the initial periodicity restriction, can keep long‐term close‐distance flying without the need of active control.FindingsBased on the theoretical analysis, some numerical simulations are carried out. The results demonstrate that each spacecraft in eccentric orbits can run in a periodic motion surrounding the center spacecraft under some conditions. And spacecraft formation reconfiguration is implementing according to missions.Originality/valueCombined with the periodicity restriction primary condition a new method about spacecraft formation reconfiguration is put forward. The method given by this paper can be applied to eccentric orbits of arbitrary eccentricity, and provides theoretical reference for orbit design of spacecraft formation flying in eccentric orbits.

We investigate the effect of a planet on an eccentric orbit on a two dimensional low mass gaseous disk. At a planet eccentricity above the planet's Hill radius divided by its semi-major axis, we find that the disk morphology differs from that exhibited by a disk containing a planet in a circular orbit. An eccentric gap is created with eccentricity that can exceed the planet's eccentricity and precesses with respect to the planet's orbit. We find that a more massive planet is required to open a gap when the planet is on an eccentric orbit. We attribute this behavior to spiral density waves excited at corotation resonances that increase the disk's eccentricity and exert a torque opposite in sign to that exerted by the Lindblad resonances. The reduced torque makes it more difficult for waves driven by the planet to overcome viscous inflow in the disk. Spectral energy distributions of transitional disks may reveal the presence of an eccentric planet if they are matched by an inner edge comprising a range of temperatures set by the semi-major axis and eccentricity of the hole.

This paper presents algorithms for the near-distance rendezvous of on-orbit-servicing spacecraft when approaching, departing and flying around a target vehicle in a circular orbit. These algorithms are based on the closed-form solution of linear Clohessy-Wiltshire equations and adapt the glideslope guidance used in the past for rendezvous and proximity operations of the space shuttle. By using the relationship of either power functions or piece linear functions between distance and speed, the multipulse glideslope approach and departure algorithms of the chaser can be applied at any time and in any direction in space for decelerating when approaching a target or a nearby location and accelerating when departing. The fly-around algorithm enables the chaser to circumnavigate a target in any plane and at any specified time. To save the pulse number for all algorithms, a way to solve the maximum allowable transfer interval between one pulse and the next one is presented, with consideration be given to the constraints about allowable safe velocity and allowable guidance error. Finally, several scenarios are simulated to illustrate these guidance algorithms.

Meta-reinforcement learning for adaptive spacecraft guidance during finite-thrust rendezvous missions

We analyse a tilt instability of the orbit of an outer planet in a two-planet circumbinary system that we recently reported. The binary is on an eccentric orbit and the inner circumbinary planet is on a circular polar orbit that causes the binary to undergo apsidal precession. The outer circumbinary planet is initially on a circular or eccentric orbit that is coplanar with respect to the binary. We apply a Hamiltonian in quadrupole order of the binary potential to show that the tilt instability is the result of a secular resonance in which the apsidal precession rate of the binary matches the nodal precession rate of the outer planet. A resonance is possible because the polar inner planet causes the apsidal precession of the binary to be retrograde. The outer planet periodically undergoes large tilt oscillations for which we analytically determine the initial evolution and maximum inclination. Following a typically relatively short adjustment phase, the tilt grows exponentially in time at a characteristic rate that is of order the absolute value of the binary apsidal precession rate. The analytic results agree well with numerical simulations. This instability is analogous to the Kozai–Lidov instability, but applied to a circumbinary object. The instability fails to operate if the binary mass ratio is too extreme. The instability occurs even if the outer planet is instead an object of stellar mass and involves tilt oscillations of the inner binary.

Eccentricities and the stability of closely-spaced five-planet systems

The nearly circular (mean eccentricity [Formula: see text]) and coplanar (mean mutual inclination [Formula: see text]) orbits of the solar system planets motivated Kant and Laplace to hypothesize that planets are formed in disks, which has developed into the widely accepted theory of planet formation. The first several hundred extrasolar planets (mostly Jovian) discovered using the radial velocity (RV) technique are commonly on eccentric orbits ([Formula: see text]). This raises a fundamental question: Are the solar system and its formation special? The Kepler mission has found thousands of transiting planets dominated by sub-Neptunes, but most of their orbital eccentricities remain unknown. By using the precise spectroscopic host star parameters from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) observations, we measure the eccentricity distributions for a large (698) and homogeneous Kepler planet sample with transit duration statistics. Nearly half of the planets are in systems with single transiting planets (singles), whereas the other half are multiple transiting planets (multiples). We find an eccentricity dichotomy: on average, Kepler singles are on eccentric orbits with [Formula: see text] 0.3, whereas the multiples are on nearly circular [Formula: see text] and coplanar [Formula: see text] degree) orbits similar to those of the solar system planets. Our results are consistent with previous studies of smaller samples and individual systems. We also show that Kepler multiples and solar system objects follow a common relation [[Formula: see text](1-2)[Formula: see text]] between mean eccentricities and mutual inclinations. The prevalence of circular orbits and the common relation may imply that the solar system is not so atypical in the galaxy after all.