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1.
We consider periodic halo orbits about artificial equilibrium points (AEP) near to the Lagrange points L 1 and L 2 in the circular restricted three body problem, where the third body is a low-thrust propulsion spacecraft in the Sun–Earth system. Although such halo orbits about artificial equilibrium points can be generated using a solar sail, there are points inside L 1 and beyond L 2 where a solar sail cannot be placed, so low-thrust, such as solar electric propulsion, is the only option to generate artificial halo orbits around points inaccessible to a solar sail. Analytical and numerical halo orbits for such low-thrust propulsion systems are obtained by using the Lindstedt Poincaré and differential corrector method respectively. Both the period and minimum amplitude of halo orbits about artificial equilibrium points inside L 1 decreases with an increase in low-thrust acceleration. The halo orbits about artificial equilibrium points beyond L 2 in contrast show an increase in period with an increase in low-thrust acceleration. However, the minimum amplitude first increases and then decreases after the thrust acceleration exceeds 0.415 mm/s2. Using a continuation method, we also find stable artificial halo orbits which can be sustained for long integration times and require a reasonably small low-thrust acceleration 0.0593 mm/s2.  相似文献   

2.
Near Earth Asteroids have a possibility of impacting the Earth and always represent a threat. This paper proposes a way of changing the orbit of the asteroid to avoid an impact. A solar sail evolving in an H-reversal trajectory is utilized for asteroid deflection. Firstly, the dynamics of the solar sail and the characteristics of the H-reversal trajectory are analyzed. Then, the attitude of the solar sail is optimized to guide the sail to impact the target asteroid along an H-reversal trajectory. The impact...  相似文献   

3.
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4.
Halo orbits for solar sails at artificial Sun–Earth L1 points are investigated by a third order approximate solution. Two families of halo orbits are explored as defined by the sail attitude. Case I: the sail normal is directed along the Sun-sail line. Case II: the sail normal is directed along the Sun–Earth line. In both cases the minimum amplitude of a halo orbit increases as the lightness number of the solar sail increases. The effect of the z-direction amplitude on x- or y-direction amplitude is also investigated and the results show that the effect is relatively small. In case I, the orbit period increases as the sail lightness number increases, while in case II, as the lightness number increases, the orbit period increases first and then decreases after the lightness number exceeds ~0.01.  相似文献   

5.
In this paper, families of Lyapunov and halo orbits are presented with a solar sail equipped with a reflectance control device in the Earth–Moon system. System dynamical model is established considering solar sail acceleration, and four solar sail steering laws and two initial Sun-sail configurations are introduced. The initial natural periodic orbits with suitable periods are firstly identified. Subsequently, families of solar sail Lyapunov and halo orbits around the \(L_{1}\) and \(L_{2}\) points are designed with fixed solar sail characteristic acceleration and varying reflectivity rate and pitching angle by the combination of the modified differential correction method and continuation approach. The linear stabilities of solar sail periodic orbits are investigated, and a nonlinear sliding model controller is designed for station keeping. In addition, orbit transfer between the same family of solar sail orbits is investigated preliminarily to showcase reflectance control device solar sail maneuver capability.  相似文献   

6.
Solar sails are a proposed form of spacecraft propulsion using large membrane mirrors to propel a satellite taking advantage of the solar radiation pressure. To model the dynamics of a solar sail we have considered the Earth–Sun Restricted Three Body Problem including the Solar radiation pressure (RTBPS). This model has a 2D surface of equilibrium points parametrised by the two angles that define the sail orientation. In this paper we study the non-linear dynamics close to an equilibrium point, with special interest in the bounded motion. We focus on the region of equilibria close to SL 1, a collinear equilibrium point that lies between the Earth and the Sun when the sail is perpendicular to the Sun–sail direction. For different fixed sail orientations we find families of planar, vertical and Halo-type orbits. We have also computed the centre manifold around different equilibria and used it to describe the quasi-periodic motion around them. We also show how the geometry of the phase space varies with the sail orientation. These kind of studies can be very useful for future mission applications.  相似文献   

7.
Results of numerical simulations of 'local-optimal' (or 'instantaneously optimal') trajectories of a space probe with a flat solar sail which moves from the circular Earth orbit to near-Sun regions are presented. We examine planar (ecliptic) solar sail transfer with gravity-assist flybys of Earth, Venus and Mercury. Several complex control modes of the sail tilt orientation angle for near-Sun orbits and for some 'falling onto the Sun' trajectories are investigated. The numerical simulations are used to examine the flight duration of some sail missions and to investigate the evolution of osculating elliptical orbits.  相似文献   

8.
This paper proposes the use of doubly-symmetric, eight-shaped orbits in the circular restricted three-body problem for continuous coverage of the high-latitude regions of the Earth. These orbits, for a range of amplitudes, spend a large fraction of their period above either pole of the Earth. It is shown that they complement Sun-synchronous polar and highly eccentric Molniya orbits, and present a possible alternative to low thrust pole-sitter orbits. Both natural and solar-sail displaced orbits are considered. Continuation methods are described and used to generate families of these orbits. Starting from ballistic orbits, other families are created either by increasing the sail lightness number, varying the period or changing the sail attitude. Some representative orbits are then chosen to demonstrate the visibility of high-latitude regions throughout the year. A stability analysis is also performed, revealing that the orbits are unstable: it is found that for particular orbits, a solar sail can reduce their instability. A preliminary design of a linear quadratic regulator is presented as a solution to stabilize the system by using the solar sail only. Finally, invariant manifolds are exploited to identify orbits that present the opportunity of a ballistic transfer directly from low Earth orbit.  相似文献   

9.
We present a detailed investigation of the dramatic changes that occur in the \(\mathcal {L}_1\) halo family when radiation pressure is introduced into the Sun–Earth circular restricted three-body problem (CRTBP). This photo-gravitational CRTBP can be used to model the motion of a solar sail orientated perpendicular to the Sun-line. The problem is then parameterized by the sail lightness number, the ratio of solar radiation pressure acceleration to solar gravitational acceleration. Using boundary-value problem numerical continuation methods and the AUTO software package (Doedel et al. in Int J Bifurc Chaos 1:493–520, 1991) the families can be fully mapped out as the parameter \(\beta \) is increased. Interestingly, the emergence of a branch point in the retrograde satellite family around the Earth at \(\beta \approx 0.0387\) acts to split the halo family into two new families. As radiation pressure is further increased one of these new families subsequently merges with another non-planar family at \(\beta \approx 0.289\) , resulting in a third new family. The linear stability of the families changes rapidly at low values of \(\beta \) , with several small regions of neutral stability appearing and disappearing. By using existing methods within AUTO to continue branch points and period-doubling bifurcations, and deriving a new boundary-value problem formulation to continue the folds and Krein collisions, we track bifurcations and changes in the linear stability of the families in the parameter \(\beta \) and provide a comprehensive overview of the halo family in the presence of radiation pressure. The results demonstrate that even at small values of \(\beta \) there is significant difference to the classical CRTBP, providing opportunity for novel solar sail trajectories. Further, we also find that the branch points between families in the solar sail CRTBP provide a simple means of generating certain families in the classical case.  相似文献   

10.
Is there an asteroid type or meteorite class that best exemplifies the materials that went into the Earth? Carbonaceous chondrites were once the objects of choice, and in the minds of many this choice is still valid. However, the origin of primitive chondritic meteorites is unclear. At the extremes they could either be fragments of very small parent bodies that never became hot enough to undergo geochemical modification other than mild lithification, or remnants of the uppermost layers of a body that had undergone a significant degree of internal differentiation, while the top layers remained cool due to radiative heat loss or loss of volatiles to space. This latter case is problematic if one considers these objects as precursors to the Earth since the timescale for the evolution of such a small body could be longer than the timescale for the accretion of the Earth. Large-scale circulation of materials in the primitive solar nebula could greatly increase the diversity of materials near 1 AU while also making the entire inner solar system both more homogeneous and much wetter than previously expected. The total mass of the nebula is an important, but poorly constrained factor controlling the growth of planetesimals. There is also a selection effect that dominates our sampling of the planetesimals that may have existed 4.5 billion years ago; namely, small fragile bodies are more likely to be lost from the system or ground down by collisions between small bodies, yet these are precisely those that may have dominated the population from which the Earth accreted. The composition of these aggregates could have played a very important role in the early chemical evolution of the Earth. In particular, the Earth may have been much wetter and richer in hydrocarbons and other reducing materials than previously suspected.  相似文献   

11.
The theory of optimal control is applied to obtain minimum-time trajectories for solar sail spacecraft for interplanetary missions. We consider the gravitational and solar radiation forces due to the Sun. The spacecraft is modelled as a flat sail of mass m and surface area A and is treated dynamically as a point mass. Coplanar circular orbits are assumed for the planets. We obtain optimal trajectories for several interrelated problem families and develop symmetry properties that can be used to simplify the solution-finding process. For the minimum-time planet rendezvous problem we identify different solution branches resulting in multiple solutions to the associated boundary value problem. We solve the optimal control problem via an indirect method using an efficient cascaded computational scheme. The global optimizer uses a technique called Adaptive Simulated Annealing. Newton and Quasi-Newton Methods perform the terminal fine tuning of the optimization parameters.  相似文献   

12.
Shymanchuk  D. V.  Shmyrov  A. S.  Shmyrov  V. A. 《Astronomy Letters》2021,47(10):710-719
Astronomy Letters - The controlled motion of a spacecraft with a solar sail in interplanetary space near the collinear libration points $$L_{1}$$ and $$L_{2}$$ of the Sun–Earth system is...  相似文献   

13.
To propel a spacecraft in the direction leaving the Sun, a magnetic sail (MagSail) blocks the hypersonic solar wind plasma flow by an artificial magnetic field. In order to simulate the interaction between the solar wind and the artificially deployed magnetic field produced around a magnetic sail spacecraft, a laboratory simulator was designed and constructed inside a space chamber. As a solar wind simulator, a high-power magnetoplasmadynamic arcjet is operated in a quasisteady mode of 0.8 ms duration. It can generate a simulated solar wind that is a high-speed (above 20 km/s), high-density (1018 m−3) hydrogen plasma plume of ∼0.7 m in diameter. A small coil (2 cm in diameter), which is to simulate a magnetic sail spacecraft and can obtain 1.9-T magnetic field strength at its center, was immersed inside the simulated solar wind. Using these devices, the formation of a magnetic cavity (∼8 cm in radius) was observed around the coil, which indicates successful simulation of the plasma flow of a MagSail in the laboratory.  相似文献   

14.
Previous studies of non-nuclear diversion of near Earth asteroids have largely ignored the use of pure kinetic energy impacts, partly due to apparent limits on impact speeds of 10-. Here, I will consider the use of a near-term solar sail to deliver an inert projectile onto a retrograde solar orbit, thus raising impact speeds to at least . Such high-energy orbits increase the energy liberated during impact by a factor of 40 or more, while reducing the required projectile mass by at least 95%. This considerable reduction in projectile mass allows kilometre-sized asteroids to be diverted with current launch vehicles, near-term technologies and at a cost comparable to a modest deep space mission.  相似文献   

15.
Abstract– We have measured the isotopic composition and fluence of solar‐wind nitrogen in a diamond‐like‐carbon collector from the Genesis B/C array. The B and C collector arrays on the Genesis spacecraft passively collected bulk solar wind for the entire collection period, and there is no need to correct data for instrumental fractionation during collection, unlike data from the Genesis “Concentrator.” This work validates isotopic measurements from the concentrator by Marty et al. (2010, 2011) ; nitrogen in the solar wind is depleted in 15N relative to nitrogen in the Earth’s atmosphere. Specifically, our array data yield values for 15N/14N of (2.17 ± 0.37) × 10?3 and (2.12 ± 0.34) × 10?3, depending on data‐reduction technique. This result contradicts preliminary results reported for previous measurements on B/C array materials by Pepin et al. (2009) , so the discrepancy between Marty et al. (2010, 2011) and Pepin et al. (2009) was not due to fractionation of solar wind by the concentrator. Our measured value of 15N/14N in the solar wind shows that the Sun, and by extension the solar nebula, lie at the low‐15N/14N end of the range of nitrogen isotopic compositions observed in the solar system. A global process (or combination of processes) must have operated in interstellar space and/or during the earliest stages of solar system formation to increase the 15N/14N ratio of the solar system solids. We also report a preliminary Genesis solar‐wind nitrogen fluence of (2.57 ± 0.42) × 1012 cm?2. This value is higher than that derived by backside profiling of a Genesis silicon collector ( Heber et al. 2011a ).  相似文献   

16.
Several methods of asteroid deflection have been proposed in literature and the gravitational tractor is a new method using gravitational coupling for near-Earth object orbit modification. One weak point of gravitational tractor is that the deflection capability is limited by the mass and propellant of the spacecraft. To enhance the deflection capability, formation flying solar sail gravitational tractor is proposed and its deflection capability is compared with that of a single solar sail gravitational tractor. The results show that the orbital deflection can be greatly increased by increasing the number of the sails. The formation flying solar sail gravitational tractor requires several sails to evolve on a small displaced orbit above the asteroid. Therefore, a proper control should be applied to guarantee that the gravitational tractor is stable and free of collisions. Two control strategies are investigated in this paper: a loose formation flying realized by a simple controller with only thrust modulation and a tight formation realized by the sliding-mode controller and equilibrium shaping method. The merits of the loose and tight formations are the simplicity and robustness of their controllers, respectively.  相似文献   

17.
Making use of the fact that, in the solar system, the angular momentum is carried predominantly by the planets while the mass is beared almost entirely by the Sun, an iterative scheme is devised to solve approximately the n-body contributions of the lunar orbit problem. The scheme envisages the Moon-Earth-Sun three-body subsystem as being nested in the grand Earth-Jupiter-Sun system. In the planetocentric representation, the orbital motion of the Sun about the solar system center of mass is transmitted to the third body via the second primary body in both the grand and nested three-body systems. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

18.
Abstract— Criteria for finding asteroid families (Zappala et al. 1995) are applied to a large (205,770 member) data set of asteroid orbital elements. The cases of the Eunomia and Themis families are considered as examples. This is combined with the cratering criteria for catastrophic disruption of small bodies in the solar system (Leliwa‐Kopystyński et al. 2008). We find that the Eunomia parent body itself was not catastrophically disrupted in the family‐generating impact event; after impact, the current body contains as much as 70% of its primordial mass. However, by contrast with Eunomia, the present mass of 24 Themis is only about 21% of that of its primordial body. Limits are placed on the sizes of the impactors in both examples, and for the case of Eunomia, the radius of the just sub‐critical crater (which may be present on 15 Eunomia) is predicted as <58 km.  相似文献   

19.
Several versions of a Mercury surface element, part of the ESA BepiColombo Mercury Cornerstone mission to be launched in 2009, have been studied. The major constraint on system design has been the need to maximise the useful system mass on the surface of Mercury. The absence of atmosphere on the planet forces the adoption of a purely propulsive descent and landing system. The need to maintain the shock level at landing below limits which are acceptable to the payload imposes the adoption of a precise guidance, navigation & control system, which allows a drastic reduction of the landing speed, and therefore the adoption of an airbag landing system. Surface mobility is an obvious requirement for the purpose of geochemical exploration, since selected rocks have a much higher scientific yield than the average regolith. Geophysical investigations require that thermal, accelerometric, and densitometric probes be brought in contact with subsurface regions, to a depth of several metres. Magnetometric measurements may need deployment of sensors to some distance from the bulk of the lander body. The thermal environment on the surface of Mercury is extreme, even in the polar regions that will be targeted by the BepiColombo lander, while the solar flux rises seasonally to 10 times the one experienced in Earth orbit. The need to provide a low-temperature heat sink to sensors is particularly critical, if these are installed on a small-size, small-mass mobile deployment device. A consequence of the landing in a polar region will be the extremely variable lighting conditions, with extended portions of the surface shrouded in darkness by any small surface obstacle. Limitations on communications between Earth and the deployed payload will be caused by the low available data rate and by visibility windows (contact may be restricted to as little as <10 min every 9.5 h). This will impose a high degree of autonomy to be built into the payload systems.  相似文献   

20.
The Sun's gradual brightening will seriously compromise the Earth'sbiosphere within 109 years. If Earth's orbit migrates outward,however, the biosphere could remain intact over the entiremain-sequence lifetime of the Sun. In this paper, we explore thefeasibility of engineering such a migration over a long timeperiod. The basic mechanism uses gravitational assists to (in effect)transfer orbital energy from Jupiter to the Earth, and therebyenlarges the orbital radius of Earth. This transfer is accomplishedby a suitable intermediate body, either a Kuiper Belt object or a mainbelt asteroid. The object first encounters Earth during an inward passon its initial highly elliptical orbit of large ( 300 AU)semimajor axis. The encounter transfers energy from the object to theEarth in standard gravity-assist fashion by passing close to theleading limb of the planet. The resulting outbound trajectory of theobject must cross the orbit of Jupiter; with proper timing, theoutbound object encounters Jupiter and picks up the energy it lost toEarth. With small corrections to the trajectory, or additionalplanetary encounters (e.g., with Saturn), the object can repeat thisprocess over many encounters. To maintain its present flux of solarenergy, the Earth must experience roughly one encounter every 6000years (for an object mass of 1022 g). We develop the details ofthis scheme and discuss its ramifications.  相似文献   

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