Evidence-based robust design of deflection actions for near Earth objects

This paper presents a novel approach to the robust design of deflection actions for near Earth objects (NEO). In particular, the case of deflection by means of solar-pumped laser ablation is studied here in detail. The basic idea behind laser ablation is that of inducing a sublimation of the NEO surface, which produces a low thrust thereby slowly deviating the asteroid from its initial Earth threatening trajectory. This work investigates the integrated design of the space-based laser system and the deflection action generated by laser ablation under uncertainty. The integrated design is formulated as a multi-objective optimisation problem in which the deviation is maximised and the total system mass is minimised. Both the model for the estimation of the thrust produced by surface laser ablation and the spacecraft system model are assumed to be affected by epistemic uncertainties (partial or complete lack of knowledge). Evidence Theory is used to quantify these uncertainties and introduce them in the optimisation process. The propagation of the trajectory of the NEO under the laser-ablation action is performed with a novel approach based on an approximated analytical solution of Gauss’ variational equations. An example of design of the deflection of asteroid Apophis with a swarm of spacecraft is presented.     

On the prevention of a possible collision of asteroid Apophis with the Earth

Currently, there is some positive probability of a collision of the asteroid Apophis with the Earth in 2036. In this study, the problem of preventing the collision by correcting the asteroid’s orbit is examined. The characteristics of the impulsive correction are investigated, as well as the ways of its implementation by kinetic and nuclear impacts. Impulsive and weak effects are compared. Weak effects leading to slow changes in the asteroid’s orbit are considered to be more usable because of the potentially higher accuracy of this correction. The characteristics of the gravitational effect of the asteroid by a special spacecraft (SC) kept by its control jet engines at a certain point near the asteroid and gravitationally perturbing the motion of Apophis are analyzed. The change in the perigee radius of the Apophis orbit in 2036 and the SC mass consumption are examined as functions of the effect duration, the SC mass, its distance to the asteroid, the start time of the correction, and the velocity of the SC engine exhaust jet.     

Feasibility study for near-earth-object tracking by a piggybacked micro-satellite with penetrators

As of August 2007, over 5000 near-earth-objects (NEO) have been discovered. Some already represent a potential danger to the Earth while others might become hazards in the future. The Planetary Society organised in 2007 the “Apophis Mission Design Competition” in response to this potential threat with the objective to identify promising concepts to track NEOs; the asteroid 99942 Apophis was taken as the study case. This paper describes the “Houyi” proposal which was evaluated by the competition jury as an innovative approach to this problem. Instead of launching a large satellite for NEO tracking, this novel concept proposes a miniaturized satellite that is piggybacked onto a larger (scientific) mission. Such mission design would drastically reduce the costs for NEO surveillance. The presented scenario uses the ESA’s SOLO mission as a design baseline for the piggyback option. This paper summarizes the architecture of this CubeSat towards Apophis and extends the previous study by focusing on the feasibility of a piggybacked mission in terms of propulsion requirements.     

Earth–Mars halo to halo low thrust manifold transfers

Application of low thrust propulsion to interconnect ballistic trajectories on invariant manifolds associated with multiple circular restricted three body systems has been investigated. Sun-planet three body models have been coupled to compute the two ballistic trajectories, where electric propulsion is used to interconnect these trajectories as no direct intersection in the Poincarè sections exists. The ability of a low thrust to provide the energy change required to transit the spacecraft between two systems has been assessed for some Earth to Mars transfers. The approach followed consists in a planetary escape on the unstable manifold starting from a periodic orbit around one of the two collinear libration points near the secondary body. Following the planetary escape and the subsequent coasting phase, the electric thruster is activated and executes an ad-hoc thrusting phase. The complete transfer design, composed of the three discussed phases, and possible applications to Earth–Mars missions is developed where the results are outlined in this paper.     

Dynamical parameters of spacecraft motion near small celestial body

The paper considers how a spacecraft can be put into orbit around a small asteroid to function as its artificial moon. We study the general behavior of perturbations that affect the current coordinates of an orbiting spacecraft and estimate the perturbations caused by the main perturbing factors, i.e., (1) the irregular shape of an asteroid and (2) celestial bodies of the Solar System. With specific orbital parameters, a long-term targeted operation of a spacecraft can be actualized in a mission to the asteroid Apophis where the spacecraft will carry a radio beacon transponder.     

Asteroid hazard,real problems and practical actions

The paper refers to the current status of asteroid hazard in Russia and abroad. The authors emphasize the relevance of a sober assessment of its real state and specific circumstances working from the principle of reasonable sufficiency. The paper presents a practical approach to the asteroid hazard problem. It consists of a proposal for a mission to the Apophis asteroid and to define the main parameters of this hazardous celestial body. The article also considers how the spacecraft would look, as well as its mission profile for the period of 2012–2014.     

Orbital YORP and asteroid orbit evolution, with application to Apophis

Photon thrust from shape alone can produce quasi-secular changes in an asteroid's orbital elements. An asteroid in an elliptical orbit with a north–south shape asymmetry can steadily alter its elements over timescales longer than one orbital trip about the Sun. This thrust, called here orbital YORP (YORP = Yarkovsky–O'Keefe–Radzievskii–Paddack), operates even in the absence of thermal inertia, which the Yarkovsky effects require. However, unlike the Yarkovsky effects, which produce secular orbital changes over millions or billions of years, the change in an asteroid's orbital elements from orbital YORP operates only over the precession timescale of the orbit or of the asteroid's spin axis; this is generally only thousands or tens of thousands of years. Thus while the orbital YORP timescale is too short for an asteroid to secularly journey very far, it is long enough to warrant investigation with respect to 99942 Apophis, which might conceivably impact the Earth in 2036. A near-maximal orbital YORP effect is found by assuming Apophis is without thermal inertia and is shaped like a hemisphere, with its spin axis lying in the orbital plane. With these assumptions orbital YORP can change its along-track position by up to ±245 km, which is comparable to Yarkovsky effects. Though Apophis' shape, thermal properties, and spin axis orientation are currently unknown, the practical upper and lower limits are liable to be much less than the ±245 km extremes. Even so, the uncertainty in position is still likely to be much larger than the 0.5 km “keyhole” Apophis must pass through during its close approach in 2029 in order to strike the Earth in 2036.     

New Challenges to Trajectory Design by the Use of Electric Propulsion and Other New Means of Wandering in the Solar System

The design of spacecraft trajectories is a crucial part of a space mission design. Often the mission goal is tightly related to the spacecraft trajectory. A geostationary orbit is indeed mandatory for a stationary equatorial position. Visiting a solar system planet implies that a proper trajectory is used to bring the spacecraft from Earth to the vicinity of the planet. The first planetary missions were based on conventional trajectories obtained with chemical engine rockets. The manoeuvres could be considered 'impulsive' and clear limitations to the possible missions were set by the energy required to reach certain orbits. The gravity-assist trajectories opened a new way of wandering through the solar system, by exploiting the gravitational field of some planets. The advent of other propulsion techniques, as electric or ion propulsion and solar sail, opened a new dimension to the planetary trajectory, while at the same time posing new challenges. These 'low thrust' propulsion techniques cannot be considered 'impulsive' anymore and require for their study mathematical techniques which are substantially different from before. The optimisation of such trajectories is also a new field of flight dynamics, which involves complex treatments especially in multi-revolution cases as in a lunar transfer trajectory. One advantage of these trajectories is that they allow to explore regions of space where different bodies gravitationally compete with each other. We can exploit therefore these gravitational perturbations to save fuel or reduce time of flight. The SMART-1 spacecraft, first European mission to the Moon, will test for the first time all these techniques. The paper is a summary report on various activities conducted by the project team in these areas.     

Peculiarities of the motion of asteroid 99942 Apophis

The Apophis asteroid attracted the attention of scientists immediately after its discovery in 2004, because the initially determined orbit of this asteroid assumes a possible collision with Earth in April 2029. The size of Apophis is about several hundred meters, and its collision with Earth might result in a large regional or even global catastrophe. At present, the trajectory of Apophis has been calculated more accurately, and a collision in 2029 has ruled out; the asteroid will pass Earth at a distance of about 37 000 km from its center. However, close approaches or collisions are possible after 2029, including the most probable in 2036. The risk of collision in 2036 is well known and actively examined by the scientists. In this study, we consider the peculiarities of the asteroid motion associated with its approach in 2029 and with a possible close approach in 2036. The trajectories scatter during the approaches and the loss of accuracy is associated with these scatterings. As a result, the trajectory of Apophis may become nondeterministic after 2036; that is, it cannot now be determined unambiguously. Although such events are very unlikely, it is interesting to examine a variety of alternative variants of Apophis’ close approaches and collisions with Earth immediately after 2036. The effects of small variations in the asteroid velocity at different moments in time after its impact with a certain mass are discussed.     

Lunar Gravity-Assist Maneuver As a Way of Reducing the Orbit Amplitude in the Spectrum–Röntgen–Gamma Project

Spectrum–Röntgen–Gamma (SRG) is a space observatory designed to observe astrophysical objects in the X-ray range of the electromagnetic spectrum. SRG is planned to be launched in 2019 by a Proton-M launch vehicle with a DM3 upper stage. The spacecraft will be delivered to an orbit around the Sun–Earth collinear libration point L2 located at a distance of ~1.5 million km from the Earth. Although the SRG launch scheme has already been determined at present, in this paper we consider an alternative spacecraft transfer scenario using a lunar gravity-assist maneuver. The proposed scenario allows a oneimpulse transfer from a low Earth orbit to a small-amplitude orbit around the libration point to be performed while fulfilling the technical constraints and the scientific requirements of the mission.     

Three-body problem, its Lagrangian points and how to exploit them using an alternative transfer to L4 and L5

An alternative transfer strategy to send spacecraft to stable orbits around the Lagrangian equilibrium points L4 and L5 based in trajectories derived from the periodic orbits around L1 is presented in this work. The trajectories derived, called Trajectories G, are described and studied in terms of the initial generation requirements and their energy variations relative to the Earth through the passage by the lunar sphere of influence. Missions for insertion of spacecraft in elliptic orbits around L4 and L5 are analysed considering the restricted three-body problem Earth–Moon-particle and the results are discussed starting from the thrust, time of flight and energy variation relative to the Earth.     

Optimal switching strategy for radially accelerated trajectories

This paper studies the problem of a spacecraft subject to an outward radial thrust, with constant modulus, that may be switched on or off at suitable time intervals. The problem is to find the optimal strategy to guarantee the possibility of transferring the spacecraft from an initial to a final position in a given time interval using the least amount of thrust level. The problem is solved in an optimal framework, using an indirect approach. A number of different mission scenarios are studied in detail: escape missions, flyby missions and rendezvous missions. In the latter case the spacecraft uses a hybrid system comprising an high thrust propulsion system for the final impulsive maneuver. The optimal switching strategy allows one to substantially decrease the thrust level when compared to the continuous case (without thrust modulation).     

How precise is the orbit of asteroid (99942) Apophis and how probable is its collision with the Earth in 2036–2037?

The nearest in time close approach of potentially hazardous asteroid (99942) Apophis with the Earth will take place on April 13, 2029, when the minimum distance of the asteroid from the Earth’s center will be as small as 38 000 km. Such a close approach will result in substantial transformation of the asteroid’s orbit. The value of the perturbations depends on the minimum distance between the bodies during the approach. Among possible transformations of the orbit are those which result in new dangerous approaches and even in probable Apophis collisions with the Earth starting from 2036. At present, at least four solutions are known for the Apophis orbit which were obtained using all radar and most of available optical observations. The procedures of assigning weights to conditional equations and the models of the asteroid’s motion have differed to some extent when finding these solutions. Of considerable interest is the comparison of the found orbital parameters with the estimates of their accuracy, since small distinctions in their values result in considerable distinctions in the forecast of Apophis’ motion after 2029 and beyond. It is shown in the paper that the estimates of the probability of an Apophis collision with the Earth in 2036 differ by some orders of magnitude, according to various solutions. The influence of factors which were disregarded in the models of motion even more increases the uncertainty in forecasting the motion after 2029. More accurate forecasting can be achieved as a result of additional optical and, to a greater extent, a series of radar observations in 2013 and then in 2020–2021, and/or as a result of processing radio signals of the transmitter delivered to the Apophis surface or to the orbit of its artificial satellite, as it was proposed in a number of papers.     

On the possibility of the guidance of small asteroids to dangerous celestial bodies using the gravity-assist maneuver

In this paper, the method of changing the trajectories of hazardous asteroids with orbits known for some years to be on a possible collision course with the Earth is considered. The method relies on the use of small asteroids (asteroid-projectiles) directed at hazardous celestial bodies by giving the projectile a sufficiently small velocity impulse ensuring the Earth gravity assist. As a result, the asteroid-projectile vector can be controllably changed over a wide range. Apophis is considered as an example of the target asteroid. The technical feasibility of this method is discussed. It is noted that despite the potential use of this elegant method, its practical implementation requires further research and development.     

A space-based decametric wavelength radio telescope concept

This paper reports a design study for a space-based decametric wavelength telescope. While not a new concept, this design study focused on many of the operational aspects that would be required for an actual mission. This design optimized the number of spacecraft to insure good visibility of approx. 80% of the radio galaxies– the primary science target for the mission. A 5,000 km lunar orbit was selected to guarantee minimal gravitational perturbations from Earth and lower radio interference. Optimal schemes for data downlink, spacecraft ranging, and power consumption were identified. An optimal mission duration of 1 year was chosen based on science goals, payload complexity, and other factors. Finally, preliminary simulations showing image reconstruction were conducted to confirm viability of the mission. This work is intended to show the viability and science benefits of conducting multi-spacecraft networked radio astronomy missions in the next few years.     

Project of the mission to Phobos

This article provides the main scientific objectives and characteristics of the Phobos-Soil project, intended to fly to the Martian satellite Phobos, deliver its soil samples to the Earth, as well as explore Phobos, Mars, and the Martian environment with onboard scientific instruments. We give the basic parameters of the ballistic scenario of the mission, spacecraft, and some scientific problems to be solved with the help of the scientific instruments installed on the spacecraft.     

On target for Venus – set oriented computation of energy efficient low thrust trajectories

Recently new techniques for the design of energy efficient trajectories for space missions have been proposed that are based on the circular restricted three body problem as the underlying mathematical model. These techniques exploit the structure and geometry of certain invariant sets and associated invariant manifolds in phase space to systematically construct energy efficient flight paths. In this paper, we extend this model in order to account for a continuously applied control force on the spacecraft as realized by certain low thrust propulsion systems. We show how the techniques for the trajectory design can be suitably augmented and compute approximations to trajectories for a mission to Venus.     

Solar radiation pressure on (99942) Apophis

Near-Earth asteroid (99942) Apophis currently resides among the top positions on the list of objects with small, yet non-zero impact probability with the Earth. For that reason an unusual observational and theoretical effort has been dedicated to precisely characterize its future orbit. Here we discuss orbital perturbation of Apophis due to incident and reflected solar radiation pressure (SRP). We both revisit recent analytical estimate of the SRP effects for this body and also formulate a numerical approach allowing us to compute the SRP orbital perturbation under general assumptions. Contrary to some previous results, we show that SRP has a much smaller effect on the Apophis trajectory than does the thermal re-radiation force which produces the Yarkovsky effect. When the Yarkovsky effect becomes constrained enough in the future, our approach may be used to improve the orbit determination for this asteroid.     

Earth impact probability of the Asteroid (25143) Itokawa to be sampled by the spacecraft Hayabusa

The Japanese spacecraft Hayabusa is planed to reach the Asteroid Itokawa in September 2005, and to bring back some samples of its surface to Earth in 2007. We have studied the future possible evolution of this asteroid by integrating numerically over 100 Myr a set of 39 initially indistinguishable orbits (clones), obtained either by small variations of the nominal initial conditions, or by using different computers (introducing different round-off errors). The results indicate that an Earth impact of this 500-m-size asteroid is likely within a million years, which is only a factor of four larger than the average impact frequency of asteroids of this size. The mission Hayabusa may thus sample a good candidate for being among the next 500-m-size Earth impactors.     

Time-delay Interferometry for ASTROD-GW

ASTROD-GW(ASTROD[Astrodynamical Space Test of Relativity using Optical Devices] optimized for Gravitational Wave detection) is an optimization of ASTROD to focus on the detection of gravitational waves. Three spacecraft in the mission are positioned respectively in the vicinity of the Sun- Earth Lagrange points L3, L4 and L5. They form a nearly equilateral interferometerarray with the arm lengths of about 260 million kilometers. A set of optimized 20-yr mission orbits of the ASTROD-GW spacecraft are worked out by us. And with this, we have performed the numerical simulation of time-delay interferometry under the CGC2.7 (CGC: Center for Gravitation and Cosmology) ephemeris framework.