Earth and space-based NEO survey simulations: prospects for achieving the spaceguard goal

We have used an improved model of the orbit and absolute magnitude distribution of Near Earth Objects (NEOs) to simulate the performance of asteroid surveys. Our results support general conclusions of previous studies using preliminary Near Earth Asteroid (NEA) orbit and magnitude distributions and suggest that meeting the Spaceguard Goal of 90% completion for Near Earth Objects (NEOs) greater than 1 km diameter by 2008 is impossible given contemporary surveying capabilities.The NEO model was derived from NEO detections by the Spacewatch Project. For this paper we developed a simulator for the Catalina Sky Survey (CSS) for which we had a complete pointing history and NEO detection efficiency. The good match between the output of the simulator and the actual CSS performance gives confidence that both the NEO model and simulator are correct. Then, in order to determine if existing surveys can meet the Spaceguard Goal, we developed a simulator to mimic the LINEAR survey, for which detailed performance characteristics were unavailable. This simulator serendipitously provided an estimate for the currently undiscovered population of NEOs upon which we base all our estimates of time to 90% completion. We also developed a set of idealized NEO surveys in order to constrain the best possible survey performance in contrast to more realistic systems.A 100% efficient, all-sky, every night survey, subject only to the constraints of detection above a specified air mass and when the Sun is 18° below the horizon provides a benchmark from which to examine the effect of imposing more restrictions and the efficacy of some simple survey strategies. Such a survey must have a limiting V-magnitude of 20.1 ± 0.2 to meet the Spaceguard Goal.More realistic surveys, limited by latitude, the galaxy, minimum rates of NEO motion, etc., require fainter limiting magnitudes to reach the same completion. Our most realistic simulations, which have been normalized to the performance of the LINEAR detector system’s operation in the period 1999-2000, indicate that it would take them another 33 ± 5 years to reach 90% completeness for the larger asteroids (?1 km diameter). They would need to immediately increase the limiting magnitude to about 24 in order to meet the Spaceguard Goal.The simulations suggest that there may be little need for distributing survey telescopes in longitude and latitude as long as there is sufficient sky coverage from a telescope or network of telescopes which may be geographically close. An idealized space-based survey, especially from a satellite orbit much interior to Earth, would offer an advantage over their terrestrial counterparts. We do not consider a cost-benefit analysis for any of the simulations but suspect that a local-area network of telescopes capable of covering much of the sky in a month to V ∼ 21.5 may be administratively, financially, and scientifically the best compromise for reaching 90% completion of NEOs larger than 1 km diameter.     

Easily retrievable objects among the NEO population

Asteroids and comets are of strategic importance for science in an effort to understand the formation, evolution and composition of the Solar System. Near-Earth Objects (NEOs) are of particular interest because of their accessibility from Earth, but also because of their speculated wealth of material resources. The exploitation of these resources has long been discussed as a means to lower the cost of future space endeavours. In this paper, we consider the currently known NEO population and define a family of so-called Easily Retrievable Objects (EROs), objects that can be transported from accessible heliocentric orbits into the Earth’s neighbourhood at affordable costs. The asteroid retrieval transfers are sought from the continuum of low energy transfers enabled by the dynamics of invariant manifolds; specifically, the retrieval transfers target planar, vertical Lyapunov and halo orbit families associated with the collinear equilibrium points of the Sun–Earth Circular Restricted Three Body problem. The judicious use of these dynamical features provides the best opportunity to find extremely low energy Earth transfers for asteroid material. A catalogue of asteroid retrieval candidates is then presented. Despite the highly incomplete census of very small asteroids, the ERO catalogue can already be populated with 12 different objects retrievable with less than 500 m/s of $\Delta v$ Δ v . Moreover, the approach proposed represents a robust search and ranking methodology for future retrieval candidates that can be automatically applied to the growing survey of NEOs.     

Solar System Science with LSST

The Large Synoptic Survey Telescope (LSST) will provide a unique tool to study moving objects throughout the solar system, creating massive catalogs of Near Earth Objects (NEOs), asteroids, Trojans, TransNeptunian Objects (TNOs), comets and planetary satellites with well-measured orbits and high quality, multi-color photometry accurate to 0.005 magnitudes for the brightest objects. In the baseline LSST observing plan, back-to-back 15-second images will reach a limiting magnitude as faint as r = 24.7 in each 9.6 square degree image, twice per night; a total of approximately 20,000 square degrees of the sky will be imaged in multiple filters, with revisits about every 3 nights over several months of each year.     

Capturing near earth objects

Recently,Near Earth Objects(NEOs) have been attracting great attention,and thousands of NEOs have been found to date.This paper examines the NEOs' orbital dynamics using the framework of an accurate solar system model and a Sun-Earth-NEO three-body system when the NEOs are close to Earth to search for NEOs with low-energy orbits.It is possible for such an NEO to be temporarily captured by Earth;its orbit would thereby be changed and it would become an Earth-orbiting object after a small increase in its velocity.From the point of view of the Sun-Earth-NEO restricted three-body system,it is possible for an NEO whose Jacobian constant is slightly lower than C1 but higher than C3 to be temporarily captured by Earth.When such an NEO approaches Earth,it is possible to change its orbital energy to nearly the zero velocity surface of the three-body system at point L1 and make the NEO become a small satellite of the Earth.Some such NEOs were found;the best example only required a 410 m s-1 increase in velocity.     

Capturing near earth objects

Recendy,Near Earth Objects (NEOs) have been attracting great attention,and thousands of NEOs have been found to date.This paper examines the NEOs'orbital dynamics using the framework of an accurate solar system model and a SunEarth-NEO three-body system when the NEOs are close to Earth to search for NEOs with low-energy orbits.It is possible for such an NEO to be temporarily captured by Earth; its orbit would thereby be changed and it would become an Earth-orbiting object after a small increase in its velocity.From the point of view of the Sun-Earth-NEO restricted three-body system,it is possible for an NEO whose Jacobian constant is slightly lower than C1 but higher than C3 to be temporarily captured by Earth.When such an NEO approaches Earth,it is possible to change its orbital energy to nearly the zero velocity surface of the three-body system at point L1 and make the NEO become a small satellite of the Earth.Some such NEOs were found; the best example only required a 410 m s-1 increase in velocity.     

ADVANTAGES OF SEARCHING FOR ASTEROIDS FROM LOW EARTH ORBIT: THE NEOSSat MISSION

Space-based observatories have several advantages over ground-based observatories in searching for asteroids and comets. In particular, the Aten and Interior to Earth’s Orbit (IEO) asteroid classes may be efficiently sought at low solar elongations along the ecliptic plane. A telescope in low Earth orbit has a sufficiently long orbital baseline to determine the parallax for all Aten and IEO class asteroids discovered with this observing strategy. The Near Earth Object Space Surveillance Satellite (NEOSSat) mission will launch a microsatellite to exploit this observing strategy complementing ground-based search programmes.     

Mars interplanetary trajectory design via Lagrangian points

With the increase in complexities of interplanetary missions, the main focus has shifted to reducing the total delta-V for the entire mission and hence increasing the payload capacity of the spacecraft. This paper develops a trajectory to Mars using the Lagrangian points of the Sun-Earth system and the Sun-Mars system. The whole trajectory can be broadly divided into three stages: (1) Trajectory from a near-Earth circular parking orbit to a halo orbit around Sun-Earth Lagrangian point L₂. (2) Trajectory from Sun-Earth L₂ halo orbit to Sun-Mars L₁ halo orbit. (3) Sun-Mars L₁ halo orbit to a circular orbit around Mars. The stable and unstable manifolds of the halo orbits are used for halo orbit insertion. The intermediate transfer arcs are designed using two-body Lambert’s problem. The total delta-V for the whole trajectory is computed and found to be lesser than that for the conventional trajectories. For a 480 km Earth parking orbit, the total delta-V is found to be 4.6203 km/s. Another advantage in the present approach is that delta-V does not depend upon the synodic period of Earth with respect to Mars.     

Orbit of comet C/1860 M1 (Great Comet of 1860)

Comet C/1860 M1 (Great Comet of 1860) is one of a large number of comets with parabolic orbits. Given that there are sufficient observations of the comet, 261 in right ascension and 251 in declination, it proves possible to calculate a better orbit. The comet's orbit is hyperbolic, and statistically different from a parabola. The comet, therefore, cannot be considered to be a Near Earth Oject. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of the transfer between libration point orbits and lunar orbits in Earth–Moon system

This paper is devoted to the study of the transfer problem from a libration point orbit of the Earth–Moon system to an orbit around the Moon. The transfer procedure analysed has two legs: the first one is an orbit of the unstable manifold of the libration orbit and the second one is a transfer orbit between a certain point on the manifold and the final lunar orbit. There are only two manoeuvres involved in the method and they are applied at the beginning and at the end of the second leg. Although the numerical results given in this paper correspond to transfers between halo orbits around the \(L_1\) point (of several amplitudes) and lunar polar orbits with altitudes varying between 100 and 500 km, the procedure we develop can be applied to any kind of lunar orbits, libration orbits around the \(L_1\) or \(L_2\) points of the Earth–Moon system, or to other similar cases with different values of the mass ratio.     

Realistic survey simulations for kilometer class near Earth objects

We present a new Near Earth Object (NEO) survey simulator which incorporates the four-dimensional population model of 4668 NEOs [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433] and the observing strategies of most asteroid search programs. With the recent expansion of survey capabilities, previous simulators focused on a specific survey facility are no longer useful in predicting the future detection rates. Our simulation is a superposition of simplified search patterns adopted by all major wide-field surveys in operation in both hemispheres. We defined five different simulation periods to follow the evolution of survey efficiencies reflecting changes in either search volume as a result of upgrades of telescopes and instruments or in observing schedules. The simulator makes remarkably good reproductions of actual survey results as of December 2005, not only the total number of detections but also (a,e,i,H) (‘H’ means absolute magnitude of an asteroid) distributions. An extended experiment provides excellent predictions for discovery statistics of NEOs (H<18) reported to the Minor Planet Center in 2006. These support that our simulator is a plausible approximation of real surveys. We further confirm that, with the Bottke et al. [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433] population model and present survey capability, the 90% completeness level of kilometer-sized NEOs will be achieved by 2010 or 2011. However, about 8% of the kilometer-sized or larger NEOs would remain undetected even after 10-year operation (2007-2016) of all current NEO survey facilities. They are apparently faint, with orbits characterized by large semimajor axis and higher eccentricity; these “hardest-to-find” objects tend to elude the search volume of existing NEO survey facilities. Our simulation suggests that 15% of undetectable objects are Atens and Inner Earth Objects. Because of their orbital characteristics, they will remain within ±45° from the Sun, thus cannot be discovered in the forthcoming decade if our effort is limited to current ground-based telescopes.     

The Soviet ASTRON mission: legacy

2013 marks the 30th anniversary since the launch of Soviet Spacecraft Astron that had been operated for 6 years as the largest ultraviolet telescope during its lifetime. The Astron orbital station was designed for the astrophysical observations. It was launched into orbit by Proton launch system on March 23, 1983. Astron had a 80 cm ultraviolet telescope with mass of 400 kg and a complex of X-ray spectrographs with mass of 300 kg on board as a payload. It’s high apogee orbit (with apogee 200000 km and perigee 2000 km) permitted the influences of the Earth’s umbra and radiation belts to be excluded from the measurements. The main astrophysical results are summarized in this paper.     

The geometry of impacts on a synchronous planetary satellite

We consider a satellite in a circular orbit about a planet that, in turn, is in a circular orbit about the Sun; we further assume that the plane of the planetocentric orbit of the satellite is the same as that of the heliocentric orbit of the planet. The pair planet–satellite is encountered by a population of small bodies on planet-crossing, inclined orbits. With this setup, and using the extension of Öpik’s theory by Valsecchi et al. (Astron Astrophys 408:1179–1196, 2003), we analytically compute the velocity, the elongation from the apex and the impact point coordinates of the bodies impacting the satellite, as simple functions of the heliocentric orbital elements of the impactor and of the longitude of the satellite at impact. The relationships so derived are of interest for satellites in synchronous rotation, since they can shed light on the degree of apex–antapex cratering asymmetry that some of these satellites show. We test these relationships on two different subsets of the known population of Near Earth Asteroids.     

On the stability of Earth-like planets in multi-planet systems

We present a continuation of our numerical study on planetary systems with similar characteristics to the Solar System. This time we examine the influence of three giant planets on the motion of terrestrial-like planets in the habitable zone (HZ). Using the Jupiter–Saturn–Uranus configuration we create similar fictitious systems by varying Saturn’s semi-major axis from 8 to 11 AU and increasing its mass by factors of 2–30. The analysis of the different systems shows the following interesting results: (i) Using the masses of the Solar System for the three giant planets, our study indicates a maximum eccentricity (max-e) of nearly 0.3 for a test-planet placed at the position of Venus. Such a high eccentricity was already found in our previous study of Jupiter–Saturn systems. Perturbations associated with the secular frequency g ₅ are again responsible for this high eccentricity. (ii) An increase of the Saturn-mass causes stronger perturbations around the position of the Earth and in the outer HZ. The latter is certainly due to gravitational interaction between Saturn and Uranus. (iii) The Saturn-mass increased by a factor 5 or higher indicates high eccentricities for a test-planet placed at the position of Mars. So that a crossing of the Earth’ orbit might occur in some cases. Furthermore, we present the maximum eccentricity of a test-planet placed in the Earth’ orbit for all positions (from 8 to 11 AU) and masses (increased up to a factor of 30) of Saturn. It can be seen that already a double-mass Saturn moving in its actual orbit causes an increase of the eccentricity up to 0.2 of a test-planet placed at Earth’s position. A more massive Saturn orbiting the Sun outside the 5:2 mean motion resonance (a _S  ≥9.7 AU) increases the eccentricity of a test-planet up to 0.4.     

Coronal Hole Influence on the Observed Structure of Interplanetary CMEs

We report on the coronal hole (CH) influence on the 54 magnetic cloud (MC) and non-MC associated coronal mass ejections (CMEs) selected for studies during the Coordinated Data Analysis Workshops (CDAWs) focusing on the question if all CMEs are flux ropes. All selected CMEs originated from source regions located between longitudes 15E?–?15W. Xie, Gopalswamy, and St. Cyr (2013, Solar Phys., doi: 10.1007/s11207-012-0209-0 ) found that these MC and non-MC associated CMEs are on average deflected towards and away from the Sun–Earth line, respectively. We used a CH influence parameter (CHIP) that depends on the CH area, average magnetic field strength, and distance from the CME source region to describe the influence of all on-disk CHs on the erupting CME. We found that for CHIP values larger than 2.6 G the MC and non-MC events separate into two distinct groups where MCs (non-MCs) are deflected towards (away) from the disk center. Division into two groups was also observed when the distance to the nearest CH was less than 3.2×10⁵ km. At CHIP values less than 2.6 G or at distances of the nearest CH larger than 3.2×10⁵ km the deflection distributions of the MC and non-MCs started to overlap, indicating diminishing CH influence. These results give support to the idea that all CMEs are flux ropes, but those observed to be non-MCs at 1 AU could be deflected away from the Sun–Earth line by nearby CHs, making their flux rope structure unobservable at 1 AU.     

The near-Earth objects and their potential threat to our planet

The near-Earth object (NEO) population includes both asteroids (NEAs) and comet nuclei (NECs) whose orbits have perihelion distances q<1.3 AU and which can approach or cross that of the Earth. A NEA is defined as a “potentially hazardous asteroid” (PHA) for Earth when its minimum orbit intersection distance (MOID) comes inside 0.05 AU and it has an absolute magnitude H<22 mag (i.e. mean diameter > 140 m). These are big enough to cause, in the case of impact with Earth, destructive effects on a regional scale. Smaller objects can still produce major damage on a local scale, while the largest NEOs could endanger the survival of living species. Therefore, several national and international observational efforts have been started (i) to detect undiscovered NEOs and especially PHAs, (ii) to determine and continuously monitor their orbital properties and hence their impact probability, and (iii) to investigate their physical nature. Further ongoing activities concern the analysis of possible techniques to mitigate the risk of a NEO impact, when an object is confirmed to be on an Earth colliding trajectory. Depending on the timeframe available before the collision, as well as on the object’s physical properties, various methods to deflect a NEO have been proposed and are currently under study from groups of experts on behalf of international organizations and space agencies. This paper will review our current understanding of the NEO population, the scientific aspects and the ongoing space- and ground-based activities to foresee close encounters and to mitigate the effects of possible impacts.     

AKARI—Infrared Satellite Mission—Present Status and Early Results

AKARI, formerly known as ASTRO-F, is a satellite mission dedicated to infrared astronomy for the first time in Japan. It has a 685-mm aperture telescope with two focal-plane instruments cooled by liquid helium (LHe) and mechanical coolers on board for observations in the 2–180 μm infrared spectral range. AKARI was launched on 2006 February 21 (UT) into a sun-synchronous polar orbit and started observations in May, 2006. It carried 179 liter LHe that lasted for 550 days and observations with LHe were carried out for more than 15 months. During the LHe holding period, AKARI made all-sky survey observations with six bands from 9 to 160 μm, which surpass the IRAS all-sky survey data in the sensitivity, spatial resolution, and spectral coverage. Together with the all-sky observation, AKARI also made pointing observations for about 10 min at a given position of the sky to execute deep imaging and spectroscopy from near- to far-infrared. Both focal-plane instruments work successfully on orbit and more than 90% of the sky was observed in the all-sky survey. After LHe exhaustion, near-infrared observations are planned to continue. This paper reports the in-orbit performance of AKARI and its early observational results so far obtained.     

Long term stability of Earth Trojans

We explore the long-term stability of Earth Trojans by using a chaos indicator, the Frequency Map Analysis. We find that there is an extended stability region at low eccentricity and for inclinations lower than about $50^{\circ }$ even if the most stable orbits are found at $i \le 40^{\circ }$ . This region is not limited in libration amplitude, contrary to what found for Trojan orbits around outer planets. We also investigate how the stability properties are affected by the tidal force of the Earth–Moon system and by the Yarkovsky force. The tidal field of the Earth–Moon system reduces the stability of the Earth Trojans at high inclinations while the Yarkovsky force, at least for bodies larger than 10 m in diameter, does not seem to strongly influence the long-term stability. Earth Trojan orbits with the lowest diffusion rate survive on timescales of the order of $10^9$  years but their evolution is chaotic. Their behaviour is similar to that of Mars Trojans even if Earth Trojans appear to have shorter lifetimes.     

Dynamical lifetime survey of geostationary transfer orbits

In this paper, we study the long-term dynamical evolution of highly elliptical orbits in the medium-Earth orbit region around the Earth. The real population consists primarily of Geosynchronous Transfer Orbits (GTOs), launched at specific inclinations, Molniya-type satellites and related debris. We performed a suite of long-term numerical integrations (up to 200 years) within a realistic dynamical model, aimed primarily at recording the dynamical lifetime of such orbits (defined as the time needed for atmospheric reentry) and understanding its dependence on initial conditions and other parameters, such as the area-to-mass ratio (A / m). Our results are presented in the form of 2-D lifetime maps, for different values of inclination, A / m, and drag coefficient. We find that the majority of small debris (\(>70\%\), depending on the inclination) can naturally reenter within 25–90 years, but these numbers are significantly less optimistic for large debris (e.g., upper stages), with the notable exception of those launched from high latitude (Baikonur). We estimate the reentry probability and mean dynamical lifetime for different classes of GTOs and we find that both quantities depend primarily and strongly on initial perigee altitude. Atmospheric drag and higher A / m values extend the reentry zones, especially at low inclinations. For high inclinations, this dependence is weakened, as the primary mechanisms leading to reentry are overlapping lunisolar resonances. This study forms part of the EC-funded (H2020) “ReDSHIFT” project.     

Velocities and Linewidths in the Network and Cell Interiors of a Polar Coronal Hole Compared with the Quiet Sun

The relative Doppler velocities and linewidths in a polar coronal hole and the nearby quiet-Sun region have been obtained from the Solar and Heliospheric Observatory (SOHO)/Coronal Diagnostic Spectrometer (CDS) observations using emission lines originating at different heights in the solar atmosphere from the lower transition region (TR) to the low solar corona. The observed region is separated into the network and the cell interior, and the behavior of the above parameters were examined in the different regions. It has been found that the histograms of Doppler velocity and width are generally broader in the cell interior than in the network. The histograms of Doppler velocities of the network and cell interior do not show significant differences in most cases. However, in the case of the quiet Sun, the Doppler velocities of the cell interior are more blueshifted than those of the network for the lowermost line He?ii 304 Å, and an opposite behavior is seen for the uppermost line Mg?ix 368 Å. The linewidth histograms show that the network–cell difference is more prominent in the coronal hole. The network has a significantly larger linewidth than the cell interior for the lowermost TR line He?ii 304 Å for the quiet Sun. For the coronal hole, this is true for the three lower TR lines: He?ii 304 Å, O?iii 599 Å, and O?v 630 Å. We also obtained the correlations between the relative Doppler velocity and the width. A mild positive correlation is found for the lowermost transition-region line He?ii 304 Å, which decreases even more or become insignificant for the intermediate lines. For the low coronal line Mg?ix 368 Å, the correlation becomes strongly negative. This might be caused by standing waves or waves propagating from the lower to the upper solar atmosphere. The results may have implications for the generation of the fast solar wind and coronal heating.