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A comprehensive survey requires monitoring a large volume of space to discover asteroids and comets whose orbits can bring them close to the Earth. Such bodies can be distinguished from main-belt asteroids by their differing motions in the sky and, in the case of comets, by visible traces of activity. To ensure reasonable levels of completeness, the volume within which we can find a 1-km or larger asteroid should extend as far as the inner edge of the main asteroid belt. Such a search could be carried out in the visible or infrared part of the spectrum, using telescopes on the Earth or in space. The analysis in this Chapter is directed toward detection of the visible sunlight reflected from these NEOs, with no distinction made between telescopes on the ground or in orbit. However, since the least expensive option -- ground-based astronomical telescopes with CCD detectors -- is capable of meeting our survey requirements, we recommend this simple and cost-effective approach.
In this chapter we define a search strategy and use computer modeling to explore its quantitative implications. In Chapter 6 we will describe the follow-up observations required to refine the orbits of newly discovered objects, and in Chapter 7 we will present a proposed plan for an international network of survey telescopes to carry out this program.
The known ECA population is biased by observational selection (which tends to favor objects with orbits that bring them often into near-Earth space) and by the reflectivities of the bodies' surfaces (which favors the detection of bright objects over dark ones). Muinonen and others (1991) computed encounter velocities and collision probabilities of individual asteroids to correct for known sources of bias. The diameter distribution was approximated by a power law, as described in Chapter 3. For our model simulation, there are about 2,100 ECAs larger than 1 km diameter, 9,200 larger than 0.5 km, and 320,000 larger than 0.1 km. Of those larger than 0.5 km in diameter, about 2 percent are Atens, 75 percent are Apollos, and 23 percent are Earth-crossing Amors. Although the ECA population is uncertain by as much as a factor of two, particularly at the smallest diameters, the results of simulated surveys and the indications they provide about observing strategy should be qualitatively correct.
The intermediate and long-period comets are quite different. For purposes of this report, we use the term LPC for all comets with period greater than 20 years. Because the majority of the LPCs discovered will make just one passage through the inner solar system during a survey of 15- to 25-yr duration, they do not provide the repeated opportunities for discovery that exist for the ECAs. The best we can do is to identify incoming LPCs in time to give the longest possible warning time of their approach. For our simulations,we have used a sample of 158 Earth-crossing LPCs observed during the last 100 years. We assume that the observations represents an unbiased sample of the true LPC population. According to this model, there are about 180 LPCs/year larger than 1 km diameter that pass within the orbit of the Earth.
In simulating the LPCs, we have also taken into the account their activity (formation of an atmosphere), which causes them to brighten much more rapidly as they approach the Sun than would be expected from their size alone. The presence of an atmosphere enhances the detectability of comets, but the effect is not large until the comet comes inside the orbit of Jupiter, at which point we typically have only about one year warning.
The model population described above has been used to estimate the apparent or sky-plane distribution of ECAs (Muinonen and others 1991). From Figure 1, one expects a prevalence of small (faint) ECAs in the opposition and conjunction directions (that is, toward the Sun and away from the Sun). We also expect a concentration toward the ecliptic, the central plane of the solar system. These expectations are confirmed in Figure 2, which shows instantaneous number-density contours of ECAs larger than 0.5 km diameter for limiting magnitudes V = 18, 20, and 22 (note that larger magnitudes refer to fainter objects). Near opposition, and ignoring detection losses other than trailing produced by the apparent motion of the object, about 160 square degrees must be searched to V = 18 to have a 50 percent chance of detecting an ECA. To detect one ECA at V = 20 we must search 25 square degrees, and 7 square degrees at V = 22.
To model the expected rate of discovery of ECAs and LPCs, and to understand how a survey for ECAs can be optimized, we have allowed for the effects of detection losses -- that is, of factors that cause some objects to be missed or reduce the probability of their detection. These losses include trailing (as noted above), confusion with main-belt asteroids, confusion with stars and galaxies, and so-called "picket-fence" losses in which an asteroid's rapid motion across the sky causes it to be missed as a consequence of the fact that only a small potion of the sky is directly observed at any one time.
No survey will cover the entire sky because of interference from the Sun and Moon and other practical considerations. But as a reference, let us calculate the percentage completeness of NEOs that would be discovered in a hypothetical whole-sky survey as function of diameter, limiting magnitude, and survey duration. Figure 3 illustrates the results of ECA-survey simulations in which detection losses are allowed for and in which the whole sky is searched once each month. At a limiting magnitude of V = 18, comparable to the limit of the 0.46-m Palomar Schmidt telescope currently used for several photographic surveys, even whole-sky surveys extending as long as 25 years would not yield a large fraction of the largest ECAs. The problem is that the volume of space being searched is so small that many of the ECAs of interest simply do not pass through the region being surveyed in a 25 year span. At V = 20, which is somewhat inferior to the current performance of the 0.9-m Spacewatch Telescope, about half the ECAs larger than 1 km diameter are accessible in 15 years. To achieve greater completeness, and therefore greater levels of risk reduction, we must utilize larger telescopes with fainter limiting magnitudes, as will be described in Chapter 7.
At fainter magnitudes, much greater completeness is attainable, and discovery is characterized by a rapid initial detection rate followed after some years by a much slower approach to completeness. To survey, for example, 90 percent of ECAs larger than 1 km, a large area of the sky must be searched each month for a number of years to a magnitude limit of V = 22 or deeper. Because of the rapid decline in the rate of discovery of large ECAs, surveys lasting many decades or even longer are mainly valuable for providing increasing discovery completeness of smaller ECAs (less than 1 km diameter) and continued monitoring of LPCs.
The LPCs spend almost all of their time in the outer solar system, and they can approach the inner solar system from any direction in space. Those with Earth-crossing orbits (that is, with perihelia within 1 AU of the Sun), take about 16 months to travel from the distance of Saturn (9.5 AU from the Sun) to that of Jupiter (5.2 AU) and a little more than an additional year to reach perihelion. At any time, it is estimated that at least one thousand LPCs are brighter than V = 22 magnitude.
Modeling searches of the whole sky once a month for LPCs to magnitude limits of V =22 and 24 gave the following results, where the completeness is expressed in terms of the warning time available before the comet reaches the orbit of the Earth:
D > Warning time % LPCs discovered
(km) (yr) V = 22 V = 24
1.0 0.25 91 97
0.5 58 88
1.0 10 43
5.0 0.25 96 99
0.5 90 92
1.0 67 83
2.0 8 25
10.0 0.5 92 95
1.0 76 88
2.0 18 68
3.0 7 28
From these numbers, it is clear that a high discovery percentage can only be achieved for warning times on the order of several months, even for a very deep limiting magnitude of V = 24. This result confirms our intuition that it is much more difficult to provide long lead times for LPCs than for ECAs.
Figure 2 indicates that a search centered on opposition (opposite the direction toward the Sun) is optimum. Surveys have been simulated that cover various areas of the sky and in which realistic detection losses have been included. Figure 4 shows the results of simulating 25-yr surveys to V = 22 for ECA diameters greater than 0.5 km. Contours showing the discovery completeness (in percent) and the area to be searched once per month are shown. Values may be compared with the 83 percent discovery completeness for a similar whole-sky (41,000 square degrees) in Figure 3. To minimize the areal coverage needed to achieve a given discovery completeness, it is clearly advantageous to search regions spanning a broader range of celestial latitude than celestial longitude. The same strategy holds for other magnitude and diameter thresholds. For plausible search areas (in the range 5,000 to 10,000 square degrees per month), one may anticipate about two-thirds discovery completeness at V = 22. However, coverage in both longitude and latitude must not be too small or some ECAs will pass through the search region undetected from one month to the next.
Atens pose a special problem because some of them make very infrequent appearances that may occur far from opposition in celestial longitude. It can be expected that only about 40 percent of the Atens sought would be discovered in a nominal 25-yr, 6,000-square degree per month survey. The discovery rate could be increased to nearly 60 percent by biasing the search away from opposition, but at a sacrifice in the overall ECA discovery rate. It should be recalled that only eleven Atens are known, so the bias-corrected estimate of their true number may be substantially in error.
In what follows, it will be useful to consider a so-called standard survey region of 6,000 square degrees, centered on opposition and extending +/-30 deg in celestial longitude and +/-60 deg in celestial latitude.
As has been pointed out above, rapid decline in discovery rate of ECAs at faint magnitudes makes increasing the duration of the survey an ineffective strategy. For reference, the whole-sky survey to V = 22 and for diameter greater than 0.5 km could yield 71 percent completeness after 10 years. Even after 20 years, completeness would rise only to 81 percent (Figure 3).
Scanning a given region of the sky twice a month is likewise not very effective. For the standard 6,000 square degree survey region, to V = 22 and 0.5-km diameter threshold, the completeness after 25 yr would rise from 66 percent to 69 percent. However, scanning 12,000 square degrees once per month could lead to 72 percent completeness.
Figures 2 and 3 attest to the high value of mounting very deep surveys (that is, to very faint magnitude limits) for ECAs, the key factor being the greatly increased volume of space in which ECAs of given diameter can be detected. Figure 6 shows discovery completeness as functions of limiting magnitude V and diameter threshold for the standard survey region. At V= 20 and for diameter greater than 0.5 km, one can expect the standard 25-yr survey to be only 27 percent complete, whereas at V = 22 completeness rises to 66 percent. If the diameter threshold is 1 km, completeness should increase to 54 percent and 88 percent, respectively. Sophisticated image processing and detection schemes can yield an equivalent gain of as much as 1.5 magnitude, resulting in gains in completeness from 66 to 87 percent and from 88 to 94 percent, respectively.
Examination of the orbits of ECAs not discovered during simulated surveys shows, not unexpectedly, that most of these bodies' orbits have large semimajor axes, high eccentricities, and/or high inclinations such that either their dwell times in near-Earth space are brief and infrequent or they never come close to Earth in their present orbits. Of course, the latter class of ECAs poses no current hazard. This result of the simulations thus confirms our intuition: the survey preferentially discovers objects that come close to the Earth and therefore favors our overall objective of reducing the hazard of impacts on our planet.
D > Warning time % LPCs discovered
(km) (yr) V = 22
1.0 0.25 29
0.5 15
1.0 3
5.0 0.25 48
0.5 37
1.0 17
2.0 3
10.0 0.5 44
1.0 25
2.0 7
3.0 4
The warning time used in these calculations is actually the time from discovery to first Earth crossing. But it is equally likely that the LPC, if it is on a collision course, will strike Earth on the outbound part of its orbit, increasing the warning by about 6 months.
The overall level of completeness, without regard to warning time, is 37 percent at 1 km, 54 percent at 5 km, and 57 percent at 10 km diameter. Clearly, a survey designed for ECAs produces inferior results for LPCs, although the rate of discovery of these comets will be much greater than that achieved by current surveys, which rely upon relatively small telescopes and visual sky-sweeping by amateur astronomers and miss the great majority of the smaller long-period comets.
Because ECAs are preferentially observable when close to Earth, the completeness level for potentially hazardous ECAs is greater than that of the population as a whole. For the standard survey, the discovery completeness of potentially hazardous ECAs is 91 percent for bodies larger than 1 km diameter (compared to 87 percent for the entire ECA population) and 73 percent for ECAs larger than 0.5 km diameter (compared to 66 percent). For LPCs, however, the discovery completeness is the same as that of the total population.
As in Chapter 3, we suppose that 75 percent of the NEO hazard arises from ECAs and 25 percent from LPCs. If we ask for a 12-month warning time for LPCs, the percentages of potentially hazardous objects larger than a given diameter discovered during a standard 25-yr survey are as follows: 69 percent at 1 km diameter, 79 percent at 5 km, and 81 percent at 10 km or larger. At the larger sizes, the missed objects are almost all comets, and they will be detected, but not with a full year warning time.
We have shown that potentially hazardous ECAs can be discovered at a sufficient rate that most of the larger members of the ECA population can be discovered and assessed within a 15-25 year time scale. By prolonging the survey, the inventory of smaller ECAs can be brought to greater completeness. Indeed, we estimate that, using current technology to continue the standard survey beyond 25 yr duration, we would stand a better-than-even chance, within 300 yr, of discovering and identifying the ECA that might cause the next Tunguska-like event. In anticipation that huge strides in technological development would reduce this interval considerably, we can be almost certain that the such an impactor could be identified by means of a prolonged telescopic search.
Since LPCs enter the inner solar system at a near-constant rate, many of them for the first time, their potential for hazard to Earth goes on forever. Thus, any survey of finite duration will be destined to ignore about 25 percent of the potential hazard posed to our planet. Only by continually monitoring the flux of NPCs into Earth's neighborhood can we hope to achieve near-complete assessment of the NEO hazard.
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