A Drake Equation for Alien Artifacts

Abstract

I propose a version of the Drake equation to include searching for alien artifacts, which may be located on the Moon, Earth Trojans, and Earth co-orbital objects. The virtue of searching for artifacts is their lingering endurance in space, long after they go dead. I compare a search for extraterrestrial artifacts (SETA) strategy with the existing listening to stars search for extraterrestrial intelligence (SETI) strategy. I construct a ratio of a SETA Drake equation for artifacts to the conventional Drake equation so that most terms cancel out. This ratio is a good way to debate the efficacy of SETI versus SETA. The ratio is the product of two terms: one is the ratio of the length of time that probes from extraterrestrial (ET) civilizations could be present in the near-Earth region to the length of time that ET civilizations transmit signals to the Solar System. The second term is the ratio of the respective origin volumes: the volume from which probes can come, which is affected by the long-term passage of stars near the Sun, to the volume of transmitting civilizations. Scenarios are quantified that suggest that looking for alien artifacts near Earth is a credible alternative approach relative to listening to stars. This argues for emphasis on artifact searches, ET archeology. I suggest study of existing high-resolution images of the Moon, imaging of the Earth Trojans and Earth co-orbitals, and probe missions to the latter two. Close inspection in these near-Earth regions, which also may hold primordial remnants of the early Solar System, yields concrete astronomical research.

1. Introduction

“To think in a disciplined way about what we may now be able to observe astronomically is a serious form of science.”—Freeman Dyson

In a recent article, I introduced the term “Lurker”: an unknown and unnoticed observing probe from an extraterrestrial (ET) civilization, which may well be dead, but if not, could respond to an intentional signal, or not, depending on unknown alien motivations (Benford, 2019). Lurkers include self-replicating probes based on von Neumann's theory of self-replicating machines, which is why they are often called von Neumann probes (Von Neumann, 1966). Recently, concepts have appeared for self-replicating probes that could be built in the near future (Borgue and Hein, 2020).

Another pioneering work on this concept was of course famously developed in “2001 A Space Odyssey” (Clarke, 1953). A solar-centric search for extraterrestrial artifacts (SETA) was advocated by Robert A. Freitas, who coined the term SETA for it in the 1980s (Freitas and Valdes, 1985). There are also the articles from the mid-1990s by Arkhipov (1995, 1998a, 1998b). Further analysis has appeared recently (Haqq-Misra and Kopparapu, 2012; Lingam and Loeb, 2018; Cirkovic et al., 2019; Shostak, 2020). SETA is a proposition about our local region in the Solar System. SETA is falsifiable in its specific domain: ET probes to investigate Earth would locate on the nearest objects down to a specified resolution. The search for extraterrestrial intelligence (SETI), on the other hand, is about messages sent from distant stars. For example, one can falsify a proposition such as “Are signals being sent to Earth at this moment within 100 light-years (ly)?” However, there is the region beyond 100 ly and beyond 1000 ly, etc. Therefore, SETI is falsifiable only within larger and larger domains. Of course, other factors can also weaken falsification: our sensitivity might be inadequate, the duty cycle might be small, and, of course, frequency coverage will always be incomplete.

Near-Earth objects could provide an ideal way to watch our world from a secure natural object (Benford, 2019). They are attractive locations for ET intelligence to locate a platform to observe Earth while not being easily seen. Co-orbitals are attractive targets for SETA because of their proximity and that they are hard to observe (small size and low albedo).

Rose and Wright (2004) pointed out the energy efficiency of an inscribed physical artifact versus an electromagnetic (EM) signal because the artifact has persistence and the EM signal has to be transmitted indefinitely. Here, I point out that artifacts are not only energy efficient but also increase the chance of contact. Rose and Wright did not explore where to locate the artifact so that it would be identified; here, I suggest that there are attractive locations near Earth where they might be readily observable.

I propose a version of the Drake equation for Lurkers on near-Earth objects. By using it, one can compare the SETA strategy of exploring artifacts with the conventional listening to stars SETI strategy, which has thus far found no artificial signals of technological origin. In contrast, SETA offers a new perspective and a new opportunity: discovering past and present visits to the near-Earth vicinity by ET space probes.

2. Drake Equations

2.1. The standard Drake equation

The standard Drake equation estimates the number of radiating civilizations that are detectable, N _C, as the product of the rate of creation of such radiating civilizations (Drake, 1965).

This modified Drake equation is as follows: $N_{C} = R_{f} x f_{p} x n_{e} x f_{l} x f_{i} x f_{C} x f_{R} x T_{R}$ (1)

I replace the usual Drake equation symbol for time over which they radiate L with T _R and I also multiply by f _R, the fraction that actually do radiate signals that might be observable at Earth. That is, they radiate with the intention of trying to communicate. Leakage radiation is unintentional, but comes in two types: radar, which has no message, and broadcasts, which come from many incoherent sources that cancel out, such as TV.

These parameters are listed in Table 1.

Table 1.

Drake Equation Parameters

Parameter	Definition
N _C	Number of civilizations in the Milky Way galaxy that are radiating electromagnetic emissions
R _f	Rate of formation of stars suitable for the development of intelligent life
f _p	Fraction of those stars with planetary systems
n _e	Number of planets, per solar system, with an environment suitable for life
f _l	Fraction of suitable planets on which life actually appears
f _i	Fraction of life-bearing planets on which intelligent life emerges
f _C	Fraction of civilizations that develop a technology that can transmit electromagnetic signs of their existence into space
f _R	Fraction that actually do radiate
T _R	Length of time such civilizations build beacons and radiate electromagnetic signals into space

Subscripts are italicized letters in definitions.

2.2. A Drake equation for alien artifacts

An equivalent to the Drake equation for the number of Lurkers in our Solar System, N _L, can similarly be expressed as the rate of creation of radiating civilizations times the fraction that also develop interstellar probe technology, f _ip, times the sojourn that Lurkers would be in the Solar System, T _L:

f _ip = fraction that also develop interstellar probe technologies and launch them and

T _L = time that Lurkers could reside in the Solar System

(note that for such civilizations, f_C = 1; a civilization with the capability to build such probes surely can build interstellar transmitters).

Then, a Drake equation for alien artifacts is $N_{L} = R_{f} x f_{p} x n_{e} x f_{l} x f_{i} x f_{i p} x T_{L}$ (2)

The new parameters are listed in Table 2.

Table 2.

Drake Alien Artifact Equation Parameters

Parameter	Definition
N _L	Number of Lurkers in our solar system
f _ip	Fraction of civilizations that develop interstellar probe technology and launch them to our solar system
T _L	Time that Lurkers could reside in the solar system

In the ratio of Eqs. (1) and (2), of the number of Lurkers in our Solar System to the number of radiating civilizations, most terms, in the first bracket, cancel out: $\frac{N_{L}}{N_{C}} = (\frac{R}{R} \frac{f_{p}}{f_{p}} \frac{n_{e}}{n_{e}} \frac{f_{l}}{f_{l}} \frac{f_{i}}{f_{l}} \frac{f_{c}}{f_{c}}) [\frac{f_{i p}}{f_{R}} \frac{T_{L}}{T_{R}}]$ (3) $\frac{N_{L}}{N_{C}} = \frac{f_{i p}}{f_{R}} \frac{T_{L}}{T_{R}}$

This initial result is that the ratio of civilizations sending probes that are now resident in our Solar System to the number sending messages is the product of two ratios:

a ratio of motives: $\frac{f_{i p}}{f_{R}}$

the fraction that also develop interstellar probe technologies and launch them divided by the fraction that only radiate, so f _ip/f _R < 1;

and a ratio of times: $\frac{T_{L}}{T_{R}}$

the time that Lurkers are present in the Solar System/the time ET civilizations release electromagnetic signals. Surely, a civilization with the capability to build such probes can build interstellar transmitters, so I will argue that T _L/T _R>1.

Our own civilization has been capable of radiating for about 50 years, including message-free Cold War radar transmissions, and inadvertent leakage radiation has been emitted for a long time (Quast, 2018). Intentional messages have also been sent but are difficult to detect with Earth-scale receiver systems (Billingham and Benford, 2014). We cannot yet build interstellar probes capable of traveling to and decelerating into a star system and conducting operations there. That may be possible in the next century [the Breakthrough Starshot project hopes to conduct interstellar flybys, a fleeting presence at ∼0.2 c in this century; Parkin (2018)]. If so, relatively soon we will be capable of both radiating to the stars and sending probes to explore nearby star systems.

However, Eq. (4) does not take into account the space volumes that the two groups operate in.

2.3. Space volume factor

Another factor must be included: Eq. (4) must be modified for V _L, the volume over which Lurkers can travel, and its corresponding range R _L versus V _B, the volume over which beacons can transmit and be plausibly detected, and its corresponding range R _B. Lurker probes traveling at a small fraction of the speed of light should be compared with the transmissions from an interstellar beacon propagating at the speed of light. That means that the volumes from which signals can be detected from beacons is much larger than the volume over which a Lurker could travel.

For example, assume that interstellar probes could operate at ∼10% c, the speed of light, as contemporary concepts of fusion rockets are designed. An example: for the Icarus Firefly magnetically confined Z-pinch concept at 4.7% c, traveling 10 ly would take about two centuries (Freeland and Lamontagne, 2015). Starshot, which is a flyby probe concept, at 0.2 c, takes more than 20 years to arrive at the Centauri system. Assuming that the attention span of the civilization is measured in centuries, a rough estimate of the distance over which probes will be launched is tens of light-years (the signal from the probe reporting back to its origin would travel at the speed of light, of course). If it is possible for probes to move close to c, then the beacon volume to probe volume would be close to unity.

In contrast, the electromagnetic waves of an interstellar beacon, be it light, millimeter waves, or microwaves, propagate ∼20 times faster at the speed of light. For example, we can estimate the range over which a beacon would be used to be hundreds of light-years. By that I again mean that the attention span of a civilization might be measured in centuries.

I define the volumes and ranges in Table 3.

Table 3.

Space Volume Factor Parameters

Parameter	Definition
V _B	Volume over which a beacon is detectable
V _L	Volume over which a Lurker could travel
R _B	Range over which a beacon is detectable
R _L	Range over which a Lurker could travel

Therefore, Eq. (3) must be multiplied by the ratio of these two volumes, V _L/V _B: $\frac{N_{L}}{N_{C}} = \frac{f_{i p}}{f_{R}} \frac{T_{L}}{T_{R}} [\frac{V_{L}}{V_{B}}]$ (4)

As volume scales as the cube of the distance to them, R _L/R _B: $\frac{N_{L}}{N_{C}} = \frac{f_{i p}}{f_{R}} \frac{T_{L}}{T_{R}} {[\frac{R_{L}}{R_{B}}]}^{3}$ (5)

This is a success ratio of searching for artifacts compared with listening to stars. It allows us to quantitatively evaluate their relative merits. Although the volume ratio would argue that long-range beacons will be much more likely to be detected than probes that come to observe Earth, the time ratio tends to mitigate that advantage.

2.4. Decision tree parameters

The ratio of the number of lurkers to the number of radiating civilizations can be estimated by using the three factors in Eq. (5), which have the following sizes: $\begin{matrix} \begin{matrix} f_{i p} ∕ f_{R} < 1 \\ R_{L} ∕ R_{B} < 1 \end{matrix} \\ T_{L} ∕ T_{R} > > 1 \end{matrix}$ (6)

Therefore, the success ratio, Eq. (5), will depend on choices for these parameters.

The key parameters making up these factors can be divided into objective and subjective components, where objective means the parameter can be quantified or at least estimated and subjective means it is a matter of opinion. Table 4 is a listing of such parameters.

Table 4.

Objective and Subjective Search for Extraterrestrial Artifacts—Parameters and Determining Factors

Objective parameters	Determined by	Subjective factors	Determined by
	Attention span of the civilization and cost of beacon	R _B	Matter of opinion
R _L	Speed and cost of starprobes
		f _ip/f _R	<1, matter of opinion
T _L	Lifetime of probe's orbit
		T _R	Matter of opinion

The issues determining the objective parameters are listed; subjective parameters are a matter of taste and underlying assumptions.

By making choices among the objective and subjective parameters, one constructs a decision tree. A set of parameter choices leads to a conclusion about the success ratio for SETA and SETI strategies, as embodied in Eq. (6). Because ET civilizations will vary enormously in motivations, we can expect a variety of outcomes for the success ratio.

2.4.1. Estimates of T _R, the time that ET beacons radiate

In the literature, estimates of T _R fall between a hundred and 100 million years, a very wide range. Shermer (2002) estimated T _R by averaging the life spans of 60 Earth civilizations, getting 420 years. Using 28 civilizations since the Roman Empire, he gives ∼300 years for modern civilizations. However, Shermer's number for the lifetime of societies is not relevant if new societies arise to replace old ones. In that case, one should take the summation of existence times for all the technological cultures on a planet. Note that the longest operating institution still existing on Earth is the Catholic Church, ∼2000 years. We will take the times to be 300–10,000 years, an order of magnitude range.

2.4.2. Estimates of T _L, the time that Lurkers could reside in the Solar System

A key point is that Lurkers will still be discoverable even though dead for a long time. That is not true of an EM transmission, which is simply passing through at the speed of light. That fact weighs to the advantage of the Lurker search strategy.

The time over which our biosphere has been observable from great distances of thousands of light-years, due to oxygen in the atmosphere, is a very long time (Fig. 1), measured in billions of years (Meadows et al., 2018; Kaltenegger et al., 2020). The first oxidation event occurred about 2.5 billion years ago and the second, largest oxidation event about 0.65 billion years ago, so 0.65 × 10⁹ < T _L < 2.5 × 10⁹ years.

FIG. 1.

History of oxygen content of Earth's atmosphere, which is observable from great distances (Wikipedia Commons). Dashed line is the present value.

Therefore, an ET civilization that passes nearby can see that there is an ecosystem here due to the out-of-equilibrium atmosphere. They could send interstellar probes to investigate.

The time that Lurkers would be in the solar system, T _L, will be limited by the lifetime of the orbits they are in, which provides an upper bound. The Moon, Earth Trojans, and co-orbitals of Earth lifetimes are as follows:

2.4.2.1. The Moon

Our Moon is thought to have formed about 4.5 billion years ago. For T _L, we use the time that life became evident in our atmosphere, 0.65 × 10⁹ < t ₁ < 2.5 × 10⁹ years.

2.4.2.2. Earth Trojans

There may be many objects in the Earth Trojan region (Malhotra, 2019). Their lifetime in Trojan orbits is likely to be on the order of billions of years, and some objects there may be primordial, meaning that they are as old as the solar system because of their very stable orbits about the Lagrange points (Ćuk et al., 2012; Dvorak et al., 2012; Marzari and Scholl, 2013; Zhou et al., 2019).

The only Earth Trojan yet discovered is TK₇. Its closest approach to Earth is about 70 times the Earth–Moon distance. It oscillates about the Sun–Earth L₄ Lagrange point, ∼60° ahead of Earth (Wiegert et al., 1997). It is not a primordial Earth Trojan and is estimated to have an orbital lifetime of 250,000 years, when it will go into a horseshoe orbit about the sun. It is clear why no other Trojans of the Earth have been found up to now: they are hard to observe from Earth.

There are large stable regions, so Trojans may exist for long timescales. It is possible that primordial Earth Trojans exist in the very stable regions around the Lagrange points. Orbital calculations show that the most stable orbits reside at inclinations <10° to the ecliptic; there, they may survive the age of the Solar System, ∼2.5 Gyr.

Note the recently discovered asteroid trailing behind Mars with a composition very similar to the Moon's (Christou et al., 2021). The asteroid could be an ancient piece of debris, dating back to the gigantic impact that formed the Moon. This suggests that we might find implications for finding such primordial objects in the Earth Trojan locations at L4 and L5.

2.4.2.3. Earth co-orbitals

See Benford (2019) for a discussion of the co-orbitals of Earth. A large number of tadpole, horseshoe, and quasi-satellites of Earth appear to be long-term stable. Morais and Morbidelli (2002) used models of main asteroid belt sources to provide the co-orbitals and their subsequent motions, estimating lifetimes to run between 1 thousand and 1 million years. They conclude that the mean lifetime for them to maintain resonance with Earth is 0.33 million years. Morbidelli (pers. comm.) says that no further studies have been done on their approach. Note that almost all of the co-orbitals have been discovered and their orbits quantified since the Morais and Morbidelli work. In addition, software for orbital calculations have become vastly more capable since then.

3. Scenarios for Success Ratio Estimates

Here, we show several scenarios, some of which show that the two strategies, SETA and SETI, are competitive.

3.1. Scenario 1: Choosing through relative costs at equal ranges

Assume the following:

The ratio of fractions of ET civilizations would be proportional to the cost of interstellar probes versus beacons. The cost of interstellar probes will be substantially more than the cost of interstellar beacons. Stated differently, beacons will have a substantially longer range for a fixed cost.

R _L and R _C are equal.

f we take, as an example, a beacon at 100 ly and a Lurker probe launched from 100 ly, then R _L and R _C in Eq. (5) cancel out. For beacons that have a range of 100 ly, the cost is of the order of $1 billion. This is from extrapolations based on current cost scaling and costs (Benford et al., 2010; Billingham and Benford, 2014). The Firefly interstellar fusion rocket has an estimated cost of $60 billion. Two thirds of that cost is for fuel to accelerate and decelerate (A. Lamontagne, pers. comm.). Therefore, the cost ratio is ∼100 in favor of beacons. If cost is the deciding factor, then f _P/f _R = 1/100 and Eq. (5) reduces to

\frac{N_{L}}{N_{C}} \approx \frac{1}{100} \frac{T_{L}}{T_{R}}

(7)

Next, one chooses an orbital location for the Lurker: our Moon is thought to have formed about 4.5 billion years ago, long before life appeared. Therefore, we use the time that life became evident in our atmosphere, 0.65 × 10⁹ < T _L <2.5 × 10⁹ years.

Next, one guesses the transmit time of the beacon: estimates of civilization radiating times T _C vary from ∼300 to 10⁵ years. Here, the “dash” means the range of credible values: $\frac{N_{L}}{N_{C}} \approx \frac{1}{100} \frac{[10^{9} - {2.510}^{9}]}{[300 - 10^{5}]} ≅ 1 0^{2} t o 1 0^{5}$ (8)

Therefore, for these parameter choices, a Lurker search is much more likely to be successful. Note, however, if we assume that the beacon civilization is at 100 ly and the probe-building civilization is at 10 ly, a factor of 1/1000 reduces the ratio to 0.1 to 100.

3.2. Scenario 2: What if cost does not matter?

That would be at variance with all that we know of economics on Earth, but it is a hypothetical possibility that we could consider. If cost does not matter, then a civilization wanting to investigate life of Earth or whether civilization was here could build probes to investigate the ecosystem, visible in spectra of our atmosphere, and also build beacons to broadcast to us. In such a case, f _P/f _R = 1, and as we are talking about a single civilization, R _L/R _C = 1. Consequently, the success ratio N _L/N _C = T _L/T _C, which would surely be >>1. Again, the lurker strategy is likely to be more successful. In this scenario, the time ratio is the important factor.

3.3. Scenario 3: Early spacefaring civilizations

A civilization such as ours, which is presently capable of only interplanetary speeds, cannot build interstellar probes as envisioned by some of our starship concepts. Starships are centuries into our future and will always be more expensive than beacons. They might build beacons and be only a radiating society. In this case, the success ratio N _L/N _C = 0, and a listen-only strategy is appropriate.

3.4. Scenario 4: Supercivilizations capable of fast interstellar flight

The opposite extreme from scenario 3 is a civilization where starships can travel at a large fraction of the speed of light. In this case, beacons, although still cheaper, would serve to reveal our civilization only if we respond by sending a message back to them. At about the same time, their probes would be arriving and could be reporting the existence of our civilization. This could have occurred over geological time frames, so in this case, N _L/N _C >> 1, and we would expect to find dead Lurkers on the nearby objects described in section 2.4.2 (Estimates of T _L, the time that Lurkers could reside in the solar system).

3.5. Scenario 5: Lurkers in co-orbitals and short radiating time

Instead of a Trojan or the Moon, we choose one of the co-orbitals, which have a mean lifetime T _L of ∼0.33 million years. (1) For T _R, choose the 300-year lifetime estimate of Shermer for the beacon to radiate. Then, T _L/T _R = 1000. (2) Let us assume that starship probes are launched from a civilization 10 ly away (a probe such as Firefly, traveling at 0.2 c and decelerating into our solar system, would take 50 years to reach 10 ly). (3) Assume the beacon civilization is at 100 ly and the probe-building civilization is at 10 ly, then R _L/R _B = 0.1. (4) Furthermore, again assume that the willingness of civilization to undertake the expense would be determined by economics. A continuous beacon at hundred light-years would cost about $1 billion and a Firefly probe is estimated to cost $60 billion (M. Lamontagne, pers. comm.), so f _P/f _R = 0.01. Therefore, the success ratio, Eq. (5), is $\frac{N_{L}}{N_{C}} = \frac{f_{i p}}{f_{R}} \frac{T_{L}}{T_{R}} {[\frac{R_{L}}{R_{B}}]}^{3} = \frac{(0.01) (1000)}{1000} ≅ 0.01$ (9)

For this case, listening to stars has a higher success ratio. However, if one assumes that the radiating civilization also develops interstellar probes, f _R∼f _p, the two strategies have a roughly equal success ratio: $\frac{N_{L}}{N_{C}} = \frac{(1) (1000)}{1000} = 1$ (10)

Therefore, one's assumptions of the parameters in the Table 4.

3.6. Estimate 6: Lurkers in co-orbitals and long radiating time

If we use the band of estimates in the literature for the co-orbital lifetime, ∼10⁵ years, and estimates of civilization radiating times T _C vary from 10² to 10⁵, then T _L/T _R varies from 1 to 1000. For the previous 100 ly/10 ly distance ratio, Eq. (5) then gives a Drake equation ratio of $N_{L} ∕ N_{C} = f_{I P} ∕ f_{R} [1 0^{- 3} t o 1]$ (11)

Consequently, the listening strategy will be preferred.

It is clear from these scenarios that (1) the two strategies, SETA and SETI, are competitive and (2) the Moon and the Earth Trojans have a greater probability of success than the co-orbitals.

4. Stars Passing by Our Sun

It is not widely known that stars come very close to our solar system frequently. About two stars per million years come within a light-year. The most recent encounter was Scholz's Star, which came 0.82 light-years from the Sun about 70,000 years ago (Mamajek et al., 2015). A star is expected to pass through the Oort Cloud about every 100,000 years (Bailer-Jones et al., 2018).

A suggestion for SETI observers: look at the specific stars that have passed our way in the last 10 million years and ask how many of them are “sunlike” and/or are known to have habitable planets. Observe those stars closely for possible emissions to Earth (Benford, 2021).

5. Research for Finding Alien Artifacts

I advocate a sequence of tasks:

We have had the Lunar Reconnaissance Orbiter (LRO) in low orbit around the Moon since 2009. It has taken about 2 million images at high submeter resolution (M. Revine, pers. comm.). We can see where Neil Armstrong walked! The vast majority of the photos have not been inspected by the human eye. Searching these millions of photographs for alien artifacts would require an automatic processing system. Development of such artificial intelligence (AI) is a low-cost initial activity for finding alien artifacts on the Moon as well as Earth Trojans or the co-orbitals (Davies and Wagner, 2013; Lesnikowski et al., 2020). Note the recent AI analysis of 2 million images from LRO, which revealed rockfalls over many regions of the Moon (Bickel et al., 2020).

Conduct passive SETI observations of these nearer-Earth objects in the microwave, infrared, and optical.

Use active planetary radars to investigate the properties of these objects.

Conduct active, simultaneous, planetary radar painting and SETI listening of these objects.

Launch robotic probes to conduct inspections and take samples of Earth Trojans and the co-orbitals. The low delta-V, 3–5 km/s, making this an attractive early option, is well within present capability (Stacey and Conners, 2009; Chandrakanth et al., 2019). China plans a mission to co-orbital 2016 HR 3 in the middle of this decade (Zhang et al., 2019).

6. Conclusion

Clearly, looking for alien artifacts in the region of the Solar System near Earth is a credible alternative approach, a strategy of ETI archeology. The formulation given here is a way of discussing the SETA strategy and comparing it with SETI.

The listening to stars strategy that SETI researchers have been following for over 50 years is now being pursued very vigorously by Breakthrough Listen. What has SETI learned so far about life in the Universe? Only that there is no intelligent life broadcasting signals toward Earth at the time we have listened, within the sensitivity levels, duty cycles, and frequencies that we have observed. If the ongoing SETI listening program continues to not hear a signal, the case for looking for Lurkers will grow ever stronger.

The SETA strategy was not pursued after it was suggested in the 1980s because listening to stars is easier and observing technologies and spacecraft were not sufficiently developed to pursue it. However, now, SETA is more attractive.

Close inspection of bodies in these regions can now be done with 21st century observatories and spacecraft.

The great virtue of searching for Lurkers is their lingering endurance in space, long after they go dead.

The Moon and the Earth Trojans have a greater probability of success than the co-orbitals. Estimates of how many probes could have come here from passing stars and where would they be found are in J. Benford (2021).

They may hold primordial remnants of our early solar system, so searching yields concrete astronomical research. It can yield new astronomy and astrophysics data, quite apart from finding Lurkers.

There are differences in detection in the two strategies: in the artifact case, we should listen to those objects and image them in the optical or radar from Earth or send probes to visit them. In SETI, we can only listen.

SETA is a concept that can be falsified, a fundamental requirement for science. SETA can be falsified or verified in practice by precisely specifying what one is looking for. For example, the statement “No artificial objects larger than 1 m exist on the surface of the Earth Trojan” can be verified by observing that object at that resolution. Smaller objects would not be resolved. If we conduct the efforts described in section 5 (Research for Finding Alien Artifacts) and do not find artifacts, the SETA concept is disproven for the near-Earth region where it is most credible. If we find them, it is verified.

Footnotes

Acknowledgments

The author gratefully acknowledges funding by the Breakthrough Prize Foundation and is thankful to Gregory Benford, Paul Davies, Paul Gilster, Robert Freeland, Robert Freitas, Michel Lamontagne, Kelvin Long, Greg Matloff, and David Messerschmitt for comments. Special thanks to the reviewers for suggesting improvements.

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work was funded by the Breakthrough Prize Foundation.

Abbreviations Used

Associate Editor: Christopher McKay

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A Drake Equation for Alien Artifacts

Abstract

1. Introduction

2. Drake Equations

2.1. The standard Drake equation

2.2. A Drake equation for alien artifacts

2.3. Space volume factor

2.4. Decision tree parameters

2.4.1. Estimates of T R, the time that ET beacons radiate

2.4.2. Estimates of T L, the time that Lurkers could reside in the Solar System

2.4.2.1. The Moon

2.4.2.2. Earth Trojans

2.4.2.3. Earth co-orbitals

3. Scenarios for Success Ratio Estimates

3.1. Scenario 1: Choosing through relative costs at equal ranges

3.2. Scenario 2: What if cost does not matter?

3.3. Scenario 3: Early spacefaring civilizations

3.4. Scenario 4: Supercivilizations capable of fast interstellar flight

3.5. Scenario 5: Lurkers in co-orbitals and short radiating time

3.6. Estimate 6: Lurkers in co-orbitals and long radiating time

4. Stars Passing by Our Sun

5. Research for Finding Alien Artifacts

6. Conclusion

Footnotes

Acknowledgments

Author Disclosure Statement

Funding Information

Abbreviations Used

References

2.4.1. Estimates of T _R, the time that ET beacons radiate

2.4.2. Estimates of T _L, the time that Lurkers could reside in the Solar System