Abstract
No intelligent beings from space are present on Earth; no evidence of alien civilizations has been observed. The Fermi Paradox is one of the most mysterious questions in astronomy. In the past two decades, thousands of exoplanets have been discovered, and a fraction of them are habitable. The newly detected planetary system may provide clues to the resolution of the Fermi Paradox. Reviewing the discovery of Newton’s law of universal gravitation, it is clear that observations of planetary motion have played an irreplaceable role. However, many habitable planets discovered recently are in significantly perturbed orbits, especially those in compact planetary systems with cool red dwarfs as their host stars. Alien, intelligent beings, even if existing there, might have no way to acquire the knowledge of gravity and to develop the technology necessary for space travel.
Introduction
The Nobel Prize in Physics 2019 awarded the first discovery of an exoplanet orbiting a Solar-type star. The exoplanet, 51 Peg b, was discovered via a radial velocity technique in 1995 by Swiss astronomers Michel Mayor and Didier Queloz[1]. In the following two decades, detection techniques have been rapidly developed, yielding over 4,000 confirmed exoplanets[2]. Exoplanetary systems exhibit great diversity, a quality which has greatly enhanced our understanding of the formation and evolution of the planetary system.
Considering the existence of long-lived liquid water on planetary surfaces, astronomers defined habitable zones around stars as where the equilibrium temperature is between water’s freezing and boiling points. Terrestrial planets in orbits inside habitable zones are the most interesting, since organisms might survive and develop there. Currently, over 50 potentially habitable exoplanets have been discovered[3]. Although no evidence of aliens has been detected, observed alien nurseries exist and are in fact not too far from Earth in terms of cosmic distance.
The age of the universe is about 14 Gyr, which is much longer than the time required for evolution and the development of intelligent beings. Since habitable planets could be abundant, intelligent beings could exist and have the capability to travel through the Milky Way. In such a long time of cosmic age, they would have enough time to visit every habitable planet in the Milky Way. However, the fact is that we observe no intelligent beings from outer space now present on Earth. The apparent contradiction between the lack of evidence for alien civilizations and various high estimates for their probability was mentioned as early as 1950 by Physicist Enrico Fermi. This phenomenon was then widely known as the Fermi Paradox.
There have been many attempts to explain the Fermi Paradox. As stated by Michael H. Hart[4], the question is perhaps the most significant of all questions in astronomy. Astronomers must therefore do their best to include all relevant observational data. The newly detected exoplanetary systems might provide us more clues to resolve this question.
This work provides a new opinion on the resolution of the Fermi Paradox: many habitable planetary systems might have significantly perturbed orbits, thus intelligent beings there cannot acquire the knowledge of universal gravitation from regular planetary motion, prohibiting the invention of spacecraft technique.
Planetary Motion & Universal Gravitation
In the early 1600s, Johannes Kepler laid the groundwork for modern celestial mechanics using an empirical approach (see Solar planetary orbits in Fig1 and Fig2). Through studying complex, planetary-motion observations in the Solar system, including those made by Tycho Brahe, Kepler deduced three laws of planetary motion: 1) the planets move in ellipses with the Sun at one focus; 2) a radius vector from the Sun to a planet sweeps out equal areas in equal intervals of times; 3) the square of the orbital period of a planet is proportional to the cube of its semi-major axis[5].
Fig1. Orbits of inner planets projected in the ecliptic plane. The positions of Mercury, Venus, Earth and Mars are presented as the date of October 1st, 2020. Produced with poliastro [6].
Fig2. Orbits of planets projected into the ecliptic plane. The positions of all planets are presented as the date of October 1st, 2020. Produced with poliastro [6].
In 1687, Isaac Newton proposed that the magnitude of the attractive force (gravity) between any two mass points in the universe is directly proportional to the product of their masses and inversely proportional to the square of the distance between them, as:
Planetary motion is a natural consequence of gravity, obeying Newton’s three laws of motion: 1) without action by a force, free bodies remain in a state of rest or motion in a straight line with uniform velocity; 2) the force experienced by a body changes its state of motion, quantitatively equating to its momentum’s rate of change; 3) action and reaction are equal but in opposite directions[5]. Newton’s theory creatively marks the unification of gravity on Earth with planetary motions and has a profound effect on our understanding of the universe.
Three hundred years after the discovery of Newton’s law of universal gravitation, human beings developed proud technology for space travel, successfully visiting every planet in the Solar system[7].
Complex Motions in Planetary Systems
The motion of two masses under their mutual gravitational attraction can be analytically solved. Their orbits are closed in the form of conic curves, which are stable and predictable. The simplicity would collapse with even one additional mass joining the system. It is well known that the general three-body problem is unsolvable, behaving in chaos for long-term evolution.
In systems with multiple planets, any individual movement under the gravitational attraction from its host star adds up attraction from other planets. In principle, any multi-planetary system descends into chaos for a long time. Our Solar system is stable in human terms, most of its main planets moving in paths very close to the orbits of two-body solutions. Thus, Johannes Kepler was able to deduce three laws of planetary motion, leading to the discovery of Newton’s law of universal gravitation. However, the main planets might collide with others or plunge into the Sun after one billion years in the future, as suggested in numerical simulations[8].
Recently, astronomers are focused on searching for habitable planets around red dwarfs with 10% Solar mass. This kind of habitable planetary system is much easier for detection since the planet-induced signals[9] of small, host stars are more observable in practice. These systems are usually compact in architecture. The planets’ orbits are closer to each other compared to in the Solar system, as small, host stars are not as strong as the Sun and cannot dominate a full gravitational field. Thus, their planets move in paths that significantly deviate from Kepler’s orbits (Fig3). In systems appearing planetary transits, the perturbed planetary orbits are commonly observed via the transit timing variations (TTVs)[9].
Fig3. Numerical Simulation of planetary orbits in a system with four Earth-mass planets. This figure is for illustration purposes only. Produced with simulator in MinuteLabs.io [10].
The Planetary System of TRAPPIST-1 As An Example
The central star of this system is an ultracool dwarf with only 8% Solar mass. A high-cadence, photometric, monitoring campaign reveals transits of seven, terrestrial planets around the star[11]. All seven planets are temperate, probably preserving long-lived liquid water on their surfaces in at least some regions. Their habitability makes the planets in this system so attractive to astronomers. The planetary system is quite compact (Fig4); the size of most outer orbits is about 0.06 AU (an astronomical unit equivalent to the average distance from Earth to the Sun), smaller than the orbit of Mercury in the inner Solar system. High-amplitude TTVs have been observed in this system, suggesting that the planetary orbits are significantly perturbed.
Fig4. The planetary system around the ultracool dwarf TRAPPIST-1. Seven terrestrial planets have been discovered in compact orbits. Orbital elements of planets are adopted from the best-fit values in the discovery paper [11].
In order to study the motion of these planets, “Mercury,” a FORTRAN N-body integrator, was utilized for a numerical simulation[12]. Assuming a coplanar configuration and circular orbits, the other initial statuses of this system are set up as:
|
Planet |
Mass |
Period |
Semi-Major Axis |
Mean Anomaly |
|
(Earth Mass) |
(Days) |
(AU) |
(Degree) |
|
|
b |
0.85 |
1.51 |
0.011 |
0 |
|
c |
1.38 |
2.42 |
0.015 |
217 |
|
d |
0.41 |
4.05 |
0.021 |
303 |
|
e |
0.62 |
6.10 |
0.028 |
140 |
|
f |
0.68 |
9.21 |
0.037 |
322 |
|
h |
1.34 |
12.35 |
0.045 |
271 |
|
g |
1.00 |
20.00 |
0.063 |
1 |
Table 1. The initial conditions for numerical integrator in planetary system TRAPPIST-1. Masses and Orbital elements of planets are adopted from the best-fit values in the discovery paper [11].
Two sets of simulations were performed in this work: long-term, dynamical evolution simulation and short-term perturbation simulation.
The period of long-term simulation is set as 10,000 years, equivalently over a million orbits for the planets in this compact system. The fluctuations of their semi-major axes are present in Fig5. Apparently, no collisions between these planets occurred in this long time, and the planets stayed close to their initial orbits. Thus, the planetary system of TRAPPIST-1 can remain stable for at least 10,000 years. In the work of Gillon et al.[11], long-term stability has been studied with more intense simulations, suggesting that the dynamical lifespan of this planetary system is 0.5 million years. However, the results are very sensitive to the precision of planetary masses and initial orbital elements, which cannot be well determined currently.
Fig5. The evolution of the planetary system TRAPPIST-1. In 10,000 years, the semi-major axes of planetary orbits just vary slightly, thus no collisions or disruptions are expected.
The short-term perturbation simulations are designed to illustrate the deviation of planetary motions from Kepler’s orbits. The period of simulation is 30 days and a fine time step is applied to preserve the details of motion. The mean anomalies of seven planets are presented with color curves in Fig6, comparing with their Kepler orbits (black dashed curves). Deviations between them are very prominent. Thus, observers living on these planets have no way of deducing Kepler’s law from the motion of planets in this system.
Fig6. The Evolution of the planetary system TRAPPIST-1. The period of simulation is 30 days. Mean anomalies (color curves) deviate greatly from Kepler’s orbits (black dashed curves) for all the seven planets in the system.
Conclusion: Many Alien Civilizations without Knowledge on Gravity
For human beings, observations of planetary motion in the Solar system enabled the discovery of Kepler’s law and further enlightened Newton’s law of universal gravitation. For an alien world, especially in the compact, multi-planet systems, intelligent beings there might have no way of acquiring the knowledge of gravity via observing the irregular movements of their planets. The lack of critical knowledge prohibits many alien civilizations from developing spacecraft to travel in the Milky Way. Considering that compact planetary systems may dominate the population, this opinion could be valuable towards the resolution of the Fermi Paradox.
Acknowledgments
The author appreciates the enlightening suggestions from Dr. Peng Jiang, an astronomer at the Polar Research Institute of China. His advice and insights have been invaluable for this work.
Reference
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[3] Habitable Exoplanets Catalog. “Habitable Exoplanets Catalog.” Accessed October 1, 2020. http://phl.upr.edu/projects/habitable-exoplanets-catalog/
[4] Hart, Michael H. 1975. “Explanation for the Absence of Extraterrestrials on Earth.” Quarterly Journal of the Royal Astronomical Society, 16: 128-135. https://ui.adsabs.harvard.edu/link_gateway/1975QJRAS..16..128H/ADS_PDF
[5] Murray, Carl D. and Dermott, Stanley F. 1999. Solar System Dynamics. Cambridge, UK: Cambridge University Press
[6] Poliastro. “Astrodynamics in Python.” Accessed October 1, 2020. https://docs.poliastro.space/en/stable/
[7] List of Solar System Probes. “List of Solar System Probes.” Accessed October 1, 2020. https://en.wikipedia.org/wiki/List_of_Solar_System_probes
[8] Lecar, Myron, Franklin, Fred A., Holman, Matthew. J. and Murray, Norman J. 2001. “Chaos in the Solar System.” Annual Review of Astronomy and Astrophysics, 39: 581-631. https://doi.org/ 10.1146/annurev.astro.39.1.581
[9] Perryman, Michael. 2018. The Exoplanet Handbook by Michael Perryman. Cambridge University Press. Second Edition
[10] MinuteLabs.io. “Chaotic Planets.” Accessed October 1, 2020. http://labs.minutelabs.io/Chaotic-Planets/
[11] Gillon, Michael, Triaud, Amaury H. M. J., Demory, Brice-Olivier, Jehin, Emmanuel, Agol, Eric, Deck, Katherine M., Lederer, Susan M., et al. 2017. “Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1.” Nature, 542: 456-460. https://doi.org/10.1038/nature21360
[12] Chambers, J. E. 1999. “A hybrid symplectic integrator that permits close encounters between massive bodies.” Monthly Notices of the Royal Astronomical Society, 304: 793-799. https://doi.org/10.1046/j.1365-8711.1999.02379.x
About The Author
Jing Liu is a high school student who is significantly inspired by physics to conduct scientific researches. He simulated the Hohmann Transfer Orbit from Earth to Mars during a program advised by prof. Gregory Tucker at Brown University. That work has been accepted for publication on ICJE. He also led teams to study alien civilizations and properties of dark matter in universe.