Galaxies look fixed in astronomical photos, but of course they’re dynamic systems ever in motion. The closest stars to Earth at Alpha Centauri will eventually close to within about 3 light years if we wait thirty thousand years or so. After that, as the system moves away again, Ross 248 will emerge as the closest interstellar target, closing to about the same distance before moving off into the night. But that will require waiting a bit longer, on the order of another 6000 years. We might also keep an eye on Gliese 445, which in 46,000 years or so will close to less than 4 light years of the Sun.
So everything is moving all the time, and we can say something more about future encounters. The REsearch Consortium On Nearby Stars (RECONS) has found that within the local 10-parsec volume, 81 percent of the 357 main sequence stars in its stellar census are less than half as massive as the Sun. That’s about the current estimate for the percentage of stars in the galaxy that are M-dwarfs, and we might expect that most close passages to our system have been and will be with this type of star.
The average distance between these stars is 3.85 light years, which again is close to what we see locally, since the Alpha Centauri stars are not far beyond that range from us. In this collection of stars, 232 single-star systems appear, and 85 multiples. This has led to interesting speculations, such as Bradley Hansen and Ben Zuckerman’s work at UCLA arguing that if stars get close enough, interstellar flight between them is more feasible. Suppose a star at 14,000 AU and the prospect seems more workable.
Stars do indeed get that close, as the example of Gliese 710 shows. If we’re patient, we can wait out the 1.3 million years it is projected for this to happen, for this star, on the borderline between M-dwarf and K-class, is headed our way from its current vantage in the constellation Serpens Cauda. As it will eventually be well inside the Oort Cloud, we can imagine quite an impact on cometary orbits and planetary ones as well over the long haul, as the paper I’m about to discuss shows. But before leaving Hansen and Zuckerman, let me mention that they calculate that if we widen the timeframe to a billion years, the likelihood of a star getting as close as 5000 AU is 81 percent.
Now let’s flip the question backward in time. Scholz’s Star (WISE J072003.20-084651.2) moved near our system about 70,000 years ago, reaching by current estimates somewhere between 52,000 AU and 68,000 AU from the Sun. Here we’ve got a binary consisting of an M-dwarf and a probable brown dwarf companion at 0.8 AU.
Image: Now about 20 light years away, Scholz’s Star (red star in the center) and its brown dwarf companion passed close to the Solar System and remained within 100,000 AU for a period of roughly 10,000 years. Image Credit: ESO VPHAS / Wikimedia Commons CC BY-SA 4.0.
Nathan Kaib (Planetary Science Institute) and Sean Raymond (Laboratoire d’Astrophysique de Bordeaux, CNRS) have gone to work on the question of passing stars as it relates to the Solar System’s evolution. Study the changes that have occurred in Earth’s climate over the millennia and it appears that fluctuations in the eccentricity of Earth’s orbit are involved. Kaib points to a specific episode that is illuminated by the analysis in this paper:
“One example of such an episode is the Paleocene-Eocene Thermal Maximum 56 million years ago, where the Earth’s temperature rose 5-8 degrees centigrade. It has already been proposed that Earth’s orbital eccentricity was notably high during this event, but our results show that passing stars make detailed predictions of Earth’s past orbital evolution at this time highly uncertain, and a broader spectrum of orbital behavior is possible than previously thought.”
So we’re digging into the history of our planet’s orbit, along with that of the other planets. The authors’ research shows that stellar encounters are not uncommon. A star passes within 50,000 AU on average every million years, and within 10,000 AU every 20 million years. To study the matter, Kaib and Raymond use a hybrid integrator – a set of specialized numerical methods – called MERCURY to simulate these encounters, under conditions described in the paper. The computer runs show that orbital changes to Earth do indeed result, or are at least accelerated, by perturbations from other stars.
Complicating these calculations is the fact that orbital evolution is chaotic, so that beyond timescales on the order of 100 million years, it is impossible to do more than characterize it statistically. The authors point out that even the long-term stability of the Solar System is not guaranteed, as over the Sun’s lifetime there is a 1 percent chance that Mercury will be lost by collision with either the Sun or Venus.
Earth’s past or future orbital evolution can only be confidently predicted inside a time horizon much shorter than Earth’s age, as small uncertainties in current planetary orbits eventually lead to dramatically divergent behavior. The time horizon set by the internal chaos among the Sun’s eight planets is ∼70 Myr, but additional strong chaos resulting from encounters between large asteroids shortens the horizon by another ∼10 Myr (Laskar et al. 2011b). However, inside this time horizon, backward integration of the Sun’s planets has been used to predict the detailed past orbital evolution of the Earth (Laskar et al. 2004).
Such perturbations make it difficult to pin down Earth’s orbital evolution the farther back in time we go, and it appears as well that perturbations from asteroid interactions are less significant than stellar encounters in degrading our ability to predict orbital changes. That’s useful information, because most simulations of the long-term evolution of the planetary orbits have modeled the Solar System in isolation. Changes in Earth’s orbit can also be the result of interactions with the giant planets, but a passing star can affect their orbits, which in turn impacts Earth’s orbital trajectory. Indeed, adding the giant planets to the simulations shows what a major factor these worlds are on Earth’s orbit once they themselves are perturbed by the passing star. Kaib and Raymond call them “a dynamical link that ultimately allows the Milky Way’s stars to influence the long-term evolution of Earth’s orbit.”
The paper turns to a specific encounter, that with the star HD 7977, which is a G-class star in Cassiopeia now some 250 light years away. 2.8 million years ago, this star moved past the Solar System at about 27 kilometers per second, its trajectory taking it somewhere in the neighborhood of 13,200 AU from the Sun, although the authors point out the wide cone of uncertainty about the distance, which may have been as little as 3900 AU. The ‘impulse gradient’ that shows the level of perturbation to the planets was over an order of magnitude higher than the norm during this time.
Working this into their models, the authors find that the median value of 13,200 AU would have had little effect on the Solar System’s long term chaotic evolution, but a passage at 3900 AU would have affected the eccentricity of Earth’s orbit. This is in addition, of course, to whatever effect such a close passage would have on Oort Cloud objects. A passage at 3900 AU would be one of the ten most powerful encounters experienced in the history of our system given the star’s above average mass and an encounter velocity that is below the average.
Image: Illustration of the uncertainty of Earth’s orbit 56 million years ago due to a potential past passage of the Sun-like star HD7977 2.8 million years ago. Each point’s distance from the center corresponds to the degree of ellipticity of Earth’s orbit, and the angle corresponds to the direction pointing to Earth’s perihelion, or closest approach distance to the Sun. 100 different simulations (each with a unique color) are sampled every 1,000 years for 600,000 years to construct this figure. Every simulation is consistent with the modern Solar System’s conditions, and the differences in orbital predictions are primarily due to orbital chaos and the past encounter with HD 7977. Credit: N. Kaib/PSI.
What’s notable here is that the authors have demonstrated that stellar encounters can be significant drivers for system evolution, an area not as widely studied as the internal dynamics of the Solar System. Here’s their conclusion:
…stellar encounters significantly accelerate the chaotic diffusion of Earth’s orbit and the time back to which numerical simulations can confidently predict Earth’s orbital evolution is ∼10% shorter than previously thought. Second, this chaotic divergence that stellar passages impart on Earth’s orbit results from their perturbations to the giant planets’ orbits, and these perturbations roughly scale with the velocity impulse gradients of stellar encounters. Third, the known encounter with HD 7977 2.8 Myr ago has the potential to unlock new sequences of Earth’s past orbital evolution beyond 50 Myr ago that have not been considered or generated in previous modeling efforts. Although it takes tens of Myr for the effects of stellar passages to significantly manifest themselves, the long-term orbital evolution of the Earth and the rest of the planets is linked to these stars.
We seem to have overestimated our ability to describe Earth’s orbital state in earlier eras given what we’re learning about the disruptive effects of stellar encounters. These close brushes with other stars can potentially cause changes in eccentricity that have been overlooked. Factoring stellar encounters into future models is going to be complicated, and necessary.
The paper is Kaib & Raymond, “Passing Stars as an Important Driver of Paleoclimate and the Solar System’s Orbital Evolution,” Astrophysical Journal Letters 962 (14 February 2024) L28 (full text). The Hansen and Zuckerman paper I mentioned above is “Minimal conditions for survival of technological civilizations in the face of stellar evolution,” Astronomical Journal Col. 161, No. 3 (25 February 2021) 145 (full text). See also Bobylev & Bajkova, “Search for Close Stellar Encounters with the Solar System Based on Data from the Gaia DR3 Catalogue,” Astronomical Letters Vol. 48 (13 February 2023), 542-549 (abstract).
If my math is right, a passage of HD 7977 at 3900 AU should have reached an apparent magnitude of -8.97, comparable to a gibbous moon. At the more probable distance of 13200 AU, I get the magnitude would be -3.67, more comparable to a crescent, but nonetheless hard to miss for some of the early putative members of the human genus at the beginning of the Stone Age. For so many centuries the passages of Moon and Star would have been always in their thoughts.
A fascinating thought!
Evolution of speech in humans
I hope that readers will forgive my brief rant. But this has been going on for too long to ignore.
Do not include the search engine user tracking aids in the links you provide. Learn how to cite the direct URL for the page if you continue use of that particular service, or use a search engine that respects my privacy. There are many of those.
Until then I will continue to ignore and avoid the links you include in your comments.
What worries me is if Gliese 710 has any companions that orbit it far out.
They could wind up in our back yard, as it were.
I wonder how this star would have affected the development of Astronomy, if its close passage had occurred during Classical times.
By Classical times there were many elaborate lunar and solar calendars already, so I think HD 7977 likely had the most impact passing when it did. Imagine that early human ancestors, though aware of the Moon, did not yet keep track of the little dots in the sky. (OK, there was probably one in the crowd somewhere, but lacking a critical mass of communications and interest) Well, once there was a month of the year without a completely dark starry night for the hyenas to sneak up on people … that had to be noticeable. Once Star got their attention, they wouldn’t have to carve a calendar stone and count cycles of days, but merely look where Star was relative to the full Moon by night, or the Sun by day. Or observe the phase of the Moon each time it passed closest to Star. I’d now suspect many of the practical benefits of ancient astronomy could have been accessible at the dawn of humanity: predicting prey behavior for hunting, plant availability for gathering produce and replanting seeds, and coordinating annual meetings for war bands.
The evolution of language seems harder to infer. In modern times we have click languages, sign languages… many options. I know little of linguistics, but from what I understand a consonants-first hypothesis has been dominant. However, when I think of the ape sounds I’m like to make when fumble-fingering fragile objects or losing footing on a hillside, or laughing, or the wide variations of ‘intonation’ that convey different meanings to a letter like the O in “forty” depending on whether someone is underwhelmed by a sale price or terrified of a group of criminals, they all seem mostly like vowels to me. So I’m not sure I believe people who say that a given ancestor could or couldn’t speak based on a few bones. I do think some practical astronomy would have given them more interesting things to talk about!
P.S. Ron: you are technically right on the links. But search engine links are bad primarily because there’s no telling what someone will see – the link above led me to a Google text about speech evolving 50,000 years ago, but I think Robin intended to support a hypothesis about 2.8 million years ago. And as for “privacy”……! Assange is in jail, the newspapers preen about helping jail leakers rather than publishing their stories, few know what Vault 7 was even about, and the leading “pro-privacy” reform is an “HTTPS Everywhere” push that demands web site operators file their ID cards with the ‘trusted third parties’ who control the security of your communications. I could go on … Criticizing spy codes in a link nowadays is like telling people in Gaza not to litter.
Human speech likely started in the region of 2.8 Mya and may have expressed the genral descriptions, even if finer descriptions and nuance may have evolved later. Sadly, accuracy in transmission falls off with time in exclusively verbal communication.
One legend among one artic native people retold over generations verbally and only written down in later centuries speak of ‘Another Sun shining with strange red beams of light’.
But 70 000 years ago, I am hesitant to say that’s a match.
Yet the legend is found in print long before Scholz star had been discovered in 2013.
There’s other old stories that seem to indicate that verbal tradition can pass on details over a very long time, there’s a native american people who claim to have myths describing the Mammoth.
I have to wonder how that close passage impacts the search for the putative ninth planet & the entire dynamics of the Kuiper Belt.
For that matter, how many objects might the two stars have exchanged? Might our Oort (or even outer Kuiper) be the home of numerous refugees from every prior close stellar encounter?
The Kaib paper on orbital perturbations suggests that the Earth’s orbit was perturbed to cause the Paleocene-Eocene Thermal Maximum (PETM). The geological record shows that CO2 levels rose in both the atmosphere and deep ocean, as well as higher CH4 levels. The record shows a more extreme version in the Permian extinction ascribed to vast volcanism at this time. Idk if there is any evidence for such volcanism around the PETM, but I do wonder if the increased CO2 and CH4 levels might have been due to cometary impacts, rather than a secondary effect of global heating on the biosphere by an orbital perturbation.
A close encounter of a star that perturbed the Oort cloud (or even the Kuiper Belt) could increase the number of comets, some of which might impact the Earth, releasing their volatiles that is associated with global heating and would be more like our own Anthropocene release of excess CO2.
How we could test either theory – orbital perturbation vs comet impacts vs volcanism seems difficult. An impact site would be useful, although small comets like the Tunguska event left no impact, just fallen trees at the time. Any pulse isotopic changes would likely be lost in the record. Any evidence of increased SO2 emissions would favor the volcanism cause, although we know from smaller scale volcanism like the Mt. Pinatubo, and the far greater Krakatoa, events cause global cooling, not heating, due to dust and SO2.
Tangentially, the Oort cloud is inferred from the orbits of the long-period comets. The inference assumes a spherical shell of comets to account for the comets that appear well away from the orbital plane of the planets. However, is it possible that a close-approach star could perturb the Kuiper Belt objects creating the same effect? The objects could be pulled towards either/both the star and the sun, causing the KBO orbit to become far more eccentric and with inclination changes. Is that possible?
Quote from authors in this paper Nathan Kaib (Planetary Science Institute) and Sean Raymond (Laboratoire d’Astrophysique de Bordeaux, CNRS) “One example of such an episode is the Paleocene-Eocene Thermal Maximum 56 million years ago, where the Earth’s temperature rose 5-8 degrees centigrade. It has already been proposed that Earth’s orbital eccentricity was notably high during this event, but our results show that passing stars make detailed predictions of Earth’s past orbital evolution at this time highly uncertain, and a broader spectrum of orbital behavior is possible than previously thought.” This statement is completely false. The Earth eccentricity and obliquity have varied little over the past billion years. There has not been any measurable effect of Earth orbit or eccentricity by interstellar stars in our past due Einstein’s principle of general relativity and Newton’s law of universal gravitation and inverse square law that gravity attenuates inversely proportion to the distance. The gravity of another star at one light year is much weaker than the Sun’s gravity on Earth or Jupiter.
Also the Milankovitch cycles still were the same fifty three million years ago in the Paleogene period. Consequently, the higher temperatures at that time as much as 21 F, or 12 Celsius higher than today were caused by the atmospheric carbon dioxide levels were 1500 parts per million being more than three times higher than today’s 420ppm. https://www.jsg.utexas.edu/news/2023/12/a-new-66-million-year-history-of-carbon-dioxide-offers-little-comfort-for-today/
There were no polar ice caps and ice ages at that time and the sea level was 230 feet higher and there were alligators in the arctic and semi tropical climate in the summer there. These higher levels of atmospheric carbon dioxide have been proven by the sea floor sediments core samples which go back 66 million years, the carbon 12/13 ratios and the boron ratios. The carbon cycle, the solubility of the oceans to absorb carbon dioxide based on ocean water temperature, the Urey reaction through rain which takes more carbon dioxide out of the air, and photosynthesis of carbon dioxide into oxygen from micro organisms, trees and planets have reduced the atmospheric carbon dioxide levels and brought us a balanced, cooler climate. The Milankovitch cycles show we have warm periods and ice ages every one hundred thousand years, so our rising and falling temperatures are the result of more or less sunlight in the northern hemisphere and the carbon dioxide levels rise and fall with amount of sunlight, the rising and falling of temperatures. https://www.carbonbrief.org/explainer-how-the-rise-and-fall-of-co2-levels-influenced-the-ice-ages/
Our climate cycle has been put out of balance by our large emission of anthropomorphic green house gasses. We would still have this same Paleogene period climate today and there would never had been any ice ages and the sea levels would still be 230 feet higher if an interstellar star was responsible a significant change in Earth’s orbital eccentricity.
The idea that interstellar stars have disturbed the stability the Oort cloud comets and sent them into our inner solar system is correct.
Re this: “The Earth eccentricity and obliquity have varied little over the past billion years.”
I strongly recommend that you read the paper to understand how chaotic systems like these do not allow this kind of blanket statement. We can only work with statistical probabilities. The paper’s discussion of the problem is excellent and contains many references to prior work on the matter. Indeed, this is the whole point of the paper.
I apologize for the too general, ambiguous statement: “The Earth eccentricity and obliquity have varied little over the past billion years.” I meant there has been little variance of the Milankovitch cycles, the precession, obliquity, the eccentricity which have remained stable over deep time as astrophysicist William R. Alschuler has commented.
@Geoffrey Hillend, Paul Gilster
Geoffrey, I support your skepticism. The image of the close encounter with HD 7977 implies an eccentricity of perhaps 0.05. It is not clear whether this is added to the current eccentricity of Earth’s orbit of 0.0167, or absolute (but see end para below). If we look at the Milankovich cycle, the eccentricity reaches 0.05 with a temperature increase of 2-6C (but where that temperature is taken from may be different from the global estimate). MilankovitchCyclesOrbitandCores
The Paleo-Eocene Thermal Maximum (PETM) had an increase in the polar temperatures of 12C, around 50 mya. Paleocene–Eocene Thermal Maximum. There is no obvious reason to believe that the Earth’s eccentricity estimated at the 5% probability of 0.05 and equivalent to the existing Milankovich cycle eccentricity of the same size could account for the PETM temperature increase unless it was in addition to to the Milankovich peak eccentricity.
Fossil evidence and cores indicate that the Milankovich cycle was operating during the time of the PETM.
That there were 2 pulses of extreme temperatures seems to invalidate the single encounter of HD 7977 as the cause due to eccentricity changes that were fast to appear and disappear.
The PETM was accompanied by an increase in CO2, possibly caused by the release of subsequently oxidized CH4 from warmed clathrates Other sources of CO2 are possible, including my hypothesized external CO2 inputs from comets due to a perturbation of the Oort cloud or KBOs.
I also note that the Kaib paper states this regarding Earth’s eccentricity:
maybe I am missing something, but I do not see the order of magnitude increase in absolute eccentricity in that statement, just the change metric.
Bottom line for me:
1. The close encounter perturbations of Earth’s orbit depend on how close and how fast the star approaches.
2. The analysis is based on the extremes.
3. The known eccentricity cycles which are the dominant cause of climate change on Earth are in the same range as this stellar approach.
4. The PETM is indicated by 2 short periods of extreme temperature change associated with 2 large increases in atmospheric GHG CO2 which is known from the sediments.
In total, this makes the analysis rather speculative as an explanation of the PETM if a perturbation in Earth’s orbital eccentricity is the proximate cause.
An eccentric bit of news today: https://phys.org/news/2024-03-mars-earth-interactions-red-planet.html Apparently 2.4-million-year “Grand Cycles”, in which interaction with Mars affects the eccentricity of Earth’s orbit, can be correlated with deep sea hiatuses. The paper is fully accessible: https://www.nature.com/articles/s41467-024-46171-5
I am skeptical of the influence of any interstellar close encounters of the past on Earth’s orbit due to aspects of the Earth’s fossil record. The ice core record for Antarctica goes back 1.2 million years. (see the image at: https://www.antarcticglaciers.org/glaciers-and-climate/ice-cores/ice-core-basics/) It shows cycles of warming and heating with a period of about 120,000 years, and this is pretty well explained by the Milankovich cycles of Earth’s orbital eccentricity, polar axis precession, and location along the orbit of northern hemisphere summer with respect to perhelion. Then there is the lower time resolution fossil record that goes back to the beginning. The precambrian explosion of multicellular life shows species that have near relatives today that and imply climatic conditions were similar then. Stromatolites form 3.3 billion years ago are algal/bacterial colonies with a few living relatives (see Shark’s Bay , Australia and the Bahamas) similarly show relative solar and orbital stability. Big influences from near misses by stars should show up in the fossil record, and should have permanently altered Earth’s climate, but we don’t see that, as far as I can see. This, of course, says nothing about the future….
I did indeed wonder briefly if Scholz star had any influence of the glacial cycle. But the close encounter happened 60 000 years ago, while the current cycle started ~115 ky.
So I agree. Scholz’s star do not appear to have had any effect on Earth, even though it should have disturbed and sent a bit more comets inward for some millenia.
Yet we might ask ourselves on the effect on the more distant worlds.
Did Chiron (2060) and Hidalgo have the orbits they got today back then? Perhaps not.
Hi William
It’s funny you should mention the “similarity” of ancient Earth’s climate. There’s quite the body of literature that the O2 levels and atmospheric pressure have varied significantly over the billennia. Then there’s the all the sea level variations which don’t seem neatly periodic, but rather chaotic. Whether the changes are exogenous or endogenous is a difficult question, but the last thing the geological record implies is “stability”.
Since the stellar buses run rather randomly but with the likelihood that one will show up every so often, it could be prudent to have a generation ship ready and on standby with a “ready, willing and able” crew + passengers rotaring on board in batches from terra firma until embarkation.
This would require among so many other things the setup and maintenance of closed circuit ecosystems for the sustenance of those on board.
An attempt should be made to “catch” every stellar bus.
Your suggestion is an interesting variant on “When Worlds Collide”.
My sense is that by the time of the next encounter, either our technology will make this wait unnecessary or we may even be extinct. A waiting starship in space might be a techno artifact for another intelligent species to discover.
Several years ago when I looked up close encounters, I don’t think they were known to even a million years out. But some great missions have been launched since then, and this data about HD 7977 at 2.8 million years out suggests that many potential future encounters might already be predictable so far in advance. That gives us ample time to build a redoubtable ark when needed.
Nonetheless, the best world ship is an actual world, namely Sedna, which could be bombarded over the next two thousand years with comets to help accelerate it outward and warm its surface, roofed in a light layer of insulating material to hold in an atmosphere, and provided with a mighty network of fusion reactors to provide the vast energies needed for terraforming and thrust. Launching the planet by its next “window” in the 78th century will probably be, well, either easy or utterly impossible for the people of that era. :) Once it is loose, its people can chart their own course through the churning galaxy, using each close encounter to steer toward the next.
Whether a star passes near the sun or not, solar system sources of perturbation will cause the Earth’s eccentricity and celestial longitude of perihelion to oscillate.
On an order of about 100,000 years due primarily to Sun -Jupiter interaction.
Now if I understand what the additional perturbation is, it would appear to be a red dwarf star or brown dwarf in the vicinity of 5000 AUs at closest passage.
The perturbation effect of 0.1 solar mass star and Jupiter can be compared to first order if we consider the gravitational forces acting on Earth from 5000 AUs and 5 AUs respectively. Jupiter mass 1,000th of solar and a star like Scholz at about a tens of solar mass.
Jupiter Visiting Star
f = m /R^2 1/1000 Ms/ ( 5AU) ^2 1/10 Ms/ (5,000 AU)^2
The visiting star at 5000 AUs would be more like a thin icing on the Jovian cake – as far as I can tell. I believe the other gas giant planets would still be of more concern. And then, of course, we are still debating whether Alpha Centauri has any terrestrial planets… What with two stars each roughly of solar mass in eccentric elliptical paths within about solar system orbital confines.
Well, there might be a rain of comets in the Earth’s case, but I think a red dwarf passage would have to try harder to get any volcanic activity on Earth.
But on the other hand, whether it is Alpha Centauri or Trappist 1, there should be some remarkable tectonic stresses exerted on terrestrial planets in those circumstances.
The timeframe of these close stellar encounters also gives us timeframes for when it would be more practical for biological interstellar visits to our solar system.
Would all these considerations of celestial mechanics make it possible to envisage the approach and contact of an ETI with the earth? The concept of moving systems rather than civilizations is an interesting one.
For those of you interested in calculating the nearest approach of your star of interest to Sol, here is a quick formula.
Any stellar catalog worth its salt usually includes three vital statistics for each star listed, mu (the proper motion, in seconds of arc per year), pi (the parallax, in seconds of arc), and R (the radial velocity in km/sec). R is negative in approach (blue shifted) and positive (red shifted) in recession. Mu and pi are determined by astrometric methods, R is determined by Doppler spectroscopy.
The formula for determining the velocity orthogonal to the line of sight of the star relative to our solar system is Velocity = 4.74 (mu/pi). The velocity along the line of sight is, of course, just R. The constant ‘4.74’ yields the velocity V in km/sec, so it is consistent with R.
The distance to the star in parsecs is 1/pi.
1 parsec = 3.26 ly = 3.086 x 10^13 km
1 year = 3.156 x 10^7 sec