Archive for the ‘Exoplanets’ Category

Super Earths, Or How The Exponential Function Can Matter

April 23, 2018

We live in the times where exponentials have come to rule, as they never ruled before. Ignore at the risk of everything we claim to hold dear. As mathematically challenged Silicon Valley nerds put it, all too simplistically, the coming “singularity” looms. Simple minds do not much understanding create, though, so here a little elaboration…

An example of exponentials in action, is graciously offered by so-called “Super Earths“, giant versions of Earths, hundreds of which have been discovered in our neighborhood.

Before I get into this, a short lesson on the exponential.

The Ancient Greeks thought they knew mathematics, but they were prisoners of linear thinking (especially after the top intellectuals spurned non-Euclidean geometry and arithmetic). The exponential is the most obvious, most crucial to understand, most vital to handle example of nonlinear thinking.

An exponential is any function which grows proportionally to itself.

Our present “leaders” (Putin, Trump, Xi, Macron, etc.), and their underlings have no idea what an exponential is, and that it feeds on itself.

Civilizations get ambushed by exponentials. This is why they so often irresistibly decay: the effect is blatant, be it the Late Roman empire, Tang China, the Maya…  


Socrates:The unexamined life is not worth living“. That was HIS (wise) feeling. His own feeling. Others don’t have to share it. Actually vain, self-admiring, erroneous, hateful people detest nothing more than self-examination. They deeply dislike, hinder those, and what, promotes self-examination.

And tell me, Socrates, you who didn’t like knowledge you didn’t already have, and you thought everybody had, when did you learn about the exponential function? How can you know something that important you never even suspected existed? And, absent that tool of the spirit, you thought you could examine everything? How stupid was that? And you, out there, the ignorant admirers of Socrates and his ilk: you don’t even have the excuse to have been dead for 24 centuries! To extract you from the gutter, seize the exponential!


After discovering a few thousands exoplanets, Super Earths are, so far, more frequent than simple Earths (it may be a bias from our present telescopes, but I don’t think so…). If the Super Earth is slightly bigger than Earth, depending upon the nature of its core, its surface gravity doesn’t have to be much higher than Earth (I computed). However, the present article considers Super Earths were the gravity is much higher than on Earth…

“Super-Earth” planets are gigantic versions of Earth. In some ways, they are more likely to be habitable than Earth-size worlds: their thicker atmospheres protect them better from radiations, either from their parent stars, supernovae, gamma ray bursts, galactic core explosions, etc.. However, it would be difficult for any inhabitants on these exoplanets to access to space. At least with known, or imaginable technologies.

To launch a vehicle as light as the Apollo moon mission capsule, a rocket on a super-Earth such as (potentially inhabitable) Kepler 20b would require more than double the escape velocity.

To leave Earth (“⊕”)’s gravitational influence, a rocket needs to achieve at minimum the escape velocity vesc = s 2GM⊕ R⊕ ∼ 11.2 km s−1 (2) for Earth, and vesc ∼ 27.1 km s−1 for a 10 M⊕, 1.7 R⊕ Super-Earth similar to Kepler-20 b. Computation shows one would need a mass of about 400,000 metric tons, mostly due to the exponential demand of fuel. That’s 5% of the mass of the Great Pyramid of Giza in Egypt (still by far the Earth’s most massive monument, excluding utilitarian walls and dams).  

That means a chemical rocket there should have one hundred times the mass of one here (Apollo’s Saturn V launcher was 3,000 tons). However, that’s not a show stopper: our largest ocean-going ships are more massive than that, and a massive rocket is imaginable. So Hippke is not correct when he says that:

“On more-massive planets, spaceflight would be exponentially more expensive,” said study author Michael Hippke, an independent researcher affiliated with the Sonneberg Observatory in Germany. “Such civilizations would not have satellite TV, a moon mission or a Hubble Space Telescope.

This is of great practical interest. Research has revealed that Super Earths are abundant, and obvious targets for human colonization. They can reach up to 10 times the mass of our own Earth (after that, they retain light gases, and turn into mini Neptunes, unsuitable for direct colonization, although Pandora like scenarios are highly plausible). Many super-Earths apparently lie in the habitable zones of their stars, where temperatures can theoretically support liquid water on the planetary surface and thus, potentially, life as it is known on Earth. Although I have had reservations about this: I view the presence of a nuclear reactor inside the planet as necessary for life, since it provides with a magnetic shield, and the recycling of the atmosphere through plate tectonic, let alone continents… (Being in the water belt and the nuclear belt simultaneously is a miracle Earth’s biosphere profits from.)

This being said, it is true that some ways to access space that we potentially have, won’t happen on Super Earths. Rockets work better in the vacuum of space than in an atmosphere: super-Earthlings might want to launch from a mountaintop. However, the strong gravitational pull of super-Earths would squash down super Alps (it’s a pure application of Quantum mechanics). Super towers won’t be be feasible, either…

Using space elevators traveling on giant cables rising out of the atmosphere depends upon the strength of the cable material. The strongest (per unit of mass) material known today, carbon nanotubes, is just barely strong enough for Earth’s gravity (it is not at this point possible to imagine stronger materials, putting in doubt the feasibility of space elevators on super-Earths). Here is Michael Hippke (Submitted on 12 Apr 2018):

Spaceflight from Super-Earths is difficult:


Many rocky exoplanets are heavier and larger than the Earth, and have higher surface gravity. This makes space-flight on these worlds very challenging, because the required fuel mass for a given payload is an exponential function of planetary surface gravity, ∼3.3exp(g0). We find that chemical rockets still allow for escape velocities on Super-Earths up to 10 times Earth mass. More massive rocky worlds, if they exist, would require other means to leave the planet, such as nuclear propulsion.

Comments: Serious version of the April Fool’s idea (arXiv:1803.11384). Submitted on April 4th 2018
Subjects: Popular Physics (physics.pop-ph); Earth and Planetary Astrophysics (astro-ph.EP)
Cite as: arXiv:1804.04727 [physics.pop-ph]
(or arXiv:1804.04727v1 [physics.pop-ph] for this version)
  1. INTRODUCTION Do we inhabit the best of all possible worlds (Leibnitz 1710)? From a variety of habitable worlds that may exist, Earth might well turn out as one that is marginally habitable. Other, more habitable (“superhabitable”) worlds might exist (Heller & Armstrong 2014). Planets more massive than Earth can have a higher surface gravity, which can hold a thicker atmosphere, and thus better shielding for life on the surface against harmful cosmic rays. Increased surface erosion and flatter topography could result in an “archipelago planet” of shallow oceans ideally suited for biodiversity. There is apparently no limit for habitability as a function of surface gravity as such (Dorn et al. 2017). Size limits arise from the transition between Terran and Neptunian worlds around 2 ± 0.6 R⊕ (Chen & Kipping 2017). The largest rocky planets known so far are ∼ 1.87 R⊕, ∼ 9.7 M⊕ (Kepler-20 b, Buchhave et al. 2016). When such planets are in the habitable zone, they may be inhabited. Can “Super-Earthlings” still use chemical rockets to leave their planet? This question is relevant for SETI and space colonization (Lingam 2016; Forgan 2016, 2017).


Pessimistically, Hippke considered another possibility, a staple of science-fiction which originated in the very serious “Orion” project of the 1950s, an apocalyptic period: nuclear pulse propulsion. It works by detonating thousands of atom bombs below a shield cum shock absorber attached to the vehicle, hurling it through space. This explosive propulsion has much more lifting power than chemical rockets, and might be the only way for a civilization to leave a planet more than 10 times Earth’s mass, Hippke (naively) said.

However, slaying the radioactive dragon he himself brought up, such a nuclear-powered spacecraft would pose not only technical challenges but political ones as well, he said: “A launch failure, which typically happens with a 1 percent risk, could cause dramatic effects on the environment. I could only imagine that a society takes these risks in a flagship project where no other options are available, but the desire is strong — for example, one single mission to leave their planet and visit a moon.”

Unwittingly, Hippke then demonstrates the danger of the single mind (in this case, his!) Indeed the most obvious way to use nuclear propulsion is simply to run a liquid, even water, through the core of a nuclear fission reactor. That was tested, and it works extremely well… and very safely! It’s much less prone to failure than a chemical rocket.  On a planet with ten times the Earth’s surface, there would be plenty of space to do such dirty launches by the thousands.

Besides, it may possible to engineer absolutely giant thermonuclear PROPULSION reactors (thermonuclear fusion is easier, the larger the reactor: the exponential at work again; if we just made a fusion reactor that was large enough, it would certainly work). The radioactivity generated would be neglectable.

So we don’t have to worry about colonizing Super Earths… We just have to worry about weight (that is, surface gravity)….

But, here, now, we have to worry about all those exponentials going crazy. Last I checked, the Arctic ice was running one million square miles below its old minimum: at some point the so-far linear decrease of Arctic ice is going to decrease exponentially, as warming there is highly self-feeding (that’s why it runs already at twice the rate of the rest of the planet…).

And as usual, let’s remember what the arrogant, stupid imperial Romans never learned, and the Maya never reached: inventing completely new, liberating, energizing technologies is how, and the only way how, to break the strangulation from the ecological, political, economical and moral exponentials which smother civilizations. A most recent example is diffuse, dim light solar cells, dye-sensitized solar cells (DSSCs), a tech already in full deployment, which has just made spectacular progress in the lab.

Even language acquisition is exponential… Let alone thought system acquisition. You want to examine life, in ultimate depth? Learn to think exponentially!

The coming “singularity” looms. How to manage it? First by understanding what makes it tick, exponentials.

Patrice Aymé



Super Earths Galore?

March 5, 2017

[Original research, as usual, explaining in a bit more detail the preceding essay, its allusions, and its background: I pointed out that Venus failed as a livable planet because of its different internal composition. I turn then that argument around to demonstrate habitable large “Super Earths” are perfectly plausible, because “Super-Earth” does not have to mean “Super-Gravity”. I ponder the reasons pushing some astrophysicists to be so dead set against Super-Earths, and track that to the usual submission to the present plutocratic Zeitgeist.]


Usually, among astronomers, the term “Super-Earth” denotes a ROCKY planet with a mass higher than Earth’s. This does not imply anything about the surface conditions, habitability, or the potential presence of indigenous life.

In the Solar System’s icy gas giants Uranus and Neptune are 15 and 17 Earth masses respectively. My idea behind the concept of Super-Earths is to avoid “Gas Dwarfs”, also called “Mini-Neptunes”, by keeping the mass low enough.

What matters, to determine the livability of a rocky planet, is its surface gravity, and its composition regarding water and magnetism. It’s not as simple as Huyghens had it: “How vast those Orbs must be, and how inconsiderable this Earth, the Theatre upon which all our mighty Designs, all our Navigations, and all our Wars are transacted, is when compared to them.” -Christiaan Huygens (17th Century; Huyghens was financed by the tyrannical Super Plutocrat Louis XIV, an intriguing twist).

3,500 planets have been found around other stars (March 2017; the High Provence observatory found the first, and then the French satellite Corot found plenty, followed by NASA’s Kepler). A great percentage of them are Super Earths in the usual sense of being more massive than Earth, but less than Uranus.

In my terminology, a large Super Earth is not necessarily a gas giant. It may well be livable. (The reason to insist on all this is that I want money for super-telescopes, which are technically feasible, now; it’s just a question of money! If one listens to Siegel/Forbes below, one would decided to only finance financiers, since they pay more…)

According to my silicate composition argument, livable Super Earths with ten times Earth's mass are imaginable, because they could have Earth-like surface gravity... Astrophysicists paid by plutocrats don't think so (thus money is best spent on their sponsors... Instead of telescope!)

According to my silicate composition argument, livable Super Earths with ten times Earth’s mass are imaginable, because they could have Earth-like surface gravity… Astrophysicists paid by plutocrats don’t think so (thus money is best spent on their sponsors… Instead of telescope!)


Ethan Siegel, a celebrity astrophysicist who writes for Forbes magazine, disagrees with the whole mood behind the concept of “Super Earth”.

Siegel claims that Super Earths are never habitable, let alone earthly: “There’s no such thing as a ‘habitable Super-Earth’. Earth is pretty much the limit of how large you can get and still be rocky. Anything much larger, and you’re a gas giant.

Bemoans Siegel: “For a long time, we thought our Solar System was the template for the planets we’d find in the Universe. Inner, rocky worlds dominate the hottest part of the Solar System, with large, gaseous planets orbiting much farther out. The largest rocky planet was Earth; the smallest gas giant was Uranus; the mass difference between the two was a factor of 17, with Uranus having four times Earth’s radius. So it was quite a surprise when exoplanet discoveries started rolling in. Not only can planets of various sizes and masses appear anywhere in a solar system’s orbit, but of all the mass-and-size combinations out there, the most common type of planet is one we don’t have at all: a Super-Earth.

May these worlds be home to the realizations of our extraterrestrial dreams? Ethan Siegel arrogantly nix the idea: “… a cold, hard look at the scientific facts — and at the physics behind planetary science — puts the kibosh on that in no uncertain terms. In fact, the most up-to-date science tells us that the very idea that there is such a thing as a “Super-Earth” is a failing on our part.

Imagining What's On The Left, Kepler 22 b as a livable Super Earth is a "failing on our part" say Forbes employed astrophysicists. Massive wealth inequality caused by lack of infrastructure, though is, presumably not a "failing on our part".

Imagining What’s On The Left, Kepler 22 b as a livable Super Earth is a “failing on our part” says Forbes employed astrophysicist. Massive wealth inequality caused by lack of infrastructure, though is, presumably not a “failing on our part”.

Ethan Siegel again:

“The planets that we’re searching for, ostensibly, are the ones that are the most Earth-like: with similar compositions, atmospheres, masses, temperatures and other conditions to our world. But until we actually find life on another world — or learn a whole lot more about these planets we’re only beginning to discover — we can’t be sure which conditions are mandatory for intelligent life and which ones are mere happenstance. When we classify worlds as Earth-like, we look to their radius and how much energy they receive from their star.

In the past, we’ve typically said that if these worlds are approximately the size of Earth and receiving approximately as much energy-per-square-meter as Earth, these are likely Earth-like worlds. But this was an assumption that we made prior to having enough data to draw a conclusion… thanks to follow-up observations of their pull on their parent star, we’ve obtained the mass for hundreds of these worlds. And the conclusion they point to is damning.”

The basic argument Ethan (and others from MIT, etc.) hint to is that Super Earths have such a high surface gravity, they hang onto considerable amounts of hydrogen and helium. Then the atmosphere becomes crushing, life can’t develop.

Professor Ethan claims, without iron-clad evidence that:

… the transition from “rocky” world to “gaseous” world occurs at just twice the Earth’s mass. If you’re more that twice the mass of Earth and you receive the same amount of energy from your star, you’ll be able to hold onto a substantial hydrogen-and-helium envelope of gas, creating an atmospheric pressure that’s hundreds or even thousands of times as great as what we have on Earth’s surface. The hope that Super-Earth worlds would be Earth-like is shattered, and we can safely put Super-Earths, Mini-Neptunes and Neptune-like worlds into the same overall category… it’s important to remember that even calling a world a “Super-Earth” is evidence of our bias. “


All too many scientists tend to be biased about bias. Why the hysteria?

But I repeat myself: Ethan Siegel works for Forbes.

His preceding conclusion is, In My Not So Humble Opinion (IMNSHO), flawed: it depends upon surface gravity, hence hypotheses about a planet’s internal composition. Basically, those scientists scale up the composition of Earth to Super-Earth”. But we have no proof of that. Quite the opposite, we have indication to the contrary.  

I already talked about Venus. Venus is nearly Earth-size is Venus’ magnetic field is weak, and make the planet appear like a comet (observing with some instrumentation).

Venus shows us a probably different composition: it is less massive because it does have Earth’s heavy radioactive iron core:


Primitive Mathematics & Geology Show Surface Gravity Can Be Low On A Super Earth:

The argument is that a Super Earth will have such a high surface gravity that it will trap an excess of hydrogen. Indeed, a planet with twice the radius of Earth will have eight times the mass of Earth. However this multiplication by 8 of its mass m is  true if, and only if, the Super Earth has the same density as Earth. Earth has density 5.5, due to a heavy iron core with density 10. Silicate rocks have only density 3.

If a Super Earth had the same exact composition as Earth, doubling the radius r would change the surface gravity, which is proportional to: m/rr. If m is multiplied by 8 and r by 2, one sees that the surface gravity is multiplied by 2.

However, if the Super Earth is mostly made of Silicates, its mass will just be multiplied by 5, not 8. Thus its surface gravity will only augment by 25%.

If now one considers a super Earth with radius three times Earth, one sees it’s volume will be 27 times greater, but, if made mostly of silicates, its mass will be no more than 15 times greater. Meanwhile 1/rr is roughly 1/10. So the surface gravity, would be only 50% greater.

Thus one sees that Super Earths with surface areas roughly ten times Earth are imaginable.

One could argue that a huge metallic iron core is necessary to create a large magnetic field protecting against radiation, in particular solar storms which may strip the atmosphere (as happened on Mars). And thus one could insist that the preceding is unrealistic that way. But we are sitting next to a mighty yellow star. Red Dwarves, although subject to flares, thus capable of ejecting radiation, may, overall, be less corrosive than Sol (as their energy output is relatively tiny).

The best way to make sure that we cannot have habitable Super Earth is to construct huge telescopes… That means high taxes in the financial sector, that useless vampire (Reminder: Obama brought in all the guys who had deregulated FDR’s financial safeguards, under Clinton in the 1990s; FDR had put those safeguards in roughly 48 hours after becoming president in March 1933!)


A grander perspective: Why Is The Anti-Super Earth Crowd So Vociferous?

Ethan Siegel: “But if you insist on calling these worlds Super-Earths, the conclusion is inescapable: whether gaseous or rocky, a Super-Earth is no place for a human.”

I hope that considering my own logic, geophysical logic, Venus, Mars, the stridency of that conclusion is perceived to be unwarranted. Actually  Laura Schaefer of Harvard thinks that surfing on Super Earths is definitively a possibility. According to her computer simulations, it’s easier to have oceans and they last longer (ten billion years) on Super Earths with 3 to 4 times the mass of Earths…

Let’s comeback to the strident enemies of livable Super Earths: they suffer from a known malady. This is the usual problem: to become stars, or super-stars, super-scientists jump to unwarranted super-conclusions which are bound to becoming “trending” on the “social networks”. There is little difference between that general mood of people sure of “The First Three Minutes” (who was measuring time, then? “God”, Dog, or super-physicists?) and “Allahu Akbar” (who told them Dog was great, Dog Himself? A friend of theirs?)

This is the moral flaw of (super) tribalism, the “Will To Power”, hubris unbounded, the ardent desire to become top primate, Super Baboon: it flushes, with neurohormones any other worries, makes one feel as if one were god. They all want to be like Obama, get it all, presidency, right of life and death onto the world, multi-billionaire friends, Nobel, etc. Just to forget their pathetic little condition on the Third Rock from Sol.

Well, the deepest thinkers are made of sturdier stuff. Build those telescope, and search for livable Super-Earths. They are out there. Tax those financiers behind Forbes and all plutocrats. Or, rather, tax their robots: most orders in the financial markets are passed by robots which trade in a way that leads the markets: 90% of the robotic orders to buy or sell are cancelled before being enacted.

Build telescopes, not cynicism!

Patrice Ayme’