Researchers looking to solve the super-Earth paradox finally have found what very likely is the resolution. Their resolution also has revealed more evidence for the fine-tuning of the solar system to support advanced life.

Super-Earths are planets possessing a mass between 1.2 and 13 times the mass of Earth. For comparison, Uranus and Neptune weigh in at 14.54 and 17.15 Earth masses, respectively. Another term for a super-Earth is a mini-Neptune. The diameters of known super-Earth planets range from about 120 to 220 percent of Earth’s diameter (about 30 to 54 percent of Neptune’s diameter). The featured image shows a comparison of the sizes of super-Earths (middle of the image) relative to Earth (left of the image) and relative to Uranus (lower left) and Neptune (upper right).

So far, astronomers have discovered 3,721 planets orbiting nuclear burning stars.¹ Of these 3,721 planets with known masses, 16.2 percent are in the super-Earth category, making it the second most populous of all planet categories. The most populous category are hot Jupiters at 20.9 percent, which are planets greater or equal to Jupiter’s mass that orbit their host stars closer than Earth orbits the Sun.

The super-Earth paradox is that, according to our best understanding of how planets form, there should not be any super-Earth planets at all. Observed super-Earths are all in the critical mass range—that is, they possess enough mass to accrete gas very efficiently. Nothing should stop them from becoming planets dominated by massive gaseous atmospheres like Jupiter, Saturn, Uranus, and Neptune.

The Kepler spacecraft clearly has proven that super-Earths do exist and that they exist in large numbers. In an effort to resolve the super-Earth paradox, in 2014, UC Berkeley astronomers Eve Lee, Eugene Chiang, and Chris Ormel proposed a metallicity gradient in the proto-planetary disks of planet-forming stars.² That is, they suggested that for proto-planetary disks, the ratio of heavy elements to light elements declines in proportion to the distance from the host star. Therefore, planets forming in close proximity to their host stars will lack the abundance of gas to accrete that exists farther out from the host stars.

There are two problems for this metallicity gradient scenario. One is that most models for the formation of super-Earths have the super-Earth planets forming far from their host stars and subsequently migrating inward toward the host stars. A second problem is that it is very difficult in proto-planetary disk models to get the necessary steep metallicity gradient.

In 2016, Lee and Chiang proposed another way to resolve the super-Earth paradox. They speculated that, while gas giant planets form early, super-Earth planets form late.³ They pointed out that, as proto-planetary disks age, the abundance of gas in the disk falls and that the gas abundance can drop by several orders of magnitude. Therefore, if super-Earth planets form late enough, they will be gas-poor compared to gas giant planets.

The gas abundance in old proto-planetary disks indeed drops precipitously. However, the abundance of dust and rocks in such disks also drops precipitously. Thus, planet formation is much less productive and efficient in older proto-planetary disks. Such low productivity and efficiency are contradicted by the very large population of super-Earth planets.

In an open access paper (yes, you can read the entire paper for free) published in the December 1, 2017 issue of the Astrophysical Journal, astronomer Cong Yu of Sun Yet-Sen University in Guangzhou, China, proposed⁴ a solution to the super-Earth paradox that avoids the problems in the scenarios developed by Lee, Chiang, and Ormel. In Yu’s model, super-Earth planets form as a result of tidally forced turbulent diffusion.

Yu notes that if a planet forms close enough to its host star, tidal interactions between the host star and the planet can periodically perturb the planet. Heating by tidal dissipation can so inhibit gas cooling in primordial super-Earth atmospheres as to dramatically limit the amount of gas that the planet can accrete. Specifically, Yu’s calculations established that “the thermal feedback associated with the externally forced turbulent stirring may greatly alter the accretion history of super-Earths.”⁵ Thus, he demonstrated that “tidally forced turbulent diffusion effectively helps super-Earths evade growing into gas giants.”⁶

Yu’s model also explains planetary systems that possess both super-Earth and gas giant planets. His calculations show that “the condition for turbulence-induced formation of super-Earths is more readily satisfied in the inner disk region but is harder to satisfy in the outer disk region.”⁷ The deductions from Yu’s calculations are consistent with observations. In planetary systems with both super-Earth and gas giant planets, the super-Earths orbit nearby their host stars while the gas giants orbit much farther away.

Yu ends his paper by admitting that not all the details are worked out. How and when the turbulence is initiated during planet formation remains to be modeled in detail. Yu used a simple opacity model for his planet atmospheres. More realistic opacities need to be invoked. Nevertheless, Yu’s model already goes a long way toward resolving the super-Earth paradox.

While the super-Earth paradox apparently is very close to being fully resolved, the solar system paradox remains. Our solar system is like no other known planetary system. It contains none of the most common planets. Neither super-Earths nor hot Jupiters exist in the solar system. Furthermore, the sizes and the orbital locations of the Sun’s four gas giant planets are unique.

As I explain in my book, Improbable Planet,⁸ there are excellent reasons for the unique features of the solar system. All eight of the Sun’s planets must possess exquisitely fine-tuned physical and orbital characteristics for advanced life to be possible on Earth. The reason why the solar system is so different compared to the other 2,792 planetary systems that have been discovered so far, is that apparently, it alone has been fashioned by the Creator of the universe to be a fit home for humans and human civilization.

This current blog series on Reflections is intended to encourage Christians to read more vigorously by providing a beginner’s guide to some of the Christian classics in such fields as theology, philosophy, and apologetics. Hopefully, a brief introduction to these important Christian texts will motivate today’s believers—as St. Augustine was called to in his dramatic conversion to Christianity—to “take up and read” (Latin: Tolle lege) these classic books.

This week’s book, Institutes of the Christian Religion, is by Protestant Reformer John Calvin and is considered one of the masterpieces of Protestant theology as well as one of the most influential works of Western civilization. According to distinguished church historian Philip Schaff, Calvin’s classic theological work is on the level of such masterworks as Augustine’s City of God and Thomas Aquinas’s Summa Theologica.¹

Why Is This Author Notable?

French theologian John Calvin (1509–1564) is, after Martin Luther, the second most recognizable person of the Protestant Reformation of the sixteenth century. Calvin is not only the most influential scholar within the broad Reformed theological tradition, but many historians consider him one of the most influential persons in the history of Western civilization itself. Because he affirmed that man’s ultimate allegiance lies only with the sovereign God and not with kings or bishops, some have argued that Calvin successfully laid the theological groundwork for democracy to flourish in the Western world.

What Is This Book About?

The first edition of Institutes of the Christian Religion was published in 1536 when Calvin was only 27 years old. Originally written in Latin, it was later translated into French and then into other European languages. The book represents a full systematic theology of the Reformed tradition within Protestantism. Calvin revised and expanded the work multiple times over the course of his career, with the full-scale work being completed in 1559 (Latin) and 1560 (French).

Intended as a basic introduction or catechism to Christian theology, the starting point of Institutes of the Christian Religion is the Apostles’ Creed. Calvin surveys the work of the Father, Son, and Holy Spirit in creation, revelation, and redemption.

The four divisions within the book reflect the following broad creedal order:

• Part 1 explores the knowledge of God the Father, who is the sovereign creator, sustainer, and director of all things.
• Part 2 addresses the work of the Son through redemption coming in the life, death, and resurrection of Jesus Christ.
• Part 3 focuses on the Holy Spirit as the one who brings about regeneration and sanctification in the life of the believer.
• Part 4 examines the critical role that the holy catholic church plays in administering Word (Scripture) and sacrament to God’s people.

John Calvin was not a philosopher but rather a literary scholar and biblical exegete. Therefore, his contemplation of the triune God is not speculative or theoretical but instead deeply personal.

Below, Calvin describes what has been called in Latin the sensus divinitatis—humankind’s inner sense of the divine (reflecting the apostle Paul’s statements in Romans 1):

There is within the human mind, and indeed by natural instinct, an awareness of divinity. This we take to be beyond controversy. To prevent anyone from taking refuge in the pretense of ignorance, God himself has implanted in all men a certain understanding of his divine majesty.2

Why Is This Book Worth Reading?

Institutes of the Christian Religion is arguably not only the most influential theological text of the Protestant Reformation but possibly of all Western Christendom. Whether adored or abhorred, John Calvin and his interpretation of historic Christianity have deeply influenced Western civilization. Every Christian and student of history should have a familiarity with this amazing work of theology.

Therefore, take up and read Calvin’s Institutes of the Christian Religion!

Resources

For more about the life and accomplishments of John Calvin, see “Christian Thinkers 101: A Crash Course on John Calvin.”

One of the most popular blogs I wrote in 2010 discussed how the recovery of the sperm whale population from near extinction to 12,000 individuals in the Southern Ocean had greatly increased that ocean’s biomass and had helped to mitigate global warming.¹ Now, studies on blue whales, fin whales, and humpback whales establish that they, too, are making an enormous contribution to increasing the marine biomass and in helping to mitigate global warming.

Environmental Benefits of Sperm Whales 
In the June 2010 issue of Proceedings of the Royal Society B, a team of eight marine biologists (seven Australian, one German) published their results of a multiyear study of sperm whales.²Sperm whales dive thousands of feet below the ocean surface to feed on giant squid. Their squid diet is very rich in iron. The eight marine biologists determined that sperm whales defecate only on the ocean surface, and noted that the whales’ feces are rich in soluble iron compounds.

Sperm whale feces fertilize the oceans’ phytoplankton with the nutrients they most need—soluble iron compounds. Thanks to sperm whales, the Southern Ocean sustains a much higher biomass (amount of living matter) of phytoplankton. This higher phytoplankton biomass permits a higher biomass of zooplankton, which in turn, makes possible a higher biomass of fish. The cascade of increased living matter explains why the return of the only predator species of giant squid has actually increased the population and body sizes of giant squid as a whole.

As a byproduct, the eight marine biologists calculated that the higher biomass of phytoplankton removes an extra 440,000 tons per year of carbon from the atmosphere through their photosynthesis. Since the 12,000 sperm whales respire 176,000 tons of carbon per year into the atmosphere, that means sperm whales are responsible for removing a net of 264,000 tons per year of carbon from the atmosphere. Thus, sperm whales are certainly doing their bit to remove carbon dioxide, a powerful greenhouse gas, from the atmosphere and, therefore, they play a significant role in mitigating global warming.

Environmental Benefits of Other Whales
New research achieved by seven marine biologists at the University of Tasmania led by Lavenia Ratnarajah extends the findings of the team of eight.³ Ratnarajah’s team focused on baleen whales and three species in particular: blue whales, fin whales, and humpback whales. Baleen whales differ from sperm whales in that they feed on krill instead of giant squid.

Krill are small marine crustaceans. They feed on phytoplankton and, to a lesser extent, on zooplankton. The diet of the whales studied by Ratnarajah’s team consists of Antarctic krill (see figure 1). Antarctic krill, in terms of total biomass, rank as Earth’s most abundant animal species. Their total biomass is approximately 500 million tonnes (550 million tons), comprised of 300–400 trillion individuals.⁴

Figure 1: Antarctic Krill. Body length = 1–6 centimeters. Image credit: Uwe Kils, Creative Commons Attribution

Ratnarajah’s team determined that the iron concentrations in Antarctic krill are a million times higher than typical Southern Ocean seawater concentrations. For the fecal matter of Southern Ocean baleen whales, the iron concentration is almost 10 million times higher. Thus, like the sperm whales, baleen whales enhance the marine biomass of phytoplankton, zooplankton, fish, marine mammals, and the removal of greenhouse gases from the atmosphere by fertilizing marine phytoplankton.

Blue whales (see figure 2) were even more impacted by the whaling industry than sperm whales. I was taught in my public school education that blue whales were extinct since a decade had gone by where not a single blue whale had been sighted. Since that time, I have had the pleasure of seeing blue whales. It is estimated that 10,000–12,000 blue whales exist in the world’s oceans today.

Figure 2: Blue Whale. The largest animal known to have ever existed, blue whales can attain a length of 98 feet and a weight of 190 tons. Image credit: NOAA

Before the proliferation of the whaling industry in the eighteenth and nineteenth centuries, the population of blue whales in the Antarctic Ocean alone was between 202,000 and 311,000.⁵ Blues whales were just as abundant in the rest of the world’s oceans.

Fin whales and humpback whales did not suffer the same impact from the whaling industry as did the blue whales. Nevertheless, the 2018 world population of fin whales, at an estimated100,000 individuals⁶, is less than half what it was before the eighteenth century. The pre-whaling industry population of humpback whales was an estimated 125,000 individuals and is less than half that number today.

Ratnarajah’s team calculated to what degree the pre-whaling industry populations of blue, fin, and humpback whales enhanced phytoplankton productivity compared to present-day levels. The enhanced phytoplankton productivity was up to 26 percent for blue whales, 16 percent for fin whales, and 3 percent for humpback whales, respectively (a total of 45 percent). However, uncertainties in the iron concentrations in krill are large. Based on the reported uncertainties,⁷ the enhanced phytoplankton productivity, if the whale populations were restored to pre-eighteenth-century levels, could be as low as 1.4 percent for blue whales, 0.8 percent for fin whales, and 0.2 percent for humpback whales, respectively (a total of 2.4 percent).

Population Restoration Produces Benefits
That is, the enhanced phytoplankton productivity for blue, fin, and humpback whales combined would range from 2.4 to 45 percent, if whale populations were restored to pre-eighteenth-century levels. The contribution from sperm whales and other species of whales would likely double (to 4.8 percent) these percentages.

Even the lower range percentage of 4.8 percent should give us humans a powerful incentive to restore the whale populations as quickly as possible. That 4.8 percent means the marine fish stocks would be increased by about 4.8 percent. It would also mean that the amount of carbon dioxide removed from the atmosphere by phytoplankton would increase by 4.8 percent. Since phytoplankton comprise about two-thirds of all the photosynthetic activity occurring on Earth, that 4.8 percent would count as a substantial step in mitigating global warming. It is also a substantial step that would augment, rather than subtract, from the global economy. The minimum benefit levels from restoring the whale populations alone give humans several more reasons to be grateful for these majestic creatures that bring us joy and appreciation for their pivotal ecological role.

Historic Christianity’s teaching that salvation is solely a gift of God’s grace stands at odds with all other religions of the world. The New Testament explicitly teaches that salvation is not earned by human moral effort but is a divinely imparted gift or endowment (χάρις [charis] is the New Testament Greek word for “grace” and means “unmerited favor”). Historic Christianity affirms that salvation comes by God’s grace alone, exclusively through faith in Jesus Christ’s unique life, death, and resurrection.

A Religion of Grace, Not Self-Help

Christianity at its heart is a religion not of self-help but of divine rescue. The apostle Paul summarizes the gracious formula of salvation in the New Testament as follows:

For it is by grace you have been saved, through faith—and this is not from yourselves, it is the gift of God—not by works, so that no one can boast. For we are God’s handiwork, created in Christ Jesus to do good works, which God prepared in advance for us to do.

–Ephesians 2:8–10, NIV

And here is another critical passage where the apostle Paul again explains the specific relationship between grace, faith, and good works:

For the grace of God has appeared that offers salvation to all people. It teaches us to say “No” to ungodliness and worldly passions, and to live self-controlled, upright and godly lives in this present age, while we wait for the blessed hope—the appearing of the glory of our great God and Savior, Jesus Christ, who gave himself for us to redeem us from all wickedness and to purify for himself a people that are his very own, eager to do what is good.

–Titus 2:11–14, NIV

Scripture therefore informs us that we are saved by grace, not by works. But that same saving grace motivates the believer to pursue godliness (good works). So here’s the biblical teaching enumerated:

1. Salvation is by grace.
2. It comes through faith (in Christ).
3. It is not earned or merited by works.
4. But saving grace motivates good works.

Thus, good works are the fruit, but not the root, of salvation. Or as the Protestant Reformers said concerning the relationship between faith and works, “Faith alone saves, but saving faith is never alone.” Martin Luther liked to say that saving faith is always pregnant with good works.

The Cognitive Dissonance over Grace

Given that God’s grace is the indispensable component in our salvation, it would seem obvious that as the recipients of God’s great generosity, we should endeavor to allow that grace to transform us. In other words, since God has been amazingly gracious toward me, how can I not at least endeavor to be gracious toward others? But that is where we encounter the cognitive dissonance (the psychological state and tension of having inconsistent thoughts, beliefs, or attitudes). When I say that God’s graciousness toward me is the most important thing in my life but show little or no grace to others, then my actions are in conflict with my deepest beliefs.

I have known Christians who preach, teach, and even screech, “SALVATION BY GRACE ALONE!”But their lives show very little grace toward other people. In fact, this sad and deeply disconcerting cognitive dissonance is one that I personally wrestle with. For if the grace that I preach and teach about is, for all intents and purposes, absent in my treatment of others, then undoubtedly that cognitive dissonance is evident for all to see. Yet by God’s grace, I know this is a problem, and it bothers me. So I sense and feel the inner dissonance. But I have asked the triune God to transform me, at least so the dissonance is not so glaring.

Christians, as forgiven sinners who have a long way to go in the process of sanctification, will always struggle with the problem of believing one thing but acting in conflict with that belief. Hypocrisy is a challenge that all Christians face. Thus, there’s bad news and good news. The bad news is that we Christians are very likely more sinful than we consciously realize. But the good news is that Jesus Christ is assuredly a much greater Savior than we realize.

Endeavoring to Be a Gracious Person

It is obviously not easy to treat all people graciously and charitably. That may be especially true on social media and the web. But I believe God greatly blesses our sincere though imperfect attempts at being respectful and gracious to others. If our deepest theological beliefs affirm God’s immeasurable grace toward us, then the logical and moral extension of that belief is to endeavor to treat other people, maybe especially the people with whom we disagree, as graciously as possible.

Even in my struggle to treat others graciously, I’m grateful for God’s unmerited favor toward me.

Resources

For more about salvation by grace and the attempt to live the Christian life by grace, see chapters 9 and 10 of my book 7 Truths That Changed the World.