S3C5: The Terrestrial Planets & the Moon

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a) The formation of the Solar system

Around the same time as the Sun formed, 4.6 billion years ago, so did the rest of the planets and other celestial objects forming part of what we call the solar system, defined as the ensemble of bodies orbiting the Sun.

The dominant theory advances the matter that ultimately coalesced originated from a molecular cloud; we will learn a little more about this type of formation in S3 Section 8.b on the formation of galaxies but for our immediate purpose, suffice is to know it comprised molecular hydrogen (H2) and other elements formed either during the Big Bang (we will cover this topic in S3 Section 7.b) or by earlier stars, as we have seen in S3 Section 4.d on stellar nucleosynthesis, including those heavier elements that will congregate into the terrestrial planets: Mercury, Venus, Earth plus the Moon, and Mars.

The distribution of matter and its movement is not uniform, and this applies to molecular clouds. In cases where such a cloud does not experience much original spin, including from other sources of gravitational interaction creating torque upon it, a star may form at the centre though it is unlikely a solar system will. Where there is sufficient spin however, under the effect of gravitation the cloud will become denser and rotates increasingly faster as its volume becomes more compact, a consequence of the conservation of angular momentum (and of energy conservation more generally) – you may want to refresh your mind about torque and angular momentum by reading S1 Section 8.d. The spinning also results in the flattening out of the cloud into what is called a protoplanetary disk and explains why the planets within the solar system have very similar orbital planes, falling within 6° of the weighted average of the angular momentum contributed by all planets. Oddly, Jupiter accounts for over 60% of the total angular momentum in the system, which leads to suppositions that it may have been on its way to become a star itself but did not reach the critical mass and pressure to start fusing hydrogen.

Nonetheless, the dominant body in the solar system is without question the Sun itself, its mass represents 99.86% of the entire mass of the system and it would have drawn in the matter that did not have sufficient velocity. As for the planets, they would have formed through accretion: small clumps and then bodies a few kilometres across called planetesimals colliding and coalescing to ultimately form planets, slowly clearing their orbits of debris. Those protoplanets with too much velocity would over time have been ejected out of the system so it is a neat case of survivor bias that all planets left have stable orbits not decaying closer or further from the Sun, or at least not in a significant degree.

The reason why the inner planets have a different makeup from the giants, from Jupiter outward, has to do with temperature: too close from the Sun and volatile molecules do not condense so the inner planets are left with compounds with high melting points. Those are rare elements in the universe but they do make up the body of the inner planets whereas the giant ones, beyond what is called the frost line, consist of the usual suspects such as hydrogen and helium. This by the way is one of the key reasons why the telluric planets are much smaller than the Jovian planets, metals and silicates only represent a small fraction of the matter in molecular clouds.

Since gravity weakens over distances but never disappears, as we have seen in the previous chapter, the boundary of the solar system or heliopause can be thought of in terms of its magnetosphere. Within it, there is solar wind and outside it the solar wind is overpowered by other stellar winds and the various matter and dynamics of the interstellar medium, that which does not belong to any star system.

b) Mercury & Venus

Let’s now make our way back to the inner region of the solar system and note interesting features and properties along the way, as we slowly radiate outward. This will give us the opportunity to focus on each planet and other celestial bodies of note in turn, and when doing so we will always have an eye on how each object got to be in the state it is now, which will often draw one or several comparisons with various aspects of our blue planet, such as the existence of liquid oceans, of an atmosphere and the possible emergence of life, whether complex or not.

And so Mercury, being the closest to the Sun, is the first one on stage. By all measurements, it has a solid inner core and a molten outer core that is mostly metallic in content, featuring iron in particular. There is also a solid crust, as there is on Earth, but no hydrosphere or atmosphere to speak of and a very weak magnetic field; taken together, this removes both a shielding from high energy solar and cosmic radiations and a liquid body with significant heat capacity, or a cloud cover, to retain heat at night. Consequently, at the equator, the temperature varies widely from −170 °C in the dark to +420° C during the day, when fully exposed to the glaring Sun, as close as 46 million kms away at the perihelion (or 0.31 AU) and 70 million kms at the aphelion (or 0.47 AU). In case you are wondering the generic names for the closest and remotest points in a planetary orbit are called the apsides and when the Sun is the primary body they are respectively named aphelion and perihelion (“Helios” refers to the Sun so it is in the name) whereas for geocentric orbits, that is around Earth, the corresponding terms are apogee and perigee.

Mercury thus has a very eccentric orbit lasting just short of 88 Earth days, which exacerbates the major fluctuations in temperature and makes the development of a carbon-based lifeform very challenging indeed. Except perhaps near the pole because the axial tilt is very limited at only 0.03°, thus there are crater regions always remaining in shadows; these will be cold certainly but less so slightly beneath the surface.

I’d like to stay with Mercury’s orbit for a while because, just as other planets can have retrograde motions when seen from the Earth, on Mercury it is the Sun itself that can display such unusual trajectory. If it wasn’t obvious for a human observer on Earth to work out the heliocentric model, it would have been truly puzzling for one on Mercury to understand what on Mercury was going on. Indeed, as the planet approaches its perihelion, its orbital velocity accelerates to the point where it becomes equal to the rotational velocity, so one point on the surface remains exactly facing the Sun for a while and as the orbital velocity keeps increasing the Sun then starts going “backward” and a few days after perihelion, as the orbital velocity slows down, the opposite occurs with the Sun coming to a standstill before resuming its “standard” course.

Finally, because the dimensions of Mercury are relatively small as planets go (2,440km radius which is less than 40% of Earth’s) and it is so close to the big shining object our Sun is, it is impractical to observe the planet during our day and, without advanced optical instruments, we can only see it properly at dawn and dusk, when the Sun’s brightness is subdued.

Venus also has some interesting orbital features up its sleeve. Eccentric it is not, with an average distance of 108 million kms from the Sun (0.72 AU) and a revolution taking approximately 225 Earth days. However, this should be put into context with a rotation lasting 243 Earth days, meaning its orbital period is shorter than a sidereal day, though it is about twice as long as a Venus solar day of 116.75 Earth Days.

Confusing? I agree it is if the definition of each term is unclear in one’s mind. The orbital period is the time it takes to revolve around a body and return exactly to the same point relative to the centre of the orbit. On Earth it is about 365.256 years with the 0.256 at the origin of the leap year once every four year (but every 3 out of four 100 years the 29^thof February is not inserted so 1900 was not a leap year, 2000 was, 2100, 2200, and 2300 will be and 2400 won’t). A sidereal day is the time it takes for a body to complete one rotation and face the same direction towards the fixed stars, i.e. relative to inertial space. Think about it as rotating exactly 360°, which on Earth takes a little less than 24 hours whereas a Solar day on Earth is exactly 24 hours, meaning a spot on the surface will be facing the Sun at the same angle on the ecliptic (being the path of our star in the sky). The difference stems from the fact that when we rotate 360 degrees, one day has lapsed and during that time we have covered 1/365.25 of our orbit around the Sun, which is just short of 1 degree – as a result a solar day on Earth requires a rotation of about 361° and if we divide a day of 24 hours = 1,440 minutes by 360, this works out to one degree being covered every 4 minutes. And so, a sidereal day on Earth is 23h56′, not 24h00. Looping back to Venus, the fact that its sidereal day is longer than its orbit period means it has a retrograde rotation with the Sun rising in the West and setting in the East, the only planet in the Solar system with this behaviour though Uranus could also be said to exhibit retrograde rotation, but that is another story we’ll discuss in S3 Section 6.b.

This sounds like a fun fact, as does the fact that Venus is the third brightest object in our sky after the Sun and the Moon or that its angular momentum is often leveraged in the form of gravity assist by interplanetary probes (as seen in S1 Section 10.f), though what is less fun is that even if Venus is much further away from the Sun than Mercury, its mean surface temperature is north of 450° C, the pressure at its surface is 93 times higher than on Earth, and it has no internally-generated magnetic field despite having a liquid mantle. All this does not bode well for the chances of life to have developed and certainly there would not be any water-based life form existing in such an inhospitable environment – perhaps it would have been possible before the runaway greenhouse effect responsible for the stifling temperatures. This should come as no surprise when we consider both the density and the composition of its atmosphere: 96.5% of it is carbon dioxide with nitrogen making up most of the rest. A cautionary tale, perhaps?

Hence, in spite of having a very similar size to Earth, its mean radius is only 5% shorter at 6,052 kms, living in a different neighbourhood from ours has led Venus on a very different path.

c) Mars

Compared to Earth and Venus, Mars, the fourth planet in the Solar system, is quite a bit smaller and colder. At 3,396 kms, its equatorial radius is 53% the size of Earth’s and its seasonal temperature varies by over 80°C, between -78°C and +5°C. This is the result of a thin atmosphere, the lack of a hydrosphere to store heat, a marked axial tilt of 25 degrees (it is 23.4° for Earth as we saw in S3 Section 3.c), and an eccentric orbit which sees the planet hover between 207 million kms (1.38 AU) and 249 million kms (1.67 AU) from the Sun.

Unlike Venus, nothing too fancy about the orbital period and sidereal day of Mars, those stand respectively at 687 Earth days and 24.6h with the solar day being only 2 minutes longer, which makes sense since the orbital period is almost twice as long as ours and we have a 4′ difference between sidereal and solar days.

It is unclear why the planet lost its magnetosphere but this development has exposed the historical atmosphere to the solar wind and there is little left with an average surface pressure of less than 1% that experienced on Earth. 96% of this is carbon dioxide with argon and nitrogen each accounting for nearly half of the remaining content. All criteria considered, this should not preclude the existence of life and it may have been present in the past with a more substantial atmosphere and liquid water at the surface, as suggested by visible landforms. Nowadays though, most of the water is stored in seasonal polar ice caps sublimating as ambient temperature rises – this type of phase transition, instead of liquefaction then evaporation, is mainly due to the low-pressure environment. I am enclosing a link to the Wikipedia entry on the thermodynamics concept of triple point at the end of this chapter if you wish to understand this better.

Similarly to Earth and Venus, Mars has a metallic core, a mantle and a crust; furthermore it is still seismically active and was for a time volcanically active too, as evidenced among other clues by the presence of Olympus Mons, towering 26km above the plains of Amazonis Planitia, though it is a question mark whether this is still the case. At the surface, there is a layer of iron oxides a few millimetres thick, and this rust is also present in the atmosphere, giving Mars its butterscotch colour and its nickname of the Red Planet.

Hardly any atmosphere and barely any oxygen in it, exposure to solar wind and cosmic rays, no liquid water at the surface and freezing temperatures, what is the attraction then? Why do some people think settling Mars is a good idea? I think it comes down to three aspects:

It is one of the three closest planets from the Earth, and the giants from Jupiter onward are too far and with much worse conditions. Mercure temperature variations are too extreme and we would boil on Venus, so Mars is the best option, by elimination.
Terraforming, the engineering of a planet to suit human life, is not a straightforward process. If we are to colonize other planets outside of the solar system one day, and I will not debate the merits of this idea here (for this you will need to wait for or head to S3 Section 10.e), then some practice is required and settlements on Mars appear a logical, if not indispensable step in that respect.
We’ll need to run the social experiments of living in small groups, living under continuous stress, on the edge of death, to work out the adequate decision-taking processes and other relationship-impacting variables that can ultimately make all the difference between a successful colony and a failed one, regardless of the engineering and technological proficiency.

My personal viewpoint is that it would be too soon technologically and therefore not only very limiting but also very costly. The shielding from radiation and the ability to move large payloads efficiently would need to be addressed in a satisfactory manner first. Patience is a virtue.

To complete this section on Mars it is worth mentioning that, like all planets in the solar system besides Mercury and Venus, Mars has moons: Phobos and Deimos. Nothing like our very own Moon though in terms of size, Phobos is about 22kms in diameter while this number is 12kms for Deimos. They are named after the two brothers, sons of Ares, the Greek equivalent of Mars in Roman mythology. Their origin is unclear and they might be asteroids captured into Mars orbit. Not for too long anymore as far as Phobos goes since it is irretrievably losing altitude and will either crash or disintegrate soon, in about 50 million years or so.

d) The asteroid belt

In between Mars and Jupiter, at a distance of between 2 AU and 4 AU, it seems another planet failed to come about from the protoplanetary disk, disrupted in the accretion by the regular gravitational pull of Jupiter, a physical phenomenon called orbital resonance (the regular push on a swing is an example of resonance; I am including a link at the end of this chapter if you wish to better understand this point and it will be featured in more details in S3 Section 6.c on the Kuiper belt). This would have perturbed the orbit of the planetesimals and led to violent collisions and the occasional impact with the other terrestrial planets.

Less than 1% of the original matter present in this region of space at the birth of the solar system is still there in the form of what we call the main asteroid belt. It comprises over one million asteroids with a diameter above 1km – an asteroid, also called minor planet, is a generic term referring to objects that are not large enough to be a planet and are not comets. That sounds like a lot and yet, let’s do some quick maths using the region of highest concentration between 2.06 AU and 3.27 AU corresponding to orbital resonance ratios of 4:1 and 2:1 with Jupiter. The surface of a disk (formula πr² ) with a radius of 3.27 AU is approx. π*10.693 AU² and that of a disk with a radius of 2.06 AU is approx. π*4.244 AU² so, subtracting the latter from the former, the area of the circular band is π*6.45 AU². Rounding up 1 AU to 150 million kms, this gives us π*6.45*22,500 x 10¹² km² ≈ 456 x 10¹⁵ km², or in alphabetical terms 456 quadrillion square kilometres to accommodate a handful of million objects that aren’t even on the same exact orbital plane so there is extra space separating them in this third dimension, the one vertically away from the average orbital plane of the solar system. All this to say that, contrary to what you may have seen in movies or cartoons, it would not be reckless to cross the asteroid belt blindfolded.

Among these asteroids, the larger ones is Ceres, with a mean diameter of just under 940 km and less than 1.3% the mass of the Moon, although it accounts for around 40% of the total mass within the asteroid belt. It completes its orbit around the Sun in 4.6 Earth years following a significantly tilted trajectory of 9.20° to the invariable plane – the plane passing through the weighted centre of mass of the solar system (excluding the Sun) – whereas for Earth it is 1.57°. The second largest asteroid in this belt is Vesta with a mean diameter of 525km, just a few kilometres more than the third, Pallas. The volumes drop very significantly after these three.

In the previous sentence I said “this belt” because there is another string of asteroids in the inner solar system, they share their orbit with Jupiter and are called Trojans, since Greek mythology seems to be the source of names for asteroids. But how could this be? How come their orbit has not been disturbed and remained stable?

The answer, as often, lies in physics. In this case, what is called Lagrange points in celestial mechanics: points of gravitational equilibrium for a small object interacting with two massive orbiting bodies. There is always five of those Lagrange points, whether the system is Jupiter-Sun or, Sun-Earth or Earth-Moon: L1 is between the two bodies, L2 and L3 are behind each of the bodies, on the same alignment, and L4 and L5 are at the front and at the back of the orbit of the less massive of the 2 bodies in the system so that the object and the two bodies form an equilateral triangle and the angles of this triangle are 60° each (180°/3). L4 is said to be 60° in front, and for Jupiter’s asteroids this is the encampment of the Greek group and L4 is 60° behind, the safe harbour of the Trojans.

Figure 3 below illustrates the position of the five Lagrange points in the context of the Sun-Earth system.

Figure 1: Lagrange points in the Sun-Earth system

Credit: by Xander89 (CC BY 3.0)

e) The Moon

We went straight from Venus to Mars, bypassing our natural satellite, the Moon. The term “moon” is actually a generic one denoting a satellite planet orbiting a larger planet, and ours comes with a capital M because it looms big in our sky, being separated from Earth by a meagre 384,000 kms on average (the perigee is closer to 360,000 kms), which is only 60 times the radius of the Earth.

With a mean diameter of 3,474km, one would think the relationship between Earth and the Moon wouldn’t be so dominated by the larger body but 27.2% in one dimension becomes 2% in three dimensions (0.272³) and since at 3.34g/cm³ its density is 60% that of Earth, altogether the ratio for the mass drops to only 1.2%. Little wonder then that the surface gravity at 1.622m/s² is also only a sixth of Earth’s.

The difference in density is due to the lower proportion of iron in the core of the Moon and is one of the clues supporting the hypothesis advancing our satellite was the result of an enormous impact with a protoplanet about 4.5 billion years ago and the matter ejected as a result of the collision, more mantle and crust than iron-rich core, later accreted as the Moon.

Travelling so close to Earth and being so dominated by its gravitational pull, the body of the Moon has been subjected to a tidal lock and the synchronization of its rotation and orbital period – a topic we broached in S1 Section 10.a on gravity. In layman terms, we always see the same side of the Moon and never the far side. Furthermore, it also means the synodic orbital period of 29.5 days, being the orbital period around Earth in this case, also works out to be a lunar day. However, since during that time Earth would have moved along its orbit around the Sun, covering 29.55/365.25 ≈ 0.08085 or 8.085% of the way around the star. If we divide the 29.53 period by 1.08085 we get 27.321 as the sidereal orbital period.

As the Moon completes its roughly once-a-Earth-month revolution around the Earth, the angle of incidence of the solar rays on its surface will shift and give rise to what we call the phases of the moon. When placed behind the Sun, we look at it illuminated, this is the full moon. It then moves towards the right side (anti-clockwise) when seen looking down at the Sun-Earth system so that from the perspective of an observer in the Northern Hemisphere it is the left side of the Moon that is illuminated, this is Waning Gibbous then Waning Crescent as less than a quarter remains visible until we reach the New Moon, when the satellite is between Earth and the Sun – in case you are wondering, the Latin etymology of “gibbous” refers to humped or convex shapes. This is also the time for a solar eclipse if the travel of the Moon crosses the ecliptic whereas the lunar eclipse occurs during the Full Moon phase, when it falls in Earth’s shadow. As the satellite progresses in its journey around Earth, the right crescent appears (still from the standpoint of an observer in the Northern Hemisphere), this is Waxing Crescent and it becomes Waxing Gibbous until after 29.5 days the lunar month is completed and we are back to a Full Moon.

Any keen observer of our natural satellite would have noted its surface can clearly be seen, courtesy of a practically inexistent atmosphere, and its main feature is the presence of enormous impact craters, the largest being the 13km-deep South Pole–Aitken basin on the far side. These hundreds of thousands or large craters have not been eroded away by liquids, weather or covered by recent volcanic activity – this seems to have ceased about 1.2 billion years ago. Nor are there tectonic plates to subduct entire surfaces or a dynamo effect to create a strong magnetic field. All-in, in current conditions, the odds are not very good for life to be present though we can’t totally dismiss the possibility of microorganisms in niche ecosystems.

f) Trivia – Mythology and days of the week

In the Western world, and therefore in Latin and Anglo-Saxon languages, the visible planets were named after Roman gods, themselves replicating equivalent deities in Greek mythology. Helios (Greek) personified the Sun and from there we have heliocentric and helium, the Moon was Selene for the Greeks and Sabine for the Roman and both names are still in use in literature, Jupiter was the mighty boss (Zeus for the Greeks), Saturn was his father (the titan Kronos for the Greeks) and the god of abundance and agriculture, Mars the god of war (Ares for the Greek) was linked to the namesake planet because of the colour red, whereas Venus the goddess of love and beauty (Aphrodite across the Ionian Sea) was the brightest in the sky and fast-moving Mercury was named after the messenger of the gods, its Greek equivalent being Hermes. Neptune and Uranus were discovered much later, in 1846 and 1781, respectively, after the telescope was invented. In keeping with the established “nomenclature”, they were given the names of deity with Neptune being the god of the sea (Poseidon for the Greeks) and Uranus, the son of Gaia and father of the Titans, represented the sky.

Because the concept of planets was somewhat different two to three millennia ago, there were seven known planets including the Sun and the Moon, and so those names were used to name the days of the week – the reason why we have 7-day weeks doesn’t have one single answer and not every culture used this system. I will run through the French days of the week first and then the English so the Latin root can best be seen and the Germanic or Scandinavian ones as well.

In French, Lundi pairs with Lune (Moon), Mardi with Mars, Mercredi with Mercure, Jeudi with Jupiter, Vendredi with Venus, Samedi with Sabbati (or the Sabbath, the day of rest), and Dimanche is the day of the Lord (Dominicus). In English, Monday pairs with Moon, Tuesday with the Norse god Týr (the closest equivalent to Roman Mars), Wednesday with the Germanic god Wodin who corresponds to Odin in Norse mythology, Thursday with Thor the Norse god of Thunder, Friday is named after Frigg – itself a rendition of the Norse god Freya who was in many ways the equivalent of Venus, Saturday is for Saturn and Sunday for the Sun of course.