Earth Features

[lpetrich]

I wanted to post this on Earth Day, April 22 this year, but I got writer's block and I got disorganized along the way, so it took me this long.

What is the shape of our home, Planet Earth?

Our planet has lots of local variations in shape. The highest point above sea level is the peak of Mt. Everest, at 8,848 m / 29,029 ft, and the lowest point below sea level is the Challenger Deep, the lowest point of the Mariana Trench, at 11,034 m / 36,021 ft.

But what is our planet's overall shape?

The first notion was that the Earth is flat. That used to be a universal belief, and it seems like common sense.

We don't know who was the first to think otherwise, but one of the earliest statements of the present belief was by Aristoteles of Stagira, known to English speakers as Aristotle. He wrote on a *lot* of things, and in his book "On the Heavens" (~350 BCE), he stated very clearly that our planet is approximately spherical. He gave three arguments:

* Sphericity makes every part as close as possible to the center. Aristotle had in mind the center of the Universe, but an updated kind of center is the centroid, the center of mass. This is nowadays called the principle of hydrostatic equilibrium, and it applies to everything where gravity is stronger than the component materials' rigidity.

* As one goes south, one can see stars to one's south that one could not see earlier.

* The Earth makes a circular shadow on the Moon in a lunar eclipse, and it does so no matter where the Moon is relative to one's location.

Although round-earthism became widely accepted in the Western world, there were some flat-earth holdouts, like the early Christian theologian Lactantius. In his book Divine Institutes (303 - 311 CE), he wrote (III.24):

How is it with those who imagine that there are antipodes opposite to our footsteps? Do they say anything to the purpose? Or is there any one so senseless as to believe that there are men whose footsteps are higher than their heads? Or that the things which with us are in a recumbent position, with them hang in an inverted direction? That the crops and trees grow downwards? That the rains, and snow, and hail fall upwards to the earth? And does any one wonder that hanging gardens are mentioned among the seven wonders of the world, when philosophers make hanging fields, and seas, and cities, and mountains?

But his fellow theologians did not make a big issue out of it the way they did such things as the Trinity, and many later ones accepted the Earth's roundness.

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Over the 17th and 18th centuries, it was discovered that the Earth's overall shape is not quite spherical, but flattened on its poles and bulging at its equator, with a flattening factor of about 1/300. The Earth's equatorial bulge has a height of 43 km / 26 mi, and that makes the farthest point from the Earth's center the top of Mt. Chimborazo in Chile. Its height above sea level is 6,268 m / 20,564 ft, and from being near the Equator, its peak is about 2,100 m / 6,800 ft farther than Mt Everest's speak from the Earth's center.

This can tell us something about the Earth's interior. For constant density, the Earth would have a flattening of about 1/230, while if all its mass was concentrated in its center, its flattening would be 1/460. A halfway case, with Jupiterlike behavior, gives 1/380. In the general case, one has to solve a differential equation called Clairaut's equation, though there is an approximation that gives good results for not much central concentration, the Radau-Darwin equation, co-credited to one of the great biologist's grandsons.

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Artificial satellites offered new evidence of the shape of the Earth, and especially that of the Earth's gravitational field or "geoid". Our planet's equatorial bulge makes satellites' orbits slowly precess, and smaller irregularities make smaller effects, but nevertheless observable ones. Some early work provoked sensational headlines about how our planet was discovered to be pear-shaped, but that was the discovery of a pear-shaped departure from reflection symmetry over the Equator, one about 1/1000 the size of the equatorial bulge. Since then, even smaller gravity irregularities have been found, and it has been possible to measure the seasonal growing and shrinking of the Greenland and Antarctica ice caps -- and their cumulative shrinking.

Space travel beyond low Earth orbit has provided very direct evidence of the shape of the Earth, since if one goes far enough, our planet easily fits inside a typical camera's field of view. In fact, if one goes far enough, our planet won't be resolved, and it looks like a pale blue dot.

Spacecraft have now been sent to all the other full planets, as they may be called, and to lots of smaller celestial bodies. Everything larger than about 100 km / 60 mi is approximately spherical, for the same reason that the Earth is, and from spacecraft travels, we have details of the gravitational fields of all the full planets, and also those of some smaller objects: the Moon, Ceres, and Vesta.

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So we have gone a long way with the shape of the Earth, with flat-earthism going all the way from being universally believed to being an archetypical example of crackpottery.

 

[lpetrich]

About our home, Planet Earth, how does it move?

At first, it seems stationary, with the exception of earthquakes.

Geocentrism is also the first thing that one would conclude. The sky looks like a big bowl overhead, a big bowl that the stars are stuck on. That is from how our visual perception works - we don't have the sorts of cues that we have for Earthbound objects and even objects like clouds.

But clouds look like solid objects, and rainbows also do so.

One of the first people to think otherwise was Aristarchus of Samos (~310 - ~230 BCE). He started off by trying to find the sizes and distances of the Sun and the Moon, and he went on from there to how those celestial bodies moved.

The Moon was fairly easy, since the Earth casts its shadow on it in lunar eclipses. The Moon's radius was a little more than 1/4 of the Earth's radius (1/3.67), and the Moon's distance about 60 Earth radii. The Moon was a world, though that would not be appreciated until Galileo's time.

The Sun was more difficult, and he did some trigonometry with the Moon and its phases. Consider when the Moon is exactly at half phase. The Sun-Moon-Earth angle is thus 90d. He tried to observe the Sun-Earth-Moon angle at that time, and that gave him the Earth-Sun-Moon angle. He found a SEM angle of 87d and thus an EMS angle of 3d. That meant that the Sun is 20 times farther than the Moon, or 1200 Earth radii, and thus that it was 6 times larger than the Earth. However, that measurement is at the edge of human visual acuity, and this SEM angle is now known to be 80d 50m, giving an EMS angle of 10m. This is from the Sun being nearly 400 times farther than the Moon, about 23,000 Earth radii away, and over 100 Earth radii in size.

Aristarchus may have thought it more reasonable for the Earth to move around the Sun than the Sun to move around the Earth, since the Sun is larger than the Earth. He was thus one of the first to advocate heliocentrism.

But there was not much going for heliocentrism, and it would be about 1800 years before it was revived by Copernicus. Even then, it was not widely accepted until Galileo's observations. With his telescope, he saw mountains on the Moon, the phases of Venus, spots on the Sun, the four big moons of Jupiter, and something or other around Saturn. The phases of Venus were what one would expect from Venus moving around the Sun, and Jupiter's moons were objects moving around something other than the Earth. Galileo became convinced of heliocentrism, and he even tried to make it theologically acceptable to the Catholic Church. He failed, and he was made to recant.

Galileo also took on a problem with heliocentrism. We ought to notice that we are traveling at super speed, but we don't. From present-day numbers, the Earth's equator rotates at 465 m/s, and the Earth goes around the Sun at 29.78 km/s. Even with the much lower estimates of the past, the numbers come out huge -- must faster than even the fastest horse. Galileo's solution was the thought experiment of the ship. If it was traveling smoothly, would one notice its motions if one was in its interior?

It was Sir Isaac Newton who clinched the case for heliocentrism with his three laws of motion and his law of gravity. He even recognized that the Sun is not exactly at the Solar System's barycenter, that that point is sometimes outside the Sun.

A consequence of his law of gravity was that the planets pull on each other and that the Sun also pulls on the Moon, thus making their orbits precess. He tried to calculate the Moon's orbit precession, with partial success, and his successors were much more successful there. His successors also calculated the precessions of the planets' orbits, a small but nevertheless observable effect. They were successful except for Mercury having a bit extra perihelion precession. Intra-Mercurian planets? That would work, but none were ever established to exist. Modification of the law of gravity? Einstein's General Relativity was essentially that, and it succeeded.

A big difficulty of heliocentrism was the lack of parallaxes of stars. One ought to observe the nearer stars move relative to the farther ones as the Earth orbits the Sun. But that was not observed for a long time.

There was a parallax-like effect observed that was about 20 seconds of arc, but it was about 90d out of phase, a sort of focusing toward the direction of the Earth's motion around the Sun. It was aberration of starlight, and it was a result of the speed of light being finite. Not parallax, but still evidence of heliocentrism.

Parallaxes were finally observed in 1838 by three different astronomers looking at three different stars: Friedrich Bessel with 61 Cygni, Wilhelm Struve with Vega, and Thomas Henderson with Alpha Centauri. The parallaxes of the three stars are 0.286, 0.130, and 0.755 arcseconds. That makes their distances 721, 1587, and 273 thousand times the Earth-Sun distance -- and these are some of the closest stars to the Sun.

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Having settled the question of the Earth's motion in the Solar System, we turn to the "fixed stars", as they were called in centuries past. They are anything but fixed, moving relative to each other at several km/s, with the Solar System moving at about 13 km/s relative to their average motion, the "Local Standard of Rest".

How far do the stars go? Galileo had the first hint of an answer when he observed the Milky Way with his telescope. He saw a huge number of stars, oodles of stars. In the late 18th cy., William Herschel carefully counted stars in different directions, and he concluded that the Milky Way was a huge disk of stars with the Sun at the center of it. By the early 20th cy., however, astronomers had concluded that the Sun is not in the center of the Milky Way, but a good way off to its outer edges, and that it orbits our galaxy's center at roughly 250 km/s.

What were sometimes called "extragalactic nebulae" or "island universes" turned out to be huge swarms of stars much like the Milky Way, and for that reason, they became known as galaxies ("Milky Ways").

The farther ones were discovered to be moving away from us faster than the nearer ones, approximately in proportion to their distance ("Hubble's law"). For position x, velocity v, and Hubble constant H,

v = H*x

Or as components 1 2 3,
v1 = H*x1, v2 = H*x2, v3 = H*x3

Now consider observing the galaxies from galaxy g, with position xg and velocity vg. Then,

vg = H*xg
(v - vg) = H*(x - xg)

Thus, one would observe Hubble's law from g also.

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As one observes farther and farther, one looks farther and farther back in time, and the champion of great observed distance is not a galaxy but the cosmic microwave background. It is redshifted by a factor of 1000 from when it formed, from the Universe becoming much less opaque as electrons combined with its hydrogen and helium nuclei to make atoms of those elements.

The Sun moves at about 370 km/s relative to it.

I've thus gone as far as I can on the Earth's motions.

 

[lpetrich]

What is the age of our homeworld, the Earth? How would one find it? I'll first discuss premodern estimates.

https://en.wikipedia.org/wiki/Age of the Earth
https://en.wikipedia.org/wiki/Dating_creation
http://www.religioustolerance.org/ev_date.htm
http://www.religioustolerance.org/ev_date1.htm

One could ask the oldest people that one knows, but they would remember the Earth being much the same over their entire lives, and they would remember from their youth having elders much like what they are like now.

One could ask such people what their elders told them in their youth, and go back even further. But that has the problem of only the more memorable events being preserved, and often without much by way of dating. People could transmit a lot of information orally, though often in stylized form for easier memorizing.

Writing was a great help, because it could easy go far beyond what anyone could memorize. But for a long time, the only way to copy a book was to do it by hand. Printing made like much easier, and computers easier still, but those are very recent. Writing had the additional limitation of being younger than humanity, so to go beyond what's written, one has to rely on oral histories.

Premodern estimates of the age of the Earth varied wildly, with some people proposing that it is infinite or unknowable. Greco-Roman historians considered the first datable event to be the great flood of legendary king Ogyges, at some 2100 - 2400 BCE in our calendar. Anything before that they considered unknowable, like when the Earth was created -- if it did not always exist. Aristotle, for instance, believed in the infinite age of the Earth and the Universe.

Egyptian estimates jumped all over the place, with values like 13,000 BCE, 18,000 BCE, 40,000 BCE, 50,000 BCE, and even 150,000 BCE. Mesopotamians had estimates like 240,000 years (Sumerian King List) and 432,000 years (Berossus).

But among believers in Judaism and Christianity, the usual method became adding up the dates in the Old Testament / Tanakh / Hebrew Bible. But some of the dating in it is not as good as one might want for this purpose, and estimates varied quite a bit. A further problem was textual differences between versions of the Tanakh. From the Masoretic Hebrew version, one calculates around 4000 BCE, while from the Septuagint Greek translation, one calculates around 5500 BCE. Archbishop Ussher's date of 4004 BCE is a Masoretic date, as is the Jewish-calendar date of 3761 BCE. Some people came up with even greater ages, like Alfonso X of Castile of 6500 - 7000 BCE.

Though Augustine is sometimes praised for rejecting Biblical literalism, he nevertheless thought that the Bible had enough literal truth in it to permit the dating of the creation of the Earth. In his book "City of God", he compares Biblical and outside histories, and in one part, he writes "About the Most Mendacious Vanity of the Egyptians, in Which They Ascribe to Their Science an Antiquity of a Hundred Thousand Years" (Bk 18, Ch 40). Much more than what one would calculate from the Bible, as he noted.

While we are on religious texts, I will close with this one:
https://en.wikipedia.org/wiki/Nasadiya_Sukta
https://sacred-texts.com/hin/rigveda/rv10129.htm - Rig Veda 10.129
1. THEN was not non-existent nor existent: there was no realm of air, no sky beyond it.
What covered in, and where? and what gave shelter? Was water there, unfathomed depth of water?
2 Death was not then, nor was there aught immortal: no sign was there, the day's and night's divider.
That One Thing, breathless, breathed by its own nature: apart from it was nothing whatsoever.
3 Darkness there was: at first concealed in darkness this All was indiscriminated chaos.
All that existed then was void and form less: by the great power of Warmth was born that Unit.
4 Thereafter rose Desire in the beginning, Desire, the primal seed and germ of Spirit.
Sages who searched with their heart's thought discovered the existent's kinship in the non-existent.
5 Transversely was their severing line extended: what was above it then, and what below it?
There were begetters, there were mighty forces, free action here and energy up yonder
6 Who verily knows and who can here declare it, whence it was born and whence comes this creation?
The Gods are later than this world's production. Who knows then whence it first came into being?
7 He, the first origin of this creation, whether he formed it all or did not form it,
Whose eye controls this world in highest heaven, he verily knows it, or perhaps he knows not.

 

[lpetrich]

Having taken on premodern age estimates, I now turn to age estimates from the last few centuries. I first consider relative dating, the first dating to be solidly figured out. This involved becoming aware of our planet's very complicated history. Very little of that was evident in premodern works, and most of them supposed that our planet was always pretty much the same over most of its history. There would sometimes be catastrophes like great floods, but not much more than that.

The first step was taken by a certain Nicholas Steno in the 1660's. He started with noticing how much "tongue stones" resemble sharks' teeth, and he concluded that they were indeed teeth of long-ago sharks. But he did not stop there, and he proposed a general principle:

* The solid-in-solid principle. If a solid object is enclosed in another solid object, then the enclosed object formed first, then the enclosing object. Thus, shark teeth then rock.

He went on from there to propose principles of stratigraphy, the study of rock layering. Principles that we still use today.

* Superposition. Going upward, rocks go from older to younger, though in some places, some younger rocks may be pushed over some older ones.

* Initial horizontality. If they are now tilted, then they became tilted after they formed.

* Continuity.

* Cross cutting. Something that cuts across some strata was formed after those strata.

It nevertheless took a lot of work to untangle the Earth's geological history. Around 1800, William Smith put together the first-ever geological map of a large region: Great Britain. It was evident that the rocks were in layers extending over large areas, and he was nicknamed "Strata Smith" as a result. By the mid 19th cy., geologists had succeeded in mapping out all the parts of the geological record with abundant fossils: the Phanerozoic Eon, everything younger than the base of the Cambrian Period. Later geologists extended their geological mapping further back in time to cover all of the Earth's history.

* (All): Precambrian or Cryptozoic (Hadean, Archean, Proterozoic Eons), Phanerozoic Eons
* Phanerozoic: Paleozoic, Mesozoic, Cenozoic Eras
* Paleozoic: Cambrian, Ordovician, Silurian, Devonian, Carboniferous (Mississippian, Pennsylvanian Subperiods), Permian Periods
* Mesozoic: Triassic, Jurassic, Cretaceous Periods
* Cenozoic: Tertiary (Paleogene, Neogene Periods), Quaternary Periods
* Paleogene: Paleocene, Eocene, Oligocene Epochs
* Neogene: Miocene, Pliocene Epochs
* Quaternary: Pleistocene, Holocene Epochs

These time divisions have further subdivisions, though I won't go into them here.

This sort of time division has been extended to other celestial bodies:

* Moon: Pre-Nectarian, Nectarian, Imbrian, Eratosthenian, Copernican
* Mars (crater density): Pre-Noachian, Noachian, Hesperian, Amazonian
* Mars (mineral alteration): Phyllocian, Theiikian, Siderikian

 

[lpetrich]

Having gotten relative ages for Earth features, let us now turn to absolute ages.

In 1779, Comte de Buffon estimated the age of the Earth at about 75,000 years from cooling from a molten state. Over the 19th cy., his successors used that and some other techniques, like sedimentation rates, ocean salinity, presumed rates of biological evolution, gravitational collapse for the Sun, ... Improved cooling estimates gave an age of the Earth of around 20 to a few hundred million years, an age range that seemed too small for evolution.

But in 1896, Henri Becquerel discovered radioactivity, and in less than a decade, it was discovered that the energy release from radioactive decay was enough to make the Earth and the Sun greatly outlast cooling-time and gravitational-collapse estimates. It took some decades to untangle the details of radioactivity, like discover isotopes and work out the details of radioactive-decay series, but over that time, some physicists started to work on radiometric dating, the likes of Bertram Boltwood and Arthur Holmes.

In 1911, Arthur Holmes found an age of 370 million years (Mya or Ma) for a Devonian rock, and in 1913 1.6 billion years (Gya or Ga) for the oldest rock that he dated. In 1927, he estimated the age of the Earth to be 3 Gya, and in the 1940's to be 4.5 Gya, an estimate from using results from several rocks.

At the present time, the oldest known age of an Earth rock is 4.03 Gya, for the Acasta Gneiss from Canada. The oldest known age of a mineral crystal is 4.2 Gya, for zircon grains from the Jack Hills in Australia, crystals found in a 3-Gya-old rock.

In 1956, the Canyon Diablo meteorite was dated at about 4.55 Gya, and numerous other meteorites were since discovered to have ages close to that age. Of rocks returned from the Moon, one of them was discovered to have an age of 4.5 Gya, and a rock on Mars was recently discovered to have an age of 3.86 - 4.56 Gya for its component rock grains.

A completely different route to the age of the Solar System is by observing sunquakes on it and using stellar-evolution modeling to find out which age gets the best fit. This method gives 4.6 Gya, in agreement with meteorite ages.

So we have found that the Solar System is about 4.57 billion years old, and that the Earth formed within a few tens of millions after that.

 

[lpetrich]

The Earth from Space (earlier thread)

Pre-Space-Age depictions of our planet had a lot of variation in their depictions of the clouds, from thin streaks to partial coverage to being almost completely clouded over.

In SUNlite3_4.pdf "So high up the Earth looked like a WHAT?" (PDF page 6) author Martin S. Kottmayer noted "Anyone who followed the space program know that astronauts have sometimes expressed almost mystical transcendent sentiments on seeing the Earth from space." and he noted some science-fiction writers anticipating that.

As to our planet as a whole, before the Space Age, many people thought that it looks green, including many science-fiction writers, though some thought that it looks blue and some yellow. This issue was settled by observations from spacecraft, firmly establishing our planet as bluish.

Simulations of Light Curves from Earth-like Exoplanets - Planetary Habitability Laboratory @ UPR Arecibo - the Sahara Desert makes the Earth look neutral-colored when well-illuminated and in prominent position.