Relevant and miscellaneous info about the Red Planet

It seems November 28 is called “Red Planet day”. I already wrote a post about Mars, but there are always additional and interesting facts and information about Mars, some of which I will present here.

The atmosphere of Mars is composed of carbon dioxide (about 95%), molecular nitrogen (2.8%), and argon (2%).It also contains trace levels of water vapor, oxygen, carbon monoxide, hydrogen, and noble gases. The atmosphere of Mars is much thinner than Earth’s. The average surface pressure is only about 610 pascals (0.088 psi) which is less than 1% of the Earth’s value. The currently thin Martian atmosphere precludes the existence of liquid water on the surface of Mars, but many studies suggest that the Martian atmosphere was thicker in the past. The Martian atmosphere is an oxidizing atmosphere. The photochemical reactions in the atmosphere tend to oxidize the organic species and turn them into carbon dioxide or carbon monoxide.

Mars has two permanent polar ice caps. During a pole’s winter, it lies in continuous darkness, chilling the surface and causing the deposition of 25–30% of the atmosphere into slabs of CO₂ ice (dry ice). The temperature and circulation on Mars vary every Martian year, as expected for any planet with an atmosphere and axial tilt.
The surface of Mars has a very low thermal inertia, meaning it heats quickly when the sun shines on it. Typical daily temperature swings, away from the polar regions, are around 100 K.

An example of a known geological feature on Mars is Olympus Mons, a large shield volcano on Mars. The volcano has a height of over 21.9 km (13.6 miles or 72,000 feet) as measured by the Mars Orbiter Laser Altimeter (MOLA). Olympus Mons is the youngest of the large volcanoes on Mars, having formed during Mars’s Hesperian Period with eruptions continuing well into the Amazonian. The volcano is located in Mars’s western hemisphere, with the center at 18°39′N 226°12′E, just off the northwestern edge of the Tharsis bulge. There is a possibility that Olympus Mons is still active.

The image below shows a colorized topographic map of the volcano Olympus Mons, together with its surrounding aureole, from the Mars Orbiter Laser Altimeter (MOLA) instrument of the Mars Global Surveyor spacecraft:

(Image source: https://en.wikipedia.org/wiki/File:Olympus_Mons_aureole_MOLA_zoom_64.jpg)

Now for some explanations of the red color of Mars. The surface of the planet Mars appears reddish from a distance because of rusty dust suspended in the atmosphere, with an omnipresent dust layer that is typically on the order of millimeters thick.. A large amount of the regolith of Mars, or its surface material, comprises iron oxide. Basically, rocks on Mars contain a lot of iron, and when they are exposed to the various atmospheric phenomena, they ‘oxidize’ and turn onto a reddish color. The surface iron on Mars became oxidized, forming iron oxide known more commonly as rust — a compound made of two iron atoms and three oxygen atoms, the chemical formula of iron (III) oxide being Fe₂O₃. The massive oxidation most likely occurred when Mars had flowing water and a thicker atmosphere.

Detailed observations of the position of Mars were made in Antiquity by Babylonian astronomers who developed arithmetic techniques to predict the future position of the planet. The late ancient philosophers and astronomers (such as Hipparchus, and then Claudius Ptolemy in his work known as the Almagest) developed a geocentric model to explain the planet’s motions, using systems and combinations of circular tracks called deferents and epicycles.

During the seventeenth century CE, Tycho Brahe measured the diurnal parallax of Mars that Johannes Kepler used to make a preliminary calculation of the relative distance to the planet. Kepler studied for years to motion and the orbit of planet Mars.
Kepler tried several oval curves for the orbit of Mars that might fit the observations, including the ellipse. He was not happy with the physical reasons for choosing any of them until he noticed that one focus of an approximating ellipse coincided with the Sun. The curve and focus made it clearer for Kepler to elaborate a physical explanation.

Kepler’s initial attempt to define the orbit of Mars as a circle was off by only eight minutes of arc, but this made him to spend six years to resolve the discrepancy. The data seemed to produce a symmetrical oviform curve inside of his predicted circle. He first tested an egg shape, then engineered a theory of an orbit which oscillates in diameter, and returned to the egg. In early 1605, he geometrically tested an ellipse, which he had previously assumed to be too simple a solution for earlier astronomers to have overlooked. He had already derived this solution trigonometrically many months earlier.
In his Astronomia Nova, published in 1609, Kepler presented a proof that Mars’ orbit is elliptical. Evidence that the other known planets’ orbits are elliptical was presented only in 1621. Kepler published his first two laws about planetary motion in 1609, having found them by analyzing the astronomical observations of Tycho Brahe.
Kepler gradually discovered that all planets orbit the Sun in elliptical orbits, with the Sun at one of the two focal points. This result became the first of Kepler’s three laws of planetary motion.

The image below depicts the orbits of the planets Mercury, Venus, Earth, and the elliptical orbit of Mars around the Sun. The date is November 28, 1613 (image made with the Starry Night astronomy software):

The first person to draw a map of Mars that displayed any terrain features was the Dutch astronomer Christiaan Huygens.

Mars comes closer to Earth more than any other planet save Venus at its nearest—56 million km is the closest distance between Mars and Earth, whereas the closest Venus comes to Earth is 40 million km. Mars comes closest to Earth every other year, around the time of its opposition, when Earth is sweeping between the sun and Mars. Extra-close oppositions of Mars happen every 15 to 17 years, when we pass between Mars and the sun around the time of its perihelion (closest point to the sun in orbit). The minimum distance between Earth and Mars has been declining over the years, and in 2003 the minimum distance was 55.76 million km, nearer than any such encounter in almost 60,000 years (circa 57,617 BCE). The record minimum distance between Earth and Mars in 2729 will stand at 55.65 million km. In the year 3818, the record will stand at 55.44 million km, and the distances will continue to decrease for about 24,000 years.

Starting in 1960, the Soviet Union launched and sent a series of probes to Mars including the first attempted flybys and hard (impact) landing. The first successful flyby of Mars was on 14–15 July 1965, by NASA’s Mariner 4. On November 14, 1971, Mariner 9 became the first space probe to orbit another planet when it entered into orbit around Mars.
The first to contact the surface were two Soviet probes: Mars 2 lander on November 27 and Mars 3 lander on December 2, 1971—Mars 2 failed during descent and Mars 3 about twenty seconds after the first Martian soft landing. Mars 6 failed during descent but did return some corrupted atmospheric data in 1974.The 1975 NASA launches of the Viking program consisted of two orbiters, each with a lander that successfully soft landed in 1976. Viking 1 remained operational for six years, Viking 2 for three. The Viking landers relayed the first color panoramas of Mars.

The image below shows the clearest image of craters of Mars taken by Mariner 4:

(Image source: https://en.wikipedia.org/wiki/File:Mariner_4_craters.gif)

In order to understand and study the gravity of Mars, its gravitational field strength g and gravitational potential U are frequently measured. Mars being a non-spherical planetary body and influenced by complex geological processes, the gravitational potential is described with spherical harmonic functions, following the conventions in geodesy, via the following formula:

Here is an explanation of the potential formula above:

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Mars will be in opposition with the Sun and in opposition to Earth on December 8, 2022. This means that Mars and the Sun will be on opposite sides of planet Earth, the two planets being the closest together in their respective orbits.

The following image shows planetary orbits, with the shining Sun in the middle of the image and with Mars in opposition to Earth, on December 8, 2022 (image made with the Mobile Observatory astronomy app):

An important event related to Mars will be evidently the first human mission to the Red Planet, which should be the outcome or result of thorough preparation and international cooperation, so that the prepared, trained and qualified crew of the first human trip to Mars will be able to travel in space, set foot and land on the Red Planet, stay there and explore for a limited period of time, and then come back safely to Earth.

Finally, the image below shows planet Mars and the orbit of one of its moons (Phobos) as seen from the surface of planet Saturn at 0°N 0°E, on November 28, 2022 (image made with the Starry Night astronomy software):

Some particular opinions and results in Newton’s Principia, and aftermath

Isaac Newton is regarded as the greatest scientist/mathematician, or natural philosopher (as scientists, physicists and mathematicians were called at that time) during the second half of the seventeenth century and the first half of the eighteenth century, and his Principia, first published in 1687, can be regarded as the greatest scientific work during that same period of time.

Newton’s Philosophiæ Naturalis Principia Mathematica was a product of its time, containing mathematical tools or methods used at that time, some of them developed by Newton himself. The work also contains important scientific theories and scientific information or knowledge that have been subjected to scrutiny, criticized, updated and/or corrected with the progress in theory and experimentation during the last three centuries.

Below is an image of the title page of Newton’s Principia, from the first edition published in 1687:

(Image source: https://en.m.wikipedia.org/wiki/File:Prinicipia-title.png)

Newton gave a determination of the speed of sound in Proposition 49 of Book II of the Principia. He provided a value (979 ft/sec) which is too low by approximately 15%. The discrepancy is due primarily to neglecting the (then unknown) effect of rapidly-fluctuating temperature in a sound wave. In modern terms, sound wave compression and expansion of air is an adiabatic process, not an isothermal process. About a century later, Pierre-Simon Laplace corrected the flaw or deficiency in Newton’s analysis and gave a more accurate formula to calculate the speed of sound.

Newton was also a product of his time and of his social environment. He was a religious person who believed in the Bible, and he reconciled his beliefs by adopting the idea that God set in place at the beginning of time the “mechanical” laws of nature, but retained the power to intervene and alter that mechanism at any time.

Newton thought that gravitation is based somewhat directly on divine influence. He sometimes mentioned in private correspondence that the force of gravity was due to a divine or an immaterial influence.

Newton’s General Scholium, published with the second edition of the Principia, contains (among other things) theological views and discussions. Newton was unable to explain all the intricacies and the details of the motions and orbits of the planets in the solar system. According to Newton, divine Providence was sometimes required to intervene in order to rectify the orbits and paths of the planets and to make the entire celestial system work correctly. In the following century and beyond, mathematicians and astronomers, such as Laplace, Lagrange, and others, provided mathematical explanations for the perturbations in the orbits of planets and for the stability of the solar system.

In the following decades and centuries, scientists and philosophers were inspired or influenced by Newton’s methods of analysis and by his scientific ideas, but many did not necessarily agree with his religious and theological views.

A shift away from Newton’s religious ideas started mainly with David Hume’s criticism of miracles and with the criticism of organized religion by philosophers of the Enlightenment. In the next two or three centuries after Newton, scientists, physicists and philosophers of science, when they were not agnostic or non-religious, tended to separate their religious views from their scientific work and research.

Clarifying the subsequent influence of Newton’s ideas and theories, and summing up:

“The test of Newtonian mechanics was its congruence with physical reality. At the beginning of the 18th century it was put to a rigorous test. Cartesians insisted that the Earth, because it was squeezed at the Equator by the etherial vortex causing gravity, should be somewhat pointed at the poles, a shape rather like that of an American football. Newtonians, arguing that centrifugal force was greatest at the Equator, calculated an oblate sphere that was flattened at the poles and bulged at the Equator. The Newtonians were proved correct after careful measurements of a degree of the meridian were made on expeditions to Lapland and to Peru. The final touch to the Newtonian edifice was provided by Pierre-Simon, marquis de Laplace, whose masterly Traité de mécanique céleste (1798–1827; Celestial Mechanics) systematized everything that had been done in celestial mechanics under Newton’s inspiration. Laplace went beyond Newton by showing that the perturbations of the planetary orbits caused by the interactions of planetary gravitation are in fact periodic and that the solar system is, therefore, stable, requiring no divine intervention.”

(Source: https://www.britannica.com/science/history-of-science/Newton)

Every great work of science becomes progressively and increasingly scrutinized, debated, and in need of updates or rectifications with the passing of time and centuries. This does not necessarily take away from its historical importance.

The development of calculus, and explaining the law of gravitation

Isaac Newton started developing methods of the Differential calculus as early as 1666. He called his findings and methods about this subject the Fluxional Calculus or also the ‘method of fluxions and fluents’.

Gottfried Wilhelm Leibniz developed his own form of calculus a few years after Newton had developed the principles of differential calculus, but Leibniz published his discovery of differential calculus a few years before Newton published his own findings about the subject.

Newton published his book Philosophiæ Naturalis Principia Mathematica or Mathematical Principles of Natural Philosophy in 1687.
In this important book Newton’s laws of motion are stated, and Kepler’s laws of planetary motion as well as Newton’s law of universal gravitation are derived.
However in the Principia the modern language of calculus was absent, and Newton mostly gave proofs in a geometric form of infinitesimal calculus, based on limits of ratios of vanishing small geometric quantities.

As an example, Kepler’s second law of motion states that:
The line joining a planet to the Sun sweeps out equal areas in equal times as the planet travels following an elliptical orbit.

In the Principia, Newton stated Kepler’s second law as follows:
The areas, which revolving bodies describe by radii drawn to an immovable centre of force do lie in the same immovable planes, and are proportional to the times in which they are described.

Below is the image taken from Newton’s Principia with which he proved geometrically Kepler’s second law:

And below is an image used by Newton in a later section of the Principia to prove geometrically (using limits of vanishing small quantities) the universal law of gravitation:

Newton proved with the help of the image above that the (centripetal) force varies as the inverse of the square of the distance between the center of force and the planet P.

The rigorous development of calculus , the clarification of its important notions and principles and its extensive use in classical and celestial mechanics and physics was carried out in the next two centuries after Newton by scientists and mathematicians such as the Bernoullis, Euler, Lagrange , Laplace, Cauchy, and others.

Additional info about the universal law of gravitation and the history of calculus can be found by searching online about these topics in resources such as Wikipedia and online Encyclopedias and websites.

The text of Newton’s Philosophiæ Naturalis Principia Mathematica can be found freely online at the Internet Archive website.

Remarks about comparing the spaceship carrying humans to Mars with a modern day Noah’s Ark

I will start with some notes about the older, ancient story of Noah and the ark, then move on to modern spaceships.

The biblical story of Noah, of the ship and of the flood was taken, inspired or borrowed from earlier stories related to older cultures and religions.

The flood could have been local, which is more plausible. Various allegorical and metaphorical elements and dramatizations were added with time, but denying the complete story of the ship and the flood is not the right approach, since the story was rooted in history.

Ancient narratives

The counterpart of Noah in the older Mesopotamian narrative, from which the Biblical flood story was taken, borrowed, or inspired, is called Utnapishtim. Utnapishtim took in the ark his wife, family, relatives, the craftsmen of his village, baby animals, and grains.

One of the metaphorical additions could have very well been the animals (or the amount or number of animals) in (or on) the ship. Noah’s counterpart or equivalent in the ancient Greek story, for example, is called Deucalion.

Deucalion and his wife Pyrrha survived the deluge unleashed by Zeus by building a chest. There are essentially no animals in this version of the flood story. Some authors added pigeons by which Deucalion tried to find out whether the waters had retired, and some later authors such as Lucian (flourished 2nd century CE) added animals that Deucalion had taken with him.

The story of the ship and the flood was explained or interpreted in relation to a decision or decree by the supreme god or deity in ancient (polytheistic) religions, and in relation to the monotheistic God in the Bible. Every ancient culture and group of people explained this story and the events related to it according to their particular social, cultural and religious environment, background, ideas and beliefs. Moreover, there is a direct relationship between the character of Noah and the supreme deity that ordered the flood in the narratives of ancient cultures and religions. This is a point or topic that I could expand on in a future article or post.

In early Antiquity an important event took place where a man built, “drove” or piloted a ship that was the first or unique of its kind and likely represented a significant technological achievement at that time. The man had the ship land on a (very) high place. This man accomplished other great things or deeds, and the story of his life and of his actions was remembered, transmitted, told, retold, interpreted and reinterpreted in various ways.

The story of the great flood and of the demise of all humans outside the ship contained dramatized or allegorical elements. I will try to present (according to my readings and analysis) a possible reasonable way to explain what happened.

The ship was unique and a technological accomplishment, it landed on a high place and the events left a big impression on the people at that time. There were possibly some local floods or one big local flood that took place. People at that time in Antiquity didn’t know about the shape of the Earth and about all its parts or regions, and they likely thought that the region or part of the planet where they lived represented the entire inhabited world, which is one of the reasons why the flood was made global and total in subsequent narratives. Some wondered or said that IF there had been really a global catastrophe or flood when the ship or ark was sailing, the only ones who would have survived would have been the people (and the other living creatures, if any) present on the ship. From the word IF to making it a reality there are only a few steps, and these steps were crossed when the story was told, retold and retransmitted generation after generation, with embellishments, metaphorical and supernatural elements gradually added to it.

In the past the ship was a boat, an Ark, and the high place where it landed was a mountain. In the future, the ship could be the first spaceship carrying humans to another planet, and the high place could be a planet such as Mars.

Modern spaceship narrative

I think a spaceship carrying humans to another planet, particularly the first ship that will carry humans in the context of the first human mission to planet Mars, will be an important event that will be remembered and interpreted in various ways in the decades and centuries following the mission. One or some of these interpretations or narratives will consider the spaceship to be somewhat similar to Noah’s ship or ark, and the leader of the first human mission or trip to Mars could be possibly viewed within these interpretations as someone similar to Noah.

Here is another related remark. It is mentioned in the Bible that Noah was about 500 years old when he had children, and about 600 years old when the flood started and he entered the ark. Taking into consideration that the ages of the first ancient patriarchs were allegorically exaggerated or extended in the early parts of the Bible, and that the real age could be found by dividing the allegorical age approximately by 10, this would mean or entail that the age of 500 can be realistically rendered as 50 approximately, and that the man named Noah in the Bible was approximately (a little more than) 60 years old when the flood began and he entered the ship. It would be interesting or relevant to know or take notice of the age of the first person who will be the leader of the first human mission to planet Mars when the speceship begins its human trip to the red planet.

There are many valid reasons that could be given to justify the human mission to Mars and the human exploration of other planets. Some of these reasons include that life could be threatened on planet Earth, that after inhabiting the entire planet humans naturally ought to go beyond Earth and explore and inhabit the Moon and other planets, and so on. However it should be taken into account that at this period of time few humans are ready or prepared to take part in a human mission to Mars, and in order to succeed, such a human mission should be the result of thorough preparation and of global and international collaboration. And the human mission to Mars is not and should not be a suicide mission. Whether a person will get on the spaceship to Mars or not depends on this person being adequately qualified, prepared and ready to do so.

In any case, let us see how future events will unfold.