The penumbral lunar eclipse takes place on Monday, March 25, 2024.
A penumbral lunar eclipse happens when only the Earth’s outer and light shadow, called the penumbra, falls on the lunar disk. During this type of lunar eclipse, the lunar disk appears only a little darkened. During the March eclipse, about 95.6% of the Moon will be in the penumbral shadow.
The image below explains the different types of lunar eclipses:
The March full “worm” moon announces the coming of spring. Named for the emergence of earthworms when the ground thaws, the worm moon is considered to represent renewal and growth.
We will take the example of the city of Rio de Janeiro in Brazil, where the penumbral lunar eclipse begins on Monday, March 25, 2024, st 01:53(AM). The maximum eclipse occurs at 04:13, the eclipse ends at 06:05. The duration of this eclipse is 4 hours and 13 minutes.
The image below shows how the Moon looks like when viewed from Rio de Janeiro at about 2:00 AM, and at the time of the maximum eclipse at 4:12 AM (Moon appearance and image made with the Stellarium astronomy app)
Historically, it is generally known or recognized that the first solar eclipse was predicted by the ancient philosopher and astronomer Thales. This eclipse most likely took place on May 28, 585 BCE.
A solar eclipse happens when the Moon comes in between the sun and the Earth. The Moon gets in the way of the Sun’s light and casts its shadow on Earth.
The following image shows the positions of planet Earth, the Moon and the Sun in the solar system at the time of the total solar eclipse on April 8, 2024 (image made with the Mobile Observatory app):
The image below shows an animation of the path of the solar eclipse:
Taking as an example the town of Tipton, Indiana, USA, the animated image below shows three steps of the total solar eclipse. The maximum of the eclipse occurs on Monday, April 8 2024 at 15:08, the eclipse ends at 16:23. The duration of the solar eclipse is 2 hours and 32 minutes (eclipse images made with the Stellarium astronomy app):
In the image above, Zeta Piscium A is the primary component of Zeta Piscium (ζ Piscium, abbreviated Zet Psc, ζ Psc), a quintuple star system in the zodiac constellation of Pisces. Zeta Piscium A consists of a pair of A-type sub-giant stars with an angular separation of 0.15 arcseconds and visual magnitude 5.28.
The image below shows the solar eclipse taking place on April 8 in Torreon, Mexico at 11:46 (AM)
Lunar and solar eclipses come in pairs, separated by an interval of two weeks.
The March lunar eclipse is the first of the year 2024. It is followed by three more eclipses: a total solar eclipse on April 8, a partial lunar eclipse on September 18, and an annular solar eclipse on October 2.
From a historical point of view, astronomy is one of the oldest natural and exact sciences, with observations and scientific explanations by various cultures dating back to early Antiquity.
Spherical or observational astronomy is the oldest branch of astronomy. Observations of celestial objects have been important for religious and astrological purposes, and for timekeeping and navigation.
Celestial Navigation has been used in position fixing and navigation by observing the positions of celestial bodies, including the sun, moon, planets and stars. Instruments such as sextants have been used since medieval times for measuring the positions of stars and the angular distances between celestial objects.
In short, what is known as the scientific revolution essentially started in the 16th century with the publication by Nicolaus Copernicus of his work about heliocentric astronomy in 1543. This was followed by the works, observations and ideas of other scientists and astronomers such as Tycho Brahe, Galileo Galilei, and Johannes Kepler, culminating with Isaac Newton’s work entitled Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687, which expounded his laws of motion and the law of universal gravitation, and established the discipline of classical mechanics.
Newton’s Principia historically had an indirect, albeit significant, influence on the progress of navigation and on related topics such as tide analysis and prediction.
Newton’s theory of gravitation first enabled an explanation of why there were generally two tides a day, not one, and gave hope for a detailed understanding of tidal forces and behavior.
Newton presented in the Principia his mathematical theory concerning tides and lunar motion, and it is known that sea travel was essential for trade to the British and other navigators, who needed to have a good knowledge of tidal cycles and patterns and how they affect navigation and the determination of longitudes.
In the 17th century, the creation of learned societies like the Royal Society in England under the patronage of the king and with the help of some known personalities, and the French academy of sciences by Louis XIV and his minister Colbert, was helpful in advancing the interest in scientific and astronomical research.
During the 18th and 19th centuries, the study of the three-body problem by Euler, Clairaut, and d’Alembert led to more accurate predictions about the motions of the Moon and planets. This work was further refined by Joseph-Louis Lagrange and Pierre Simon Laplace, allowing the masses of the planets and moons to be estimated from their perturbations.
The scientists and astronomers who came after Newton and continued or developed his work made additional contributions to the theory of tides. As an example, in 1776, Laplace formulated a set of linear partial differential equations, for tidal flow described as a barotropic two-dimensional sheet flow (this is a flow whose density is a function of pressure only). Laplace obtained these equations by simplifying the fluid dynamic equations.
Nathaniel Bowditch, regarded as the founder or one of the founders of modern maritime navigation, read Newton’s Principia as a young man, and then translated Laplace’s Mécanique céleste (Celestial Mechanics), a work that extended and completed Newton’s Principia and Newton’s theories.
Sometimes scientists and astronomers were helped or supported by the state, and sometimes they were helped by influential personalities. In addition to his contributions to mathematics, Carl Friedrich Gauss is also known for his contributions to astronomy and planetary theory, having among other things published a book or work entitled Theoria motus corporum coelestium in sectionibus conicis solem ambientum (Theory of motion of the celestial bodies moving in conic sections around the Sun). Gauss was financially supported during his years of study by the Duke of Brunswick.
Larger and more powerful telescopes were developed and built during the 18th and 19th centuries, contributing to the progress in observational and theoretical astronomy. One of the famous applications of astronomical theories and celestial mechanics around the middle of the 19th century was the prediction of the existence and position of planet Neptune, mainly by Urbain Leverrier, using only mathematics and astronomical observations of planet Uranus. Telescopic observations confirming the existence of a major planet (subsequently called or named Neptune) were made on September 1846 at the Berlin Observatory.
William Thomson (Lord Kelvin) applied Fourier analysis to the determination of tidal motion and to explain tidal phenomena in relation to harmonic analysis. As a practical application of the astronomical theory of tides and lunar theory (i.e. the theory of the moon’s motion as deduced from the law of gravitation with its perturbations), at the end of the 19th century Thomson and others conceived tide-predicting machines, which were special-purpose mechanical analog computers constructed and set up to predict the ebb and flow of sea tides and the irregular variations in their heights – which change in mixtures of rhythms, that never (in the aggregate) repeat themselves exactly. Their purpose was to shorten the difficult and error-prone computations of tide prediction. These machines provided predictions valid from hour to hour and day to day for a year or more ahead. They were widely used for constructing official tidal predictions for general marine navigation, and were viewed as of strategic military importance until the second half of the 20th century.
The image below shows the tide predicting machine by Sir William Thomson in 1876. This machine combined ten tidal components, one pulley for each component. It could trace the heights of the tides for one year in about four hours.
Tide-predicting machines became generally used for constructing official tidal predictions for general marine navigation, and were viewed as of strategic military importance until the second half of the 20th century.
Important advances were made in astronomy during the 18th and 19th centuries due to observations as well as theoretical investigations and publications. These advances were accompanied or followed by applications related to navigation and nautical astronomy, sometimes stimulated or supported by societal and commercial interests or needs.
Progess in astronomical theory, research and applications continued during the 20th century in several directions. In the late 19th century and most of the 20th century, astronomical images were made using photographic equipment. Modern images are obtained using digital detectors, particularly using charge-coupled devices (CCDs) and recorded on modern media.
Radio astronomy flourished mostly after the second half of the 20th century The discovery of the cosmic microwave background radiation, regarded as evidence for the Big Bang theory, was made through radio astronomy. Radio astronomy uses large radio antennas known as radio telescopes, that are either used singularly, or with multiple linked telescopes utilizing the techniques of radio interferometry and aperture synthesis.
Other observational branches of astronomy include infrared astronomy, x-ray astronomy, and ultraviolet astronomy.
Related fields or subfields of astronomy that were developed during the 20th century include astrophysics, astrochemistry, stellar astronomy, galactic astronomy, physical cosmology, astrobiology, …
Theoretical astronomy in the 20th century studied the existence of objects such as black holes and neutron stars, which have been used to explain such observed phenomena as quasars, pulsars, blazars, and radio galaxies. Physical cosmology made advances during the 20th century. In the early 1900s the model of the Big Bang theory was formulated, supported by cosmic microwave background radiation, Hubble’s law, and the cosmological abundances of elements.
Space telescopes have enabled measurements in parts of the electromagnetic spectrum normally blocked or blurred by the atmosphere.
Operational space telescopes orbiting Earth outside the atmosphere avoid light pollution from artificial light sources on Earth. Their angular resolution is often much higher than a ground-based telescope with a similar aperture.
The image below shows the Hubble Space Telescope, which was launched into low Earth orbit in 1990, and remains in operation in 2023:
During the 1990s, the measurement of the stellar wobble (or Doppler spectroscopy) of nearby stars was used to detect large extrasolar planets orbiting those stars.
Human missions and crewed spaceflights have been sent to explore outer space (until now mostly in the vicinity of planet Earth and to the Moon) since after the second half of the 20th century. Interplanetary space probes have flown to all the observed planets in the Solar System as well as to dwarf planets Pluto and Ceres, and several asteroids. Orbiters and landers usually return more information than fly-by missions.
Over the past several decades, the topic of time travel has been considered and discussed by physicists, philosophers, journalists, presenters, and lay people. Movies have been made that feature time travel as the main plot or as one of the essential elements of the movie plot.
Some of these movies were entertaining or pleasant, but that does not mean that these movies are accurate or that time travel is possible.
Time travel, whether backwards or forwards, including changing or turning back time, is essentially a speculative, theoretical extrapolation of existing physical theories such as the theory of special relativity. Without getting into all the details or into long philosophical considerations, I esteem that time travel is not really possible or realistically doable.
Various explanations or interpretations have been provided in books or textbooks concerning time travel.
In some good textbooks dealing with the theory of relativity, it is pointed out that experiments have been carried out and have verified the time dilation equation (for example, expriments with muons, with mu mesons, …), but it is also indicated that the phenomenon is called apparent time dilation. In a similar way the phenomenon of length contraction is called apparent length contraction.
Let’s analyze as examples one or two movies featuring time travel and related effects in their plot.
In the movie Superman I starring Christopher Reeve, Superman turns back time as an emotional reaction to the death of Lois Lane. This type of action can be realistically described as a useless, naive action going against the rules of physics.
The scene in the Superman movie seems to assume that the entire world consists of planet Earth. How about “turning around” the solar system, or around the Galaxy, or around the Local Group of galaxies, and so on.
Turning back the rotation of the Earth could very well have devastating effects on everything and everyone on the planet. Not to mention the gravitational perturbations and disturbances affecting the Moon, the planets, the entire solar system, and beyond.
I think it would have been better if the writers had told the story differently, without killing Lois Lane or having Superman “turn back time”.
Time travel has been used and abused in sci-fi movies, and in movies or tv series by DC comics and Marvel comics, as some sort of deus ex machina or ultimate solution to fix everything or to set everything straight. Regrettably, this does not add to the accuracy or credibility of these movies. It also does not make them more realistic or convincing, even when exercising or trying to apply one’s suspension of disbelief.
In the movie Interstellar, physicist Kip Thorne worked out the equations that depict the path of light waves traveling through a wormhole or around a black hole. The visual effects in the film are based on the gravitational theory and the field equations of general relativity.
“Interstellar” is based on generally accurate existing theoretical and scientific concepts like neutron stars, spinning black holes, accretion disks, and time dilation.
Wormholes are theoretical physical entities that are considered to be like tunnels or shortcuts through the geometry of spacetime, connecting different parts of the universe.
According to the story in the movie, a crew of space explorers travel on an extra-galactic journey through a wormhole. They reach on the other side another solar system with a spinning black hole for a sun.
The spaceship’s destination is Gargantua, a supermassive black hole with a mass 100 million times that of the sun, located about 10 billion light-years from Earth. Gargantua rotates at 99.8 percent of the speed of light.
The movie refers to five-dimensional reality, and five-dimensional space is described in the movie as a form of extra-dimensional “tesseract” where time appears as a spatial dimension. The movie plot mentions and uses the concepts of time travel and time dilation.
I want to note that while this movie uses mostly accurate existing theoretical notions in physics, I think that the concepts of time travel and time dilation are nevertheless debatable theoretical and speculative consequences and extrapolations of physical theories such as the theory of relativity, that time travel cannot physically happen, and that it can generally be clarified by other explanations, such as being an apparent effect. In this sense, I think the use of time travel and time dilation diminishes the preciseness and undermines the realistic, plausible character of the movie.
Considering the possibility that in the future rigorous scientific experiments are made and these experiments prove the possibility of faster-than-light speeds and travel, the effects, nature and consequences of faster-than-light speeds should be carefully studied, but I don’t think time travel will be one of those consequences.
Then perhaps new equations, new explanations or new physics rules or laws would have to be formulated. Or perhaps the speed of light would be somewhat viewed like the speed of sound as a limiting speed representing a certain type of singularity. In any case, these are just speculations or general ideas at the present time.
To conclude (again), I think time travel (to the past as well as to the future ) is not possible and will not happen.
A way of proving this could be found not only in physics or in the physical or natural sciences, but also in the objective study of the structure and the rules of (human) historical events, and the realization that there are ‘laws’, patterns and regularities which govern these events.
There will be regrettably no “quantum leap time travel machine”, and no “quantum realm time machine”, these expressions illustrating how the word “quantum” is inaccurately used as a hype word in a attempt to add a veneer of “scientificity” or plausibility to the movies using them. Nobody will be able to travel in time to kill this or that person, or to change history. The Terminator will not and cannot be sent back in time, neither to save nor to kill John and Sarah Connor. The time machine in the eponymous novel by H.G. Wells is not feasible and will not work. The DC comics character the Flash will sadly not be able to change and reverse timelines, or to travel back in time to change past events. I could go on mentioning other examples, novels, works and movies, but I think I got the idea across.
The last several decades witnessed a craze or a fad for entertaining movies involving or dealing with time travel, but I consider that time travel movies, or in general movies that rely on time travel as a plot twist, plot device or as a deus ex machina to solve everything, lack scientific accuracy, and I suggest that moviemakers increasingly stop using time travel altogether, because in the future or in the next decades these types of movies will be viewed or assessed negatively.
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:
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:
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:
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):
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:
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.”
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.
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.
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.
Earth is the third planet from the sun, an Earth year is approximately equal to 365.26 days.
Mars is the fourth planet from the sun, a year on Mars is approximately equal to 687 (Earth) days.
Earth moves in an orbit around the sun at an average (semi-major axis) distance of 149,598,023 km, or 92,955,902 miles, or 1 AU (astronomical unit).
Mars moves in an orbit around the sun at an average distance 227,939,200 km , or 141,634,850 miles, or 1.523679 AU.
Mars Oppositions occur when Earth passes between the Sun and planet Mars. Mars oppositions take place approximately every 2 years and 2 months, or every 779.94 Earth days. During these times of opposition, the two planets have the closest distance to each other.
Two useful or interesting dates of closest encounter and closest distance between Earth and Mars are the following ones.
The first date of closest encounter is June 27, 2033. At this date, the distance between Earth and Mars will be approximately 0.428 AU.
To visualize things better, below is an image showing the positions of Earth and Mars and of neighboring celestial bodies on January 29, 2033 (image source: 3D Solar System Simulator):
Below is an image showing the positions of Earth and Mars and of neighboring celestial bodies on June 29, 2033 (image source: 3D Solar System Simulator):
A second date of closest encounter is September 15, 2035. At this date, the distance between Earth and Mars will be approximately 0.381 AU.
The first of these two dates of closest encounter, June 27, 2033 (give or take a few days), could be realistically chosen as the time and date when a human will land on Mars.
People and humans have been planning and wanting to go and set foot on the red planet for the last few decades, some intending to go there in an unprepared and unrealistic way.
In order to ensure the success of the first human mission or trip to Mars, the mission should be the result of international cooperation, everyone taking part in the trip ought to be very well trained and prepared. All the aspects of the mission (technological, scientific, computational, financial, …) ought to be thoroughly taken into consideration, so that the human crew will be able to land on Mars, stay there for a determined short period of time, and return back safely to Earth.
The human mission or trip to Mars is not a game or a one-way voyage with uncertain or harmful results and consequences.This will be a very important event in the history of humankind, and not everyone is ready or able to make the journey to Mars .But those humans who will travel to Mars should be prepared to the maximum.
The human crew would be sent a few months earlier to Mars, so that they would land on Mars at a date approaching the date of closest Earth-Mars distance of June 2033. Hence one of the best dates for humans to set foot on Mars for the first time would be in the summer of 2033.
Among the various factors upon which the progress and success of the mission will depend, one important factor would be the readiness and sagacity of the leader of the first human mission to Mars, who will most likely be the first person to set foot on Mars, and whose decisions will be essential and vital to the suitable choice of dates, and to the successful planning, unfolding, development, and accomplishment of the first human mission to planet Mars.
What were the benefits for early human groups and populations to travel and discover new lands, or to build rafts, boats or ships, move from seashore to seashore and inhabit different regions and continents?
What were the benefits for the explorers or navigators of the past to risk traveling across seas and oceans or to circumnavigate this planet?
Ever heard about human curiosity, human ingenuity and inventiveness, the human desire, inclination and potentiality to know, to learn, to adapt, to investigate, to discover, to transcend, to go beyond the limits, to rise above adversity, “to boldly go where no one has gone before”?
Robots, spacecrafts or space probes can help humans gather information and make new discoveries, but they are not meant to replace them.
It has been said that exploring and inhabiting Mars would turn humanity into a bi-planetary or a multi-planetary species, which I think is advantageous and important. And as Konstantin Tsiolkovsky stated: “The Earth is the cradle of humanity, but one cannot remain in the cradle forever.” Sending humans to Mars and humans going there is a very significant event, a necessary endeavor and the logical next step in the progress and evolution of humankind. Of course this event should be well planned, well organized and should be done the right way.
In order to make the human mission to Mars a reality, a crew of several men and women will constitute the group of people who will make the first trip to planet Mars. This trip will have to be the result of meticulous preparation, international efforts and international cooperation.
It is reasonable to assume that the nations which are capable of sending humans and astronauts to outer space by their own means, will have to and will want to play a primary role in this endeavor, but the first human trip to Mars must be a global, international and joint effort in order to succeed.
Moreover, it would be best for the leader of the first manned mission to Mars, and the first one to set foot on Mars, to rise above national allegiances and narrow interests, and to act as a representative of the entire human species.
Setting up a “colony”, or establishing a constant human presence on Mars and inhabiting the red planet would require many things.
Here are some things or points to take into consideration, and some requirements that come to mind.
Having or getting access to water (frozen or otherwise) on Mars through drilling.
Building or creating artificial Mars habitats with complex life-support systems.
Equipment for energy production and energy storage, and equipment for moving over the Martian surface.
Equipement necessary to produce food, propellant, water, energy, and breathable oxygen.
Basic utilities to deal or cope with the inhospitable Martian environment.
Establishing the necessary means of communication with Earth.
The following facts have to be taken into account:
Mars has a weaker global magnetosphere than Earth does. Combined with a thin atmosphere, this allows a significant amount of ionizing radiation to reach the Martian surface.
Mars has a surface gravity 0.38 times that of Earth. The density of its atmosphere is about 0.6% of that on Earth. Moreover, landing piloted missions on Mars would require braking and landing systems different from those used to land crewed spacecraft on the Moon or robotic missions on Mars.
That being said, we are getting ahead of ourselves.
The first human mission to planet Mars will not and should not be a one-way trip or a suicide mission. As a result of meticulous preparation and global cooperation, a crew or “team” of thoroughly trained, qualified and prepared astronauts will go to Mars, most likely in the first years of the third decade of this century. They will land on Mars, stay there and explore for a limited period of time (possibly a few weeks), and then come back safely to Earth.
At this time, few people are prepared or ready to go to Mars. Sending many or lots of humans to Mars around 2050 is an unrealistic project. Such ill-considered, incautious, precipitate ideas or plans will very likely end or result in failure, tragedy, disaster, and people getting killed.
A number of years or a few decades after the first human mission to Mars, when the time is right, there will be a second exploratory mission, and a third one if necessary. These successive missions could gradually and properly pave the way for a more permanent human presence on Mars.
It is also to be noted that the existing formal educational system (which needs to be reformed) with its structure and requirements doesn’t prepare people or make them better candidates to travel to Mars or to another planet. If a person for example entered the university at the age of 18 or higher and obtained a higher education diploma or degree, such as a master’s degree or a science PhD, this might be useful for going to the Moon or traveling in the vicinity of planet Earth, but it does not qualify the aforesaid person to be able or be ready to go or to travel to Mars.
I will add some remarks on using the words colony and colonize.
According to the Shorter OED, a colony is “ A settlement in a new country; a body of settlers forming a community fully or partly subject to the mother state; the territory of such settlers”.
Another dictionary definition of the word colony is “A group of people living in colony, comprising the original settlers and their descendants and successors”.
Yet another definition is “a group of people of a particular nationality, race or ethnicity living in a foreign place“.
The word or verb (to) colonize means “to establish a colony”, or “send settlers to a place and establish control over it”, or “settle and establish control over the indigenous people of a place”.
There are no humans or indigenous people present or living on planet Mars.
I often prefer to use the expression “human exploration” instead of the word “colonize” or “colonization” in relation to Mars, as the term “colonize” includes meanings or historical connotations involving aggressiveness, brutality, and the subjugation of others. But since there are no existing humans or intelligent life forms on Mars, I guess the word “colonize” could be used as well.
At any rate, the first one or two human missions to Mars ought to be dedicated to exploration instead of “colonization”, in the sense that it is early and premature for the first humans who will set foot on Mars to start building habitations or “colonies” and to stay for a long time on the red planet.
Knowledge mix 
