Johann Daniel Titius: Original Author Of Bode’s Law?

Even though he’s not a well known household name like Newton, did the astronomer and mathematician Johann Daniel Titius the original author of Bode’s Law?

By: Ringo Bones

It has since been rechristened as the Titius-Bode Law and in his honor, an asteroid – 1998 Titius - and a crater on the Moon was named after him, the 18^th Century German mathematician and astronomer Johann Daniel Titius never became a well-known household name like the Englishman Isaac Newton. But nonetheless, Titius did make some important contributions to mathematics, physics, astronomy and biology during his lifetime.

Johann Daniel Titius (1729 – 1796) was born on January 2, 1729 in Konitz Royal Prussia – a fiefdom of the Crown of Poland – to Jakob Tietz, a merchant and council member from Konitz, and Maria Dorothea, née Hanow. His original name was Johann Tietz, but as was customary in the 18^th Century, when he became a university professor, he Latinized his surname to Titius. Teitz attended school in Danzig (Gdansk) and studied at the University of Leipzig (1749-1752). He died in Wittenberg, Electorate of Saxony on December 16, 1796.

Titius proposed his law of planetary distances in an unsigned interpolation in his German translation of the Swiss philosopher Charles Bonnet’s Contemplation de la nature (“Contemplation of Nature”). Titius fixed the scale by assigning 100 to the distance of the planet Saturn from the Sun. On this scale, planet Mercury’s distance from the Sun is approximately 4. Titius therefore proposed that the sequence of planetary distances (starting from Mercury and moving outward) has the form:  4,4 + 3,4 + 6,4 + 12,4 + 24,4 + 48,4 + 96,…

There was an empty place at distance 28, or 4 + 24 (between the planets Mars and Jupiter), which Bode asserted, the Founder of the Universe surely has not left unoccupied. Titius’ sequence stopped with the planet Saturn, the most distant planet then known. His law was reprinted, without his credit, by Johann Elert Bode in the second edition of his Deutliche Anleitung zur Kenntniss des gestirnten Himmels (Clear Guide to Knowledge of the Starry Heaven) in 1772. In later editions, Bode did credit Titius, but this mostly escaped notice and during the 19^th Century the law was usually associated with Bode’s name.

Titius published a number of works on other areas in physics, such as a set of conditions and rules for performing experiments and he was particularly focused in thermometry. In 1765, he presented a survey of thermometry up to that date. He wrote about the metallic thermometer constructed by Hans Loeser. In his treatises on both theoretical and experimental physics, he incorporated the findings of other scientists, such as the descriptions of experiments written by Georg Wolfgang Kraft in 1738.

As a confirmed polymath, Titius was also active in biology, particularly in classification of organisms and minerals. His biological work was influenced by Carolus Linnaeus. Lehrbegriff der Naturgeschichte Zum ersten Unterrichte, his most extensive publication in biology, was on the systematic classification of plants, animals and minerals, as well as the elemental substances: ether, fire, air, water and earth. The standard author abbreviation Titius is used to indicate Johann Daniel Titius as the author when citing a botanical name.

The Mysterious Bode’s Law: The Most Puzzling Law Of Science?

Often cited as the most productive – and most puzzling – scientific law at the same time, are there any mysteries behind Bode’s Law?

By: Ringo Bones

This rather “curious” scientific law was named after an 18^th Century German astronomer and mathematician named Johann Elert Bode, but contrary to popular belief, it was actually discovered by Johann Daniel Titius – a German mathematician – back in 1766. However, the empirical relation that gives the approximate distances of the planets from the Sun did not attract attention to the 18^th Century astronomical community until it was publicized by Johann Elert Bode – whose name has since then associated with it – back in 1772.

To the uninitiated, Johann Elert Bode (1747-1826) was an Eighteenth Century era German astronomer who popularized an empirical law that was later named after him, which gives the approximate distances of the planets from the Sun. Bode was also famous for naming the planet Uranus that ended the confusion in the astronomical community at the start of the 19^th Century when the British astronomer William Herschel desired to name the then newly discovered planet as Georgium Sidius after King George III of England.

After examining the work of fellow German mathematician, Johann Daniel Titius, Bode noted that the distances of the various planets from the Sun fell into a curious mathematical sequence. Bode then published a paper which arbitrarily assigned numbers to the planets: 0, 3, 6, 12, 24, 48, 96, and 192. Thus the planet Mercury was numbered 0, planet Venus 3, planet Earth 6, planet Mars 12, and so on, each number being double the last one. When 4 was added to each of these numbers and the result is divided by 10, figures emerged which almost exactly equaled the planets’ distances from the Sun, measured in astronomical units. By the way, an astronomical unit is a unit of distance between the planet Earth and the Sun – which is around 93-million miles or 150-million kilometers.

The only trouble with the law was that back in the time when Bode published it in 1772, there were no planets found at positions 24 or 192. But astronomers searching in position 24 located the asteroids – around the start of the Nineteenth Century – i.e. the discovery of asteroid Ceres in 1801. The planet Uranus, which was discovered back in 1781, occurs at position 192 and conforms almost exactly to Bode’s calculations. Only the outermost planets – Neptune and the dwarf planet Pluto – failed to obey Bode’s Law. Although many attempts have been made to derive a physical explanation for the law, none has completely succeeded.  Today, many astronomers dismiss Bode’s Law as a coincidence and that Bode’s Law is not a rule governing planetary systems. Yet it remains one of the most mysterious statements of natural law formulated by man.

Can We Build A Cosmic Telescope With Gravitational Lenses?

Using the principles behind Einstein’s General Relativity, is it possible to create a space based telescope with virtually no Raleigh Criterion limits?

By: Ringo Bones

I’ve first heard of the working principle of a cosmic telescope was in an episode of Cosmos: Possible Worlds where Prof. Neil DeGrasse Tyson explains how a space-based telescope using existing – i.e. late 20^th century to early 21^st Century technology - could take advantage of the Sun’s gravitational lensing effect in order to create a telescope capable of seeing the surfaces of extrasolar planets better than the ones we currently use like the Kepler Space Telescope. But first, here’s a brief primer on the principles of gravitational lensing.

The Gravitational lensing effect is a consequence of Einstein’s General Relativity. Often referred by astronomers as a “natural telescope”, gravitational lensing occurs when a huge amount of matter – such as clusters of galaxies – creates a gravitational field that distorts and magnifies the light from distant galaxies that are behind it, but in the same line of sight. The effect allows astronomers to study the details of early galaxies too far away to be seen with current technology and telescope. The gravitational lensing cause by our Sun’s gravitational field can also be used in a similar fashion. You can also spot distant extra-solar planets when a star itself is the interloper if it carries any planets in orbit around it, they will change - ever so slightly – the momentary brightness during the microlensing event.

There are already plans for a “viable” cosmic telescope that could – in theory – make the Raleigh Criterion limitations of the telescopes we currently use, space based or earthbound, completely irrelevant. The Fast Outgoing Cyclopean Astronomical Lens – or FOCAL – is a proposed space telescope that would use our Sun as a gravity lens. The concept of a space-based telescope that takes advantage of the Sun’s gravitational lensing effect was first suggested by Prof. Von Eshleman and analyzed further by Italian astronomer Claudio Maccone and others. In order to use the Sun as a gravitational lens, it would be necessary to position our space telescope to a point in space of at least 550 astronomical units away from the Sun.

The proposed FOCAL telescope can actually use current technology that’s already in use on operational space-based telescopes for astronomical use, however, there are difficulties. The Voyager 1 and Voyager 2 probes are currently at distances within 147 astronomical units and 122 astronomical units. It took them over 40 years to reach those distances using rocket technology we currently have – by the way, both Voyager spacecraft were launched back in 1977. It looks like we won’t be sending space telescopes with comparable technology to the James Webb Space Telescope to a point in space 550 astronomical units – or 51 billion miles or 82.5 billion kilometers– away from our Sun. By way of comparison, the dwarf planet Pluto is “only” 3.7 billion miles or 5.97 billion kilometers away from the Sun.

SpaceX’s Starlink Satellites: Light Pollution Problem For Astronomers?

Intended to improve internet connectivity in far-fringe areas, could the fleet of SpaceX’s Starlink satellites be a source of light pollution problem for astronomers?

By: Ringo Bones

Near the end of 2019, the world’s astronomical community – including a growing number of amateur astronomers – has voiced their concerns that SpaceX founder Elon Musk’s upcoming fleet of satellites intended to provide and improve internet coverage and reception in far-fringe areas - called Starlink - could eventually become a source of light pollution that could eventually interfere with astronomy. But are the concerns of the astronomers valid?

As of May 7, 2020, SpaceX had unveiled plans to make their Starlink satellites “invisible” in order to make them not a source of light pollution that could interfere with astronomical observations. A software upgrade and a new design for the satellites are intended to reduce the interference for astronomers.

Near the end of 2019, the company’s billionaire founder Elon musk had denied claims that the eventual 12,000-strong fleet of satellites could ruin the night sky for astronomers. Bowing to growing pressure from the global astronomical community, SpaceX eventually made plans to make its satellites “generally invisible to the naked eye within a week of launch” following complaints about light pollution and actual photos taken by scores of amateur astronomers of the first batch of the Starlink satellites as a visual proof that it became an unnecessary source of light pollution on various social media sites.

Is The Universe Getting Younger?

Though the new figure might yet be “too old” to satisfy America’s staunchest far-right Creationists, is our universe much, much younger than it really is?

By: Ringo Bones

America’s staunchest far-right Creationist may be buying their time, just waiting for a scientific consensus proving that the entire universe began in 9 o’clock in the morning Greenwich Mean Time on the 23^rd of October 4004 BC. Even the Creationist US Secretary Of State Mike Pompeo was probably elated to hear that the universe could be 2 billion years younger than it actually is. Will it be a matter of time that the universe is proven to be only 6,000 years old to the delight of America’s far-right Creationists and white nationalists?

Scientists estimate the age of the universe by using the movement of stars to measure how fast it is expanding. If the universe is expanding faster, that means it got to its current size more quickly and therefore must be relatively younger. The expansion rate called the Hubble Constant makes for a fast moving – and younger – universe. The generally accepted age of the universe is 13.7 billion years based on a Hubble Constant of 70. But lately a team of astronomers from the Max Plank Institute led by Inh  Jee came up with a Hubble Constant of 82.4, which would put the age of the universe at around 11.4 billion years.

It is somewhat disconcerting that while our understanding of our universe has vastly increased during the past 50 years while that same understanding told us that the universe was much younger than what we knew before. Remember the time when the scientific consensus was that the whole universe is a little over 18 billion years old? Then by the latter half of the 1990s, when the prior discovery and / or conjecture of the concept of dark matter and dark energy a few years before has slashed the age of the universe to 13.8 billion years. And now it is only a little over 11 billion years old. Could the 6,000 year old age of the universe embraced by America’s far-right Creationists, white nationalists and Trump supporters be proven during Mike Pompeo’s lifetime?

First True Picture Of A Black Hole Captured: Astronomical Breakthrough?

Despite of the astronomical community’s over 200 year fascination of the concept, does the recent true picture ever captured of a black hole truly an astronomical breakthrough?

By: Ringo Bones

Maybe we should be thanking first Katie Bouman, a former computer science student at MIT, now at Cal Tech, who developed the sophisticated computer algorithm that made possible the first ever interferometer-based photograph of a black hole. Although it was entirely a team effort, the astronomical community’s fascination of these enigmatic astronomical objects that are commonly referred to as black holes dates back over 200 years.

Now largely forgotten many credit the English clergyman and polymath John Michell for theorizing the existence of black holes, which he then referred to as dark stars and he does it using only Newtonian Physics. During 1783, geologist John Michell wrote a letter to Henry Cavendish outlining the expected properties of dark stars that got published by The Royal Society in their 1784 volume. Michell calculated that that when the escape velocity at the surface of a star was equal to or greater than the speed of light, the generated light would be gravitationally trapped so that the star would not be visible to a distant astronomer. The Sun’s escape velocity = 1/500^th that of the speed of light, would a star with more than 500 times more massive than our Sun has an escape velocity greater than that of the speed of light and would therefore be invisible to nearby astronomers?

It was when Albert Einstein published his General Relativity when our modern understanding of black holes gained widespread popularity. Popular enough that many science fiction writers often used it in their action-adventure scenes. The black hole’s popularity to the general public gained more impetus back in 1964 during the discovery of Cygnus X-1, a strong X-ray source in the constellation Cygnus. His work on stars and how they could become black holes got Subrahmanyan Chandrasekhar the 1983 Nobel Physics Prize.

The recent Event Horizon Telescope breakthrough image shows a halo of dust and gas, tracing the outline of a colossal black hole at the heart of the Messier 87 galaxy, which is 55-million light years from Earth and about 6-billion times the mass of our Sun. The Event Horizon Telescope (EHT) is composed of a network of eight radio telescopes spanning locations from Antarctica to Spain and Chile – was made possible by the involvement of more than 200 scientists. The Event Horizon Telescope achieved the necessary resolution by combining data from the eight of the world’s leading radio observatories, including the Atacama Large Millimetre Array (ALMA) in Chile and the South Pole Telescope, creating a virtual telescope akin to the size of planet Earth.

Despite of the renewed fascination of anyone interested in astronomy and theoretical physics, a number of science fiction writers and Hollywood visual special effects artists were a bit “underwhelmed” because the recently published “true pictures” of the super-massive black hole at the heart of the M 87 galaxy only confirms that their visual representation or artist’s rendering of black holes were right all along. Nonetheless, the resulting astrophysical data obtained by the Event Horizon Telescope may prove to be more useful than the iconic M 87 galaxy super-massive black hole image.

Is Asteroid Cruithne Earth’s Second Moon?

Although now dismissed as just one of the Earth’s 18,000 so-called mini-moons, is asteroid 3753 Cruithne just one of the most popular candidates for Earth’s “second moon”?

By: Ringo Bones

Some astronomers claim that asteroid 2016 HO₃ that was discovered back in April 27, 2016 is the best candidate for Earth’s so-called “second moon” because it is possibly the most stable quasi-satellite of Earth, asteroid 3753 Cruithne still remained very popular of the other 18,000 candidate asteroids that qualified to be Earth’s second moon. Even though all of them never truly orbit around the Earth like the Moon, it seems though that at the moment, asteroid 3753 Cruithne is the most popular candidate for Earth’s second moon.

The name Cruithne is from Old Irish reference to the early Picts, the asteroid was discovered back in October 10, 1986 by Duncan Waldron on a photographic plate taken with the UK Schmidt Telescope at Siding Spring Observatory, Coonabarabran, Australia. Although an earlier discovery of the asteroid back in 1983, when it was still designated as 1983 UH, is credited to Giovanni de Sanctis and Richard M. West of the European Southern Observatory in Chile. It was not until 1997 that asteroid 3753 Cruithne’s unusual orbit was determined by Paul Wiegert and Kimmo Innanen working at York University in Toronto and Seppo Mikkola working at the University of Turku in Finland.

As a Q-type Aten asteroid, 3753 Cruithne got the dubious designation of “Earth’s Second Moon” despite there are other 18,000 asteroids that are viable candidates for this category because it orbits around the Sun in 1:1 orbital resonance with Earth, making it a co-orbital object. Seen from the Earth’s surface, 3753 Cruithne seem to orbit around the Sun in a bean-shaped orbit that effectively describes a horseshoe that can change into a quasi-satellite orbit. Cruithne does not orbit Earth and at times it is on the other side of the Sun, placing Cruithne well outside of Earth’s Hill sphere. Cruithne’s orbit takes it inside the orbit of Mercury and outside the orbit of Mars. Cruithne orbits the Sun in about 1 year but it takes 770 years for the series to complete a horseshoe-shaped movement around the Earth.

At about 5-kilometers, or 3-miles, in diameter, asteroid 3753 Cruithne is far too small in size to achieve hydrostatic equilibrium to achieve a spherical shape. Its closest approach to Earth is 12-million kilometers, or 7 and a half million miles, approximately three times the separation between Earth and the Moon. From 1994 through 2015, Cruithne made its annual approach to Earth every November but it is far too small to be seen on the Earth’s surface at night via the naked eye. While the Moon’s surface gravity is about one-sixth that of Earth, on the surface of asteroid 3753 Cruithne, the surface gravity is probably one-one hundred thousandth that of Earth akin to what the Philae spacecraft experienced when it landed on the Comet 67P / Comet Churyumov - Gerasimenko back in 2014.