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Italy Scholarship/Erudition

Jupiter, Io, and the Speed of Light

Ole Rømer first demonstrated in 1676 that light does not travel instantaneously by studying the apparent motion of Jupiter’s moon Io.

The speed of light in vacuum, commonly denoted c, is a universal physical constant that is exactly equal to 299,792,458 meters per second.

It is exact because, by a 1983 international agreement, a meter is defined as the length of the path traveled by light in vacuum during a time interval of 1⁄299792458 second. This particular value was chosen to provide a more accurate definition of the meter that still agreed as much as possible with the definition used before. See, for example, the NIST website or the explanation by Penrose.

The second is, in turn, defined to be the length of time occupied by 9192631770 cycles of the radiation emitted by a cesium-133 atom in a transition between two specified energy states.

John Haytack / Neil deGrasse Tyson Facebook page, 3/20/2024 8:58pm

Ole Christensen Rømer

Wait, how do you get calculate the speed of light 350 years ago, by studying Jupiter’s moon Io?

Ole Christensen Rømer (25 September 1644 – 19 September 1710) was a Danish astronomer who, in 1676, made the first measurement of the speed of light and discovery that light travels at a finite speed. Rømer also invented the modern thermometer showing the temperature between two fixed points, namely the points at which water respectively boils and freezes.

Rømer measured the speed of light to be approximately 220,000 kilometers per second while working at the Royal Observatory in Paris. Rømer made this approximation while he was conducting studies of Jupiter’s moon Io. As of the 21st century, the speed of light has been measured to be just under 300,000 kilometers per second.

Wikipedia / Photo By SFDan – Own work, CC BY-SA 3.0

Ole Rømer was into a lot of things.

In 1700, Rømer persuaded the king to introduce the Gregorian calendar in Denmark and Norway – something Tycho Brahe had argued for in vain a hundred years earlier.

Rømer developed a temperature scale while convalescing from a broken leg. After visiting with Rømer in 1708, Daniel Gabriel Fahrenheit began making his thermometers using a modified version of Rømer’s scale that eventually evolved into the Fahrenheit scale still popular in the United States and a few other countries.

Wikipedia / Photo of Academie Royale des Sciences, December 7, 1676., Public Domain

In 1705, Rømer was made the second Chief of the Copenhagen Police, a position he kept until his death in 1710. As one of his first acts, he fired the entire force, being convinced that the morale was alarmingly low.

Wikipedia

An interesting series of events led up to Rømer’s discovery of the speed of light.

Where am I here? Once you lose sight of land, how can you tell where your ship is? Longitude proved to be especially tricky. Latitude was a little easier – measure the elevation of the sun at noon, then use a table lookup based on the date.

Philip III of Spain offered a prize for a method to determine the longitude of a ship out of sight of land, and Galileo proposed a method of establishing the time of day, and thus longitude, based on the times of the eclipses of the moons of Jupiter, in essence using the Jovian system as a cosmic clock

Wikipedia

There was actually great interest throughout Europe in determining an accurate longitudinal position, with significant financial incentives. There is a Wikipedia page dedicated to chasing the longitudinal prize.


Philip II of Spain offered [a reward] in 1567, Philip III in 1598 offered 6,000 ducats[1] and a pension, whilst the States General of the Netherlands offered 10,000 florins shortly after. In 1675 Robert Hooke wanted to apply for a £1,000 reward in England for his invention of a spring-regulated watch.

Wikipedia

[1] The gold-based ducat is worth about $149 in today’s money, so
6,000 * $149 = $894,000.


Semi-Sequitur: Philip III of Spain

Philip III (14 April 1578 – 31 March 1621) was King of Spain. As Philip II, he was also King of Portugal, Naples, Sicily and Sardinia and Duke of Milan from 1598 until his death in 1621.

Philip married his cousin, Margaret of Austria, on 18 April 1599, a year after becoming king.

Wikipedia

History has not been kind:

Historians C. V. Wedgwood, R. Stradling and J. H. Elliott have described him, respectively, as an “undistinguished and insignificant man,” a “miserable monarch,” and a “pallid, anonymous creature, whose only virtue appeared to reside in a total absence of vice.”

Wikipedia

Mr. and Mrs. Philip III:

Galileo proposed this method [the times of the eclipses of the moons of Jupiter] to the Spanish crown (1616–1617) but it proved to be impractical, because of the inaccuracies of Galileo’s timetables and the difficulty of observing the eclipses on a ship. However, with refinements, the method could be made to work on land.

After studies in Copenhagen, Rømer joined Jean Picard in 1671 to observe about 140 eclipses of Jupiter’s moon Io on the island of Hven at the former location of Tycho Brahe’s observatory of Uraniborg, near Copenhagen, over a period of several months, while in Paris Giovanni Domenico Cassini observed the same eclipses. By comparing the times of the eclipses, the difference in longitude of Paris to Uraniborg was calculated.

Wikipedia

Semi-Sequitur: The Galilean Moons

The Galilean moons, or Galilean satellites, are the four largest moons of Jupiter: Io, Europa, Ganymede, and Callisto. They are the most readily visible Solar System objects after the unaided visible Saturn… The invention of the telescope enabled the discovery of the moons in 1610. Through this, they became the first Solar System objects discovered since humans have started tracking the classical planets, and the first objects to be found to orbit any planet beyond Earth.

As a result of improvements Galileo Galilei made to the telescope, with a magnifying capability of 20×, he was able to see celestial bodies more distinctly than was previously possible. This allowed Galileo to observe in either December 1609 or January 1610 what came to be known as the Galilean moons.

Galileo proposed determining longitude based on the timing of the orbits of the Galilean moons. The times of the eclipses of the moons could be precisely calculated in advance and compared with local observations on land or on ship to determine the local time and hence longitude. Galileo applied in 1616 for the Spanish prize of 6,000 gold ducats with a lifetime pension of 2,000 a year, and almost two decades later for the Dutch prize, but by then he was under house arrest for possible heresy.

Io (Jupiter I) is the innermost of the four Galilean moons of Jupiter; with a diameter of 3642 kilometers, it is the fourth-largest moon in the Solar System, and is only marginally larger than Earth’s moon. It was named after Io, a priestess of Hera who became one of the lovers of Zeus. It was referred to as “Jupiter I”, or “The first satellite of Jupiter” until the mid-20th century.

With over 400 active volcanos, Io is the most geologically active object in the Solar System. Its surface is dotted with more than 100 mountains, some of which are taller than Earth’s Mount Everest. Unlike most satellites in the outer Solar System (which have a thick coating of ice), Io is primarily composed of silicate rock surrounding a molten iron or iron sulfide core.

The orbital period of IO is 1.769 days, compared to Earth’s moon, at about 27.3 days [2]. In practical terms, Io is hauling freight, and an Earth-based observer can view the Ioian eclipse fairly frequently

Wikipedia

[2] Nothing is simple:

The Moon takes about one month to orbit Earth (27.3 days to complete a revolution, but 29.5 days to change from New Moon to New Moon). As the Moon completes each 27.3-day orbit around Earth, both Earth and the Moon are moving around the Sun.

NASA

Back to the Speed of Light

Cassini had observed the moons of Jupiter between 1666 and 1668, and discovered discrepancies in his measurements that, at first, he attributed to light having a finite speed. In 1672 Rømer went to Paris and continued observing the satellites of Jupiter as Cassini’s assistant. Rømer added his own observations to Cassini’s and observed that times between eclipses (particularly those of Io) got shorter as Earth approached Jupiter, and longer as Earth moved farther away. Cassini made an announcement to the Academy of Sciences on 22 August 1676:

This second inequality appears to be due to light taking some time to reach us from the satellite; light seems to take about ten to eleven minutes [to cross] a distance equal to the half-diameter of the terrestrial orbit.

Oddly, Cassini seems to have abandoned this reasoning, which Rømer adopted and set about buttressing in an irrefutable manner, using a selected number of observations performed by Picard and himself between 1671 and 1677. Rømer presented his results to the French Academy of Sciences, and it was summarised soon after by an anonymous reporter in a short paper, Démonstration touchant le mouvement de la lumière trouvé par M. Roemer de l’Académie des sciences, published 7 December 1676 in the Journal des sçavans. Unfortunately, the reporter, possibly in order to hide his lack of understanding, resorted to cryptic phrasing, obfuscating Rømer’s reasoning in the process. Rømer himself never published his results.

Wikipedia

A Wikipedia article goes into greater detail here: Rømer’s determination of the speed of light.

There is also a Techno video aide:


More moon, please….

Snopes approved….


Mythology

Io was an Argive priestess of Hera, the daughter of the river god Inachus or, in some accounts, of the Argive king Iasus.

A lover of Zeus, Io was transformed into a cow when Zeus’ wife Hera discovered their affair. This metamorphosis, though dramatic, was not enough for Hera; the jealous goddess also had her rival held prisoner, appointing the many-eyed monster Argus Panoptes to watch over her.

After Io escaped from Argus (with the help of the god Hermes), Hera next sent a gadfly to chase her to Egypt. It was in Egypt that Io was at last restored to her true form and gave birth to a son, Epaphus. In later times, Io was often identified with the Egyptian goddess Isis.

Io’s story is one of many myths describing Zeus’ adulterous (and disastrous) affairs. Her metamorphosis has sometimes been interpreted as a metaphor for initiation rites and the transition of girls into adulthood.

Mythopedia

Io was a priestess of the Roman goddess Juno. Juno was the jealous wife of Jupiter, the king of the gods. Jupiter was very unfaithful. When Jupiter fell in love with Io, he changed himself into the shape of a dark cloud to hide himself from his jealous wife Juno.

However, Juno looked down on earth and noticed the small cloud. She knew it was her husband. As soon as Juno arrived, Jupiter immediately transformed Io into a white cow to avoid his wife’s wrath. But Juno tied the poor cow and sent her faithful servant Argus to watch over Io. Argus had a hundred eyes and only a few were ever closed at any time.

Windows To the Universe

More Io

Io (Ancient Greek: Ἰώ [iːɔ̌ː]) was, in Greek mythology, one of the mortal lovers of Zeus. An Argive princess, she was an ancestor of many kings and heroes, such as Perseus, Cadmus, Heracles, Minos, Lynceus, Cepheus, and Danaus. The astronomer Simon Marius named a moon of Jupiter after Io in 1614.

Wikipedia

And What About “Ides”?

The Ides (the midpoint of the month, with a full moon) was sacred to Jupiter, because on that day heavenly light shone day and night. Some (or all) Ides were Feriae Iovis, sacred to Jupiter. On the Ides, a white lamb (ovis idulis) was led along Rome’s Sacred Way to the Capitoline Citadel and sacrificed to him. Jupiter’s two epula Iovis festivals fell on the Ides, as did his temple foundation rites as Optimus Maximus, Victor, Invictus and (possibly) Stator.

Wikipedia

Semi-Sequitor: Galileo’s Telescope

It’s amazing how something we take for granted today (a child’s toy!) changed the world. Gallio’s telescope was 20x.

For 1/10 to 1/5 ducat, you could now buy:

Or, for around a ducat:

The Museo Galileo

The Museo Galileo has a cool website. The museum is located at Piazza dei Giudici 1 – 50122 Florence, Italy.

And before you ask, No and No.

Google Street View lets you drive around the inside of the Museo.


Research Notes

WLBOTT Wonders: Under King Philip III of Spain, how many ducks could you purchase with a single ducat?

ChatGPT: Ah, during the reign of King Philip III of Spain, the purchasing power of a ducat could vary depending on several factors such as location, market conditions, and the quality of the duck. However, let’s indulge in some historical silliness!

In the spirit of silliness and without exact historical data, let’s imagine that during King Philip III’s reign, a single ducat could buy you approximately 10 ducks. Of course, this is a purely speculative and whimsical estimation, as ducks were likely not priced in ducats during that time. But hey, in the realm of silliness, anything is possible!

[So, the longitudinal prize money could be used to by 60,000 ducks.]

WLBOTT: I like your phrase, “the quality of the duck”.

ChatGPT: Thank you! After all, when it comes to ducks, one must consider their quack-tastic qualities: feather fluffiness, waddle elegance, and, of course, their quacking proficiency! Quality is key, even in the whimsical world of duck purchasing with ducats.


ChatGPT: Using the moons of Jupiter to calculate longitude might sound like something out of a science fiction novel, but it’s actually a fascinating historical method known as the method of lunar distances.

Here’s how it works:

1. **Observation**: Astronomers would observe the positions of Jupiter’s moons (specifically the Galilean moons: Io, Europa, Ganymede, and Callisto) relative to Jupiter.

2. **Record Time**: They would record the exact time of these observations.

3. **Reference Tables**: By consulting precomputed tables or equations, they could determine the precise positions of Jupiter’s moons at Greenwich Mean Time (GMT) for that particular moment.

4. **Comparison**: By comparing the observed positions of Jupiter’s moons with their positions as predicted for GMT, they could calculate the time difference between the observed local time and GMT.

5. **Longitude Calculation**: Since Earth rotates 15 degrees longitude every hour (or 1 degree every 4 minutes), this time difference could be converted into a longitudinal difference.

6. **Navigation**: Sailors would then use this longitudinal difference to determine their position relative to Greenwich, aiding in navigation.

This method was particularly useful before the invention of accurate timekeeping devices, as it provided a way to calculate longitude at sea, where precise timekeeping was challenging due to the motion of the ship. However, it required careful observation and calculation skills, as well as accurate astronomical tables.

2 replies on “Jupiter, Io, and the Speed of Light”

“whose only virtue appeared to reside in a total absence of vice.” – I thought this described Mike Pence.

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