{"id":22312,"date":"2024-03-22T18:41:06","date_gmt":"2024-03-22T23:41:06","guid":{"rendered":"https:\/\/www.wlbott.com\/?p=22312"},"modified":"2024-03-22T18:53:41","modified_gmt":"2024-03-22T23:53:41","slug":"jupiter-io-and-the-speed-of-light","status":"publish","type":"post","link":"https:\/\/www.wlbott.com\/?p=22312","title":{"rendered":"Jupiter, Io, and the Speed of Light"},"content":{"rendered":"\n
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Ole R\u00f8mer<\/strong> first demonstrated in 1676 <\/strong>that light does not travel instantaneously by studying the apparent motion of Jupiter’s moon Io<\/strong>.<\/p>\n\n\n\n

The speed of light in vacuum, commonly denoted c, is a universal physical constant that is exactly equal to<\/strong> 299,792,458 meters per second.<\/p>\n\n\n\n

It is exact<\/strong> 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\u2044299792458<\/strong> 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.<\/p>\n\n\n\n

The second is, in turn, defined to be the length of time occupied by 9192631770 cycles<\/strong> of the radiation emitted by a cesium-133 atom in a transition between two specified energy states.<\/p>\nJohn Haytack \/ Neil deGrasse Tyson Facebook page, 3\/20\/2024 8:58pm<\/cite><\/blockquote>\n\n\n\n

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Ole Christensen R\u00f8mer<\/h3>\n\n\n\n

Wait, how do you get calculate the speed of light 350 years ago, by studying Jupiter’s moon Io?<\/p>\n\n\n\n

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Ole Christensen R\u00f8mer<\/strong> (25 September 1644 \u2013 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. R\u00f8mer also invented the modern thermometer showing the temperature between two fixed points, namely the points at which water respectively boils and freezes.<\/p>\n\n\n\n

R\u00f8mer measured the speed of light to be approximately 220,000 kilometers per second while working at the Royal Observatory in Paris. R\u00f8mer 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.
\"\"<\/p>\nWikipedia<\/a> \/ Photo By SFDan – Own work, CC BY-SA 3.0<\/cite><\/blockquote>\n\n\n\n

Ole R\u00f8mer was into a lot of things.<\/p>\n\n\n\n

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In 1700, R\u00f8mer persuaded the king to introduce the Gregorian calendar <\/strong>in Denmark and Norway \u2013 something Tycho Brahe had argued for in vain a hundred years earlier.<\/p>\n\n\n\n

R\u00f8mer developed a temperature scale while convalescing from a broken leg. After visiting with R\u00f8mer in 1708, Daniel Gabriel Fahrenheit <\/strong>began making his thermometers using a modified version of R\u00f8mer’s scale that eventually evolved into the Fahrenheit scale still popular in the United States and a few other countries.<\/p>\nWikipedia<\/a> \/ Photo of Academie Royale des Sciences, December 7, 1676., Public Domain<\/cite><\/blockquote>\n<\/div><\/div>\n\n\n\n

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In 1705, R\u00f8mer 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.<\/strong><\/em><\/p>\nWikipedia<\/a><\/cite><\/blockquote>\n\n\n\n

An interesting series of events led up to R\u00f8mer’s discovery of the speed of light.<\/p>\n\n\n\n

Where am I here?<\/strong> 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.<\/p>\n\n\n\n

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Philip III<\/strong> 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<\/strong>, in essence using the Jovian system as a cosmic clock<\/p>\nWikipedia<\/a><\/cite><\/blockquote>\n\n\n\n

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

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Philip II of Spain offered [a reward] in 1567, Philip III in 1598 offered 6,000 ducats<\/strong>[1]<\/sup> and a pension<\/strong>, whilst the States General of the Netherlands offered 10,000 florins shortly after. In 1675 Robert Hooke wanted to apply for a \u00a31,000 reward in England for his invention of a spring-regulated watch.
\"\"<\/p>\nWikipedia<\/a><\/cite><\/blockquote>\n\n\n\n

[1]<\/sup> The gold-based ducat is worth about $149 in today’s money, so
6,000 * $149 = $894,000.<\/p>\n\n\n\n

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Semi-Sequitur: Philip III of Spain<\/h3>\n\n\n\n
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Philip III<\/strong> (14 April 1578 \u2013 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.<\/p>\n\n\n\n

Philip married his cousin, Margaret of Austria, on 18 April 1599, a year after becoming king.<\/p>\nWikipedia<\/a><\/cite><\/blockquote>\n\n\n\n

History has not been kind: <\/p>\n\n\n\n

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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<\/em>.”<\/p>\nWikipedia<\/a><\/cite><\/blockquote>\n\n\n\n

Mr. and Mrs. Philip III:<\/p>\n\n\n\n

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Galileo<\/strong> proposed this method [the times of the eclipses of the moons of Jupiter] to the Spanish crown (1616\u20131617) 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.<\/p>\n<\/blockquote>\n<\/div><\/div>\n\n\n\n

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After studies in Copenhagen, R\u00f8mer<\/strong> joined Jean Picard<\/strong> in 1671 to observe about 140 eclipses of Jupiter’s moon Io on the island of Hven at the former location of Tycho Brahe<\/strong>\u2019s observatory of Uraniborg, near Copenhagen, over a period of several months, while in Paris Giovanni Domenico Cassini<\/strong> observed the same eclipses. By comparing the times of the eclipses, the difference in longitude of Paris to Uraniborg was calculated.<\/p>\nWikipedia<\/a><\/cite><\/blockquote>\n\n\n\n

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Semi-Sequitur: The Galilean Moons<\/h3>\n\n\n\n
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The Galilean moons, or Galilean satellites, are the four largest moons of Jupiter: Io<\/strong>, Europa<\/strong>, Ganymede<\/strong>, and Callisto<\/strong>. They are the most readily visible Solar System objects after the unaided visible Saturn… The invention of the telescope<\/strong> enabled the discovery of the moons in 1610<\/strong>. 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.<\/p>\n\n\n\n

As a result of improvements Galileo Galilei made to the telescope, with a magnifying capability of 20\u00d7<\/strong>, 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.<\/p>\n\n\n\n

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<\/strong><\/em>, and almost two decades later for the Dutch prize, but by then he was under house arrest for possible heresy.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

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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.<\/p>\n\n\n\n

The orbital period of IO is 1.769 days<\/strong>, compared to Earth’s moon, at about 27.3 days<\/strong> [2]<\/sup>. In practical terms, Io is hauling freight, and an Earth-based observer can view the Ioian eclipse fairly frequently<\/p>\nWikipedia<\/a><\/cite><\/blockquote>\n\n\n\n

[2]<\/sup> Nothing is simple:<\/p>\n\n\n\n

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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.<\/p>\nNASA<\/a><\/cite><\/blockquote>\n\n\n\n

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Back to the Speed of Light<\/h3>\n\n\n\n
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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 R\u00f8mer went to Paris and continued observing the satellites of Jupiter as Cassini’s assistant. R\u00f8mer 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:<\/p>\n\n\n\n

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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.<\/p>\n<\/blockquote>\n\n\n\n

Oddly, Cassini seems to have abandoned this reasoning, which R\u00f8mer adopted and set about buttressing in an irrefutable manner, using a selected number of observations performed by Picard and himself between 1671 and 1677. R\u00f8mer presented his results to the French Academy of Sciences, and it was summarised soon after by an anonymous reporter in a short paper, D\u00e9monstration touchant le mouvement de la lumi\u00e8re trouv\u00e9 par M. Roemer de l’Acad\u00e9mie des sciences, published 7 December 1676 in the Journal des s\u00e7avans. Unfortunately, the reporter, possibly in order to hide his lack of understanding, resorted to cryptic phrasing, obfuscating R\u00f8mer’s reasoning in the process. R\u00f8mer himself never published his results.<\/p>\nWikipedia<\/a><\/cite><\/blockquote>\n\n\n\n

A Wikipedia article goes into greater detail here: R\u00f8mer’s determination of the speed of light<\/a>.<\/p>\n\n\n\n

There is also a Techno video aide: