Galileo's telescope - Jovilabe

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In January 1610, while exploring the heavens with his telescope, Galileo (1564-1642) discovered four small star-like objects around Jupiter. Having soon concluded that these were the planet's satellites or moons, he sought to establish their orbits and periods.
The velocities of orbital motion decrease from the innermost to the outermost moon. All four display almost the same brightness. It was difficult, therefore, to work out which was which and calculate how long they took to complete their orbits around the planet.
To determine the positions of the moons without having to perform complex calculations each time, Galileo developed a diagram-a sort of analog calculator-called the Jovilabe. The design shows Jupiter and the orbits of the four moons to scale. The orbits are placed in a grid of parallel vertical lines spaced at intervals equal to the radius of Jupiter.
While making his telescopic observations, Galileo would estimate the apparent distance of a moon from the planet in units equal to Jupiter's radius. The intersection between the vertical line corresponding to this distance and the circle representing the moon's orbit gave its position instantly. By means of a thread, one could read the value on the marked scale drawn in the margin.
However, the moons' observed positions vary with the relative positions of Jupiter and the Earth in the course of their revolutions around the Sun. For example, the timing of a moon's passage in front of Jupiter, as seen from the Earth, differs from the timing of the same phenomenon if it were observed from the Sun. The time difference depends on the Earth-Jupiter-Sun angle, known as the annual parallax.
To cancel this continuously variable effect, Galileo recorded the motion of the moons relative not to the Earth, but to the Sun. To avoid complicated calculations, he developed a second diagram consisting of a representation, to scale, of the orbits of Jupiter and the Earth around the Sun. Jupiter is assumed to be immobile at the moment of the observation. The diagram features a graduated scale giving the Earth's position relative to Jupiter. The parallax value could be read instantly on another graduated scale.
The two diagrams were combined into a single instrument, known as the Jovilabe. Jupiter's position at the moment of observation was computed by means of a rotating disk. A moving pointer, fixed with an arm to the instrument's plate, served to determine the Earth's position at that same moment. The arm thus represents the Earth-Jupiter link, i.e., the observer's continually changing line of sight. The parallax value for any position of the Earth relative to Jupiter could be read directly on a scale on the upper rim of the instrument.


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