sidereal) period in Appendix C, table titled "Planetary Orbital and Satellite Data." We find P = 0.6152 yr. Planet has only gone n degrees total distance around its orbit atĪt a similar expression for an inferior planet: 360 The Earth has to go 360 oĪround, then go another n degrees to make up for the motion of the The synodic period, S, is the number ofĮarth years it takes for Earth to "lap" a planet (i.e., for an outer planet, itĬould be from opposition to opposition, while for an inner planet it couldīe from greatest elongation to greatest elongation).ĭerive an expression for the relationship between S and Pįor a superior (outer) planet. What is the value of E? Since the Earth orbits in exactly 1 Earth year (by definition), Eįor another planet. Where P is the sidereal period in Earth years. Then the rate in degrees/year is just 360 o / P. We pass by a planet, we "nod" at the sy nodic If you wish, you can keep these straight by the following mnemonic: as Orbital periods in this course, we will always mean sidereal period. Of where we are, and does not depend on the motion of the Earth. Once around the Sun (with respect to the stars). This is as seen from Earth, and involves the motion of the Earth. In the same place in the sky relative to the stars (in the same constellation). (this is a superior conjunction, actually), but when nearest the Earth Figureġ also shows how a superior planet reaches conjunction only once When the planet lines up on the opposite side of its orbit. The Sun on the near side, relative to Earth, and a superior conjuction, Have both an inferior conjuction, when the planet lines up with The inferior planets never wander too far from the Sun, but rather reachĮlongation and then appear to move back toward the Sun. Geometry of planetary motions, showing how retrograde motion arisesįrom the orbital motions of Earth and a superior (outer) planet. Of planetary positions, showing greatest elongation, superior conjunction,Īnd inferior conjunction, for inferior (inner) planets, and conjuctionĪnd opposition for superior (outer) planets. Let us examine the motions of the planets in the sky, and how they areĪccounted for by the geometry of the heliocentric model (Figures 1 and How the accuracy of the Copernican model could be improved, but first, In planet positions than did the Ptolemaic system with epicycles. Planets, the planetary motions in perfect circles did not give better accuracy It could account for retrograde motion and the changing brightness of the Although this view is far simpler, andĪccounts more naturally for the motions of the heavens, it had three problems:Įarth did not agree with everyday experience.Įarth took it from its exalted place at the center of the universe. The Moon (which was considered a planet), and the rotation of the starsĪnd planets once every 24-hours was simply accounted for by the turning In a perfect circle about the Sun (the influence of Aristotle's perfect heavens idea), as do all of the other planets except Suggested much earlier, the heliocentric model is attributed to NicholasĬopernicus who wrote the first "modern" description in his book, De To fit almost any situation within the accuracy of observations of his These adjustments, always involving perfect circles, could be adjusted Motion and the fact that planets vary in brightness, Ptolemy introduced Planets moving in perfect circles around the Earth, could not account for
These motions can be demonstrated in any planetarium program (e.g. Mercury and Venus, never wander very far from the Sun, and so reach a maximumĪngular distance, called greatest elongation. Stop, reverse direction ( retrograde motion), Where they often become faintest, and they appear opposite the Sun ( opposition ), They align with the Sun ( conjunctions ), Observations of the sky over many years show that planets obey certain 150 BC) proposed a system of circles to explain the odd motions of the planets as seen from Earth. Having to do with the heavens had to be perfect, hence circular. Handed down from Aristotle (384-322 BC) was the notion that all motions The Sun and planets going around it (attached to heavenly spheres). Or geocentric, system, it placed the immovable Earth at the center, with "obvious" model that originated in prehistory.
100 AD) in his 13-book work, the Almagest, although it is an System, because it was written down by Claudius Ptolemy The Ptolemaic System The ancient modelįor the solar system is called the Ptolemaic
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