![]() ![]() By plotting the orbits and retrogrades simultaneously, the relationship between the positions of the planets and the observed retrograde motion becomes more clear. The purpose of my project is educational, to illustrate a concept which is difficult to grasp when witnessing it in nature and greatly benefits from additional visual aids. The result is a loop or zig-zag in the sky over time.įor my project, I wanted to create a simulation that would plot the retrograde motion in the sky in a way that looked like Figure 3, showing the planets orbiting and showing a line of sight plotting out the typical retrograde loop. From the inner planet’s perspective, the outer planet appears to slow in the sky and then reverse its orbit for a time, before continuing forward again. Retrograde occurs when an inner planet laps and passes and outer planet. However, Kepler’s law proves that planets with greater semi-major axis have greater periods of orbit, which account for the differential speeds of orbit and by extension the apparent retrograde motion. The planets in the solar system have much lower eccentricities than what I’ve illustrated above. Because of Kepler’s third law, and the varying speeds of the orbit at different point of orbit, t1=t2 and a1=a2. At this point, the planet travels distance cd at time t2, sweeping out the area a2. When traveling from c to d, the planet is near aphelion, the furthest point in its orbit from the sun, causing it the travel more slowly. The planet travels fastest in this area, slingshotting around the sun and covering distance ab at time t1, sweeping out the area a1. ![]() When a planet is traveling from a to b, it is near perihelion, the point in the orbit closest to the sun. The sun is at one of the foci in the elliptical orbit. Kepler’s third law states t^ 2 ∝ a^ 3, the period of orbit squared is proportional to the semi-major axis of its orbit. Towards the 1600s, Kepler’s revelations in astronomy further disproved the epicyclic models by proving that the planets orbited in elliptical paths rather than circular. Retrograde motion was not understood to be an illusion until the 1500s, when Copernicus proposed the heliocentric model. The epicycle model was highly accurate because any smooth curve can be approximated to arbitrary accuracy with a sufficient number of epicycles, as would later be shown by Fourier analysis. The geocentric epicycle model proposed that as a planet traveled around Earth in a circular orbit on a path called the deferent, it also traveled in a smaller circular orbit in the same direction, the epicycle, causing the planets orbit to appear like a spiral that backtracked on itself and at times seemed to pause altogether. As it is, it takes around 3 hours to run Saturn for 500π without multiplying the time by a constant. The planets beyond Saturn are too far out and orbit too slowly to present in this project. It was used to explain the variations in speed and direction of the five planets known at the time, which I present here. In ancient Greece, the theory of epicyclical motion was formalized. With all of that aside, retrograde motion is a bizarre visual phenomenon that puzzled ancient astronomers to no end, especially those who believed in a geocentric model of the solar system. As a result, when Mercury is retrograde, communication tends to break down which can result in some (non-physics-realated) chaos. When a planet retrogrades, astrologically it is in a resting or sleeping state, and by extension, the activities it governs do not have their planet to govern them properly. One of the most well known astrological tropes these days is ‘Mercury in retrograde.’ The terminology here is wrong, Mercury is not ‘in’ retrograde, it is just retrograde. Mercury rules all types of communication, including listening, speaking, learning, reading, editing, researching, and negotiating. Because of this, each planet has a purpose or area of life with which it corresponds. Astrology is based in the saying “As above, so too below.” This means that there is a relationship between the movements of the planets and what happens on Earth. As much as astronomers hate to be mistakenly called astrologers, a little astrological mumbo-jumbo can’t hurt. ![]()
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