cs & Aero ti sp au a n c o e r E e Junior, J Aeronaut Aerospace Eng 2015, 4:2 n A g f i o n Journal of Aeronautics & Aerospace l e DOI: 10.4172/2168-9792.1000145 a e r n i r n u g o J Engineering ISSN: 2168-9792 Research Article Open Access Paradoxical Variation of the Solar Day Related to Kepler/Newton System Luiz Sampaio Athayde Junior* Professor at School of Accounting Sciences, Federal University of Bahia, Brazil Abstract According to the first law of Kepler, the planets orbit the sun in elliptical path. This ellipse causes a slowdown in the world when it goes from the nearest point of the sun to the farthest point and also causes acceleration when the opposite occurs. This variation of the velocity of the planet combined with the inclination of its imaginary axis creates the analemma chart, which can be found with the overlap of the positions of the sun in a particular location always in the same timeset on a watch. The analema, in turn, describes variations in the durations of the solar day. In some dates, these variations in solar days occur in accordance with the change in velocity of the planet, but at other times, they get along perfectly Conversely, showing in some parts of the solar days year that will gradually reducing their periods as the planet decelerates and also increases periods as the planet accelerates. Keywords: Kepler’s laws; Law of universal gravitation Newton; Not to be confused with the 360​​° rotation around the imaginary Analemma; Equation of time; Solar day axis itself and also according to the authors: Introduction It’s 3 m 56 s and longer than the sidereal day because the sun is moving in the opposite direction of diurnal motion, that is, from Due the laws of planetary motion, specifically described by the first west to east. This difference is due to the Earth translation movement law of Kepler and the law of universal gravitation of Newton, the planets around the Sun, of about 1 degree (4 minutes) per day (360/y = 360°/ have speed variations in its orbit by traffic and also in its rotation. (365.25 days) = 0.9856°/day) (Figure 1). Because of the speed variations the meridian passage of the sun Thus the solar day is longer than a full rotation of 360° on the on your east of apparent westward movement across the planet also planet, because when the sun in its passage east to west, focuses exactly occurs with varying speed, and its faster passage when the planet is on the meridian passage of a certain locality, only focus again on the slower when compared to the time of a clock, and slower when the same meridian passage or that same Location ~360,9856º and not the planet is faster. If we took pictures of where the sun shines in the zenith exact 360 what would be a complete rotation of the planet around its every day in a same time on the clocks, considering only the variation imaginary axis. described speed, the analemma would be a horizontal line, describing only the delays and lates of light in its apparent movement. However, The difference occurs because the time of one complete rotation of the planet also has an inclination in its imaginary axis, which gives the planet space is also moving along its orbit. rise to the seasons, specifically in the temperate zone, which makes The laws of Kepler the analemma also present a variation between north and south and in their form as we know, that resembles the number eight or infinity Johannes Kepler, German astronomer who lived between 1571 symbol. and 1630, although it has not given due importance in the time he published his works, formatted the three laws that describe the motions The variations in the analemma chart indicate variations in periods of the planets, published in different works and not in the same work, of solar days that in some parts of the year occur concurrently with the that are named today as the three laws of Kepler. change in velocity of the planet, that is, when the planet accelerates, periods of solar days successively decrease and the opposite also. Various trigonometric operations were employed to design the first However, the chart also shows that in other parts of the year variations two. For them, we used data from another important astronomer who occur completely contrary to variations in the speed of the planet, preceded him called Tycho Brahe, referring to its observations on the in which slows down the planet and the sun days have successively planet Mars. decreasing periods and otherwise, too. Working with Brahe, Kepler could conceive the first of its laws, In studies of physics, it uses the concept of speed for moving bodies, which states that the planets orbit around the sun not in circular orbits, as stated in relation to the planets, while for the solar day, which is not a mobile; the term is used in reference to the period duration. *Corresponding author: Luiz Sampaio Athayde Junior , Professor at School of Solar days measurements were taken on a few dates for Accounting Sciences, Federal University of Bahia, Brazil, Tel: 55 71 99211 93; demonstration of paradoxical changes in periods of solar days. E-mail: [email protected] Received September 26, 2015; Accepted October 15, 2015; Published October Theoretical 24, 2015 Solar day Citation: Junior LSA (2015) Paradoxical Variation of the Solar Day Related to Kepler/Newton System. J Aeronaut Aerospace Eng 4: 145. doi:10.4172/2168- According to Oliveira Filho and Saraiva, solar day is “the time 9792.1000145 interval between two successive passages of the sun across the meridian Copyright: © 2015 Junior LSA. This is an open-access article distributed under of the place”. Can be measured with a gnomon that can demonstrate the terms of the Creative Commons Attribution License, which permits unrestricted the meridian passage of the sun on a date and the next date. use, distribution, and reproduction in any medium, provided the original author and source are credited. J Aeronaut Aerospace Eng ISSN: 2168-9792 JAAE, an open access journal Volume 4 • Issue 2 • 1000145 Citation: Junior LSA (2015) Paradoxical Variation of the Solar Day Related to Kepler/Newton System. J Aeronaut Aerospace Eng 4: 145. doi:10.4172/2168-9792.1000145 Page 2 of 12 law. The simulator present, is hereinafter in this work simply first simulator. Consider the graphic demonstration of tarceira law of Kepler in the simulator (Figure 4). Law of Newton gravitation After finding that the land attracted all objects, starting with the picturesque episode of the falling apple, Isaac Newton further narrowed the ties between physics and astronomy through his Law of Universal Gravitation. He also concluded that the same way force that attracted the objects to the Earth center kept the moon in orbit around them and the planets around the sun. In a single theoretical framework, Newton was able to explain all gravitational phenomena (Figure 5). The title of his work is PhilosophiaeNaturalis Principia Mathematica. It derived Kepler’s Laws of first principles. Thus, many Figure 1: Solar Day. of the foundations of modern physics were created by theoretical but in elliptical orbits and the Sun is at one of the focus. The second teaches us that an imaginary radius of the orbit, joining the sun to the planet takes equal areas in equal times. When the planet is closer to the sun logically has lower imaginary rays than when the planet is farthest. Kepler also found that when this is the earliest time, position called perihelion or perigee, the planet moves faster in its rotation and its translation and the opposite occurs when the planet is farthest from the sun, called aphelion position or height when travels slower through its orbit and also features slower speeds. The University of Nebraska in United States of America - USA, provides on its website several simulators of planetary movements, through its Nebraska Astronomy Applet Project - NAAP. We will use here some pictures of the simulator entitled Planetary Orbit Simulator to help us understand Kepler’s Laws. Let´s check the demonstration of the first law in Figure 2. To improve the understanding of the subject, we can determine, Figure 2: First Kepler’s Law. through controls of the simulator, the empty focus, which is in opposition to the sun, the center of the ellipse, besides the semimajor and semimenor, or larger radius and smaller radius of the ellipse, as is done in the figure. When opens the simulator is already selected Mercury, having more eccentric ellipse, which also helps to understand. The simulator also allows increase esssa eccentricity for better visualization of the listed laws, by controlling “eccentricity”. Now a graphic demonstration of the second law for the same simulator is shown in Figure 3. The simulator lets you paint areas covered by the planet at the same time at the moment is slower and faster (when it’s out of the sun or closer, respectively). Obviously when slower travel a shorter distance in its orbit, as it were, than when it is faster. Kepler discovered that the painted areas (as shown in the simulator) of two imaginary triangles formed by imaginary rays of the planetary orbits, are equal. This is a very important finding in an attempt to derive the planetary motions by physical causes. If we consider the time in which he lived, we can not fail to recognize how much is an amazing discovery. Finally, in the year 1619, was published work called Harmonices Mundi by Kepler, in which it is prescribed that the square of the orbital period of the planets is directly proportional to the cube of the average distance of the planet to the Sun, which is known today as your third Figure 3: Second Kepler’s Law.