Applications of celestial mechanics in natural objects and spacecrafts
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Applications of celestial mechanics in natural objects and spacecrafts Vivian Martins Gomes1 · Cristiano Fiorilo de Mello2 · Elbert E. N. Macau3 · Antonio Fernando Bertachini de Almeida Prado3 · Othon Cabo Winter1
© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017
Abstract Studies related to Celestial Mechanics started long ago, and it is one of the oldest fields in Astronomy. It started to try to explain the motions of the stars in the sky, in particular the irregular motion of some of those of then, which were really the planets of the Solar System. In the 20th century, with the arrival of the “Space Age”, many applications related to the motion of artificial spacecrafts appeared. This new field was called “Astrodynamics”, to designate the use of Celestial Mechanics in man-made objects. Several aspects, like orbit determination, maneuvers to change the orbit of the spacecraft, etc., are covered by this topic. The present Focus Issue in Celestial Mechanics publishes a list of papers in topics related to applications in Celestial Mechanics to both situations: natural and artificial satellites. Keywords Celestial mechanics · Astrodynamics · Orbital dynamics Mathematics Subject Classification 37N05 The science of “Celestial Mechanics” was born to study the motion of the celestial bodies. It started with the observation of the motion of the stars in the night sky, which has been made probable, since the first form of humans was able to understand what they could see in the sky. The time and the evolution of technology improved our knowledge in Celestial Mechanics. A major series of steps were made in the years near 1600. Tycho Brahe (1546–1601) made accurate observations of the motion of the stars which moved against the fixed ones. Those data were than studied by Johannes Kepler (1571–1630), which made the important “Three Laws of Kepler” of the orbital motion: 1. The orbit of each planet is an ellipse with the Sun occupying one of the focus.
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Elbert E. N. Macau [email protected]
1
Unesp, Universidade Estadual Paulista, Guaratinguetá, SP, Brazil
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Universidade Federal de Minas Gerais, UFMG, Belo Horizonte, MG, Brazil
3
Instituto Nacional de Pesquisas Espaciais, INPE, São José dos Campos, Brazil
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2. for each planet, the radius vector of the planet covers equal areas in equal times, so its motion is faster at perihelion and slower at aphelion. 3. the cube of the semi-major axis of the planet’s orbit is proportional to the square of its orbital period. Based on those laws, Isaac Newton (1642–1727) formulated the famous Law of Universal Gravitation, showing that mass attracts mass according to the product of their masses divided by the square of the distances between them. Many other advances came with time: the invention of the telescope, the construction of large arrays of observations using radio and optical telescopes, etc. Currently, not only the Solar System is well mapped, but also a large number of exoplanets are known (Domingos et al. 2006; Rodl
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