AE554 Applied Orbital Mechanics. Hafta 1 Egemen Đmre

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1 AE554 Applied Orbital Mechanics Hafta 1 Egemen Đmre

2 A bit of history the beginning Astronomy: Science of heavens. (Ancient Greeks). Astronomy existed several thousand years BC Perfect universe (like circles and spheres), so must be the paths of planets and stars. Geostatic and geocentric universe. Stars and planets on perfect crystalline spheres Universe is perfect and Changeless Aristotle (circa 350BC): Heavy objects fall quicker than lighter ones. His geocentric model dominated astronomy for 2000 years Kinematics (description of the motion) and dynamics (causes of the motion)

3 A bit of history the Arab era Middle Ages: Arabic rather than European Trigonometry Zero (Indian concept) Arabic rather than Roman numerals Commentary Some examples: Calculation of the obliquity of the ecliptic Omer Khayyam: Calculation of the duration of a year (correct to a few seconds) and a calendar more accurate than Julian Fall of Toledo: 1085AD. Arabic knowledge became available to a Europe in the Dark Age

4 A bit of history the European era Nicolaus Copernicus ( ) Heliocentric system Denied by Catholics and Protestants alike Tycho Brahe ( ) Naked eye observations accurate to 1/60th of a degree Moon and Sun around Earth, everything else around Sun Galileo Galilei ( ) crafted his own 20x telescope Moon craters, Jupiter s moons, Venus has phases like Moon Sunspots Disproved Aristotle s theorem

5 A bit of history Kepler Johannes Kepler ( ) Puzzled by Mars Came up with three laws kinematics "The orbit of every planet is an ellipse with the sun at one of the foci. "A line joining a planet and the sun sweeps out equal areas during equal intervals of time. "The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits." P = orbital period of planet a = semimajor axis of orbit

6 A bit of history Newton Isaac Newton ( ) Universal gravitation Came up yet more laws (in his spare time) Principles of conservation of momentum and angular momentum. Also: Reflecting telescope An empirical law of cooling Studied the speed of sound. Development of calculus Bible chronology and the Bible code Alchemy Counterfeit coins (eradication of) and making sure counterfeiters were hanged, drawn and quartered

7 Newton and His Laws of This and That First Law: Law of Inertia Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed. Second Law: Law of Acceleration The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction. Third Law: Law of Reciprocal Actions All forces occur in pairs, and these two forces are equal in magnitude and opposite in direction. Law of Universal Gravitation G is approximately equal to N m2 kg 2 (first measured at Cavendish experiment-1798) "If I have seen further it is by standing on the shoulders of giants" Isaac Newton

8 Motion in Space Motion in space Governed by Newton s Laws of Motion (sort of) Exhibits the characteristics described by Kepler (sort of) Orbit: Balance of forces that determine the complete trajectory. "The Guide says that there is an art to flying," said Ford, "or rather a knack. The Knack lies in learning how to throw yourself at the ground and miss." from Life, the Universe and Everything by Douglas Adams

9 Stuff that is in Motion in Space Natural: Meteors and asteroids Planets Stars Solar Systems Galaxies Others Man-made: Satellites Space Station(s) Debris, i.e. junk (lots of it)

10 A Closer Look at Satellites Communications High altitude Remote sensing Low altitude Optical or radar Navigation GPS/GLONASS/GALILEO Scientific Earth gravitational field Limb measurement Meteorology

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