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THIS PRESENTAION HAS BEEN RATED TG-13 TEACHERS’ GUIDANCE STRONGLY ADVISED Some Material May Be Unintelligible For Students Under 13. Intense Frames of Scientific Instruction, Analysis, Comparing and Contrasting, Description, and for Some Vocabulary. BY THE CLASSIFICATION AND RATING ADMINISTRATION © 1852 All Rights Reserved VOID WHERE PROHIBITED BY LAW PBIS ANTI-VACUITY The authorized reproduction or distribution of this copyrighted work is highly encouraged. Lethargic obtuseness is insubordinate and is discouraged by PBIS, as it may result in little or no monetary gain after secondary education or a fine of $250,000. © 1852 All Rights Reserved VOID WHERE PROHIBITED BY LAW ASTRONOMY ORBITAL MECHANICS OBJECTIVES By the end of this presentation, students will be able to • Contrast the differences between the types of orbits. • Explain the use of these orbits to launch rockets to inner and outer planets. MOTION OF A SATELLITE According to the law of gravitation, gravity maintains all planets, rockets and satellites in circular - near circular motion around the planet and sun. What, then, is the velocity of a satellite in a low-earth, near-circular orbit? Fnet = Fg = mac mg = m v2 r g = v2 g = G mp r r2 v2 = G mp r Since the velocity of a satellite on the surface of a planet is vo… …then the velocity needed to launch a rocket into orbit of radius r; altitude of r-rp is v2 = vo2 + vL2 vL2 = v2 - vo2 MOTION OF A PLANET though planet orbits are nearly circular, they really cannot be approximated as circular… VIS VIVA EQUATIONS - used to determine the velocity of the planet at any point in its orbit: a circular orbit an elliptical orbit a parabolic orbit a hyperbolic orbit VIS VIVA EQUATIONS – Circular orbit (satellites and such) semi major axis = radius eccentricity = 0 Etot = -G2mp3T2 8p2a4 v2 = G(mo + mp) ( 1) r VIS VIVA EQUATIONS – Elliptical orbit (moons, asteroids, planets, etc) eccentricity: 0<e<1 Etot is less than zero v2 = G(Mo + Mp) (2 - 1) r a VIS VIVA EQUATIONS – Parabolic orbit (some comets) semi major axis = infinity eccentricity =1 Etot = 0 v2 = G(mo + mp) (2) r VIS VIVA EQUATIONS Hyperbolic orbit (Imperial Death Star) Eccentricity is less than zero Etot is more than zero v2 = G(Mo + Mp) (2 - 1) r |a| To launch a rocket from the earth to an inner planet - Venus, for example … sun Venus Earth …means the rocket is put into an elliptical orbit around the sun with the Earth located at the aphelion and Venus located at the perihelion. sun Venus vL2 = v⊕2 - v♀2 Earth To launch a rocket from the earth to an outer planet - Mars, for example … Mars sun Venus Earth • …means the rocket is put into an elliptical orbit around the sun with the Earth located at the perihelion and Mars located at the aphelion. Mars sun Venus vL2 = v♂2 - v⊕2 Earth A geosynchronous satellite makes one complete orbit in the same time that it takes for the earth to spin once. At what altitude must a geosynchronous satellite be placed? T = 24hrs (3600 s) = 86,400 s (1 hr) At what altitude must a geosynchronous satellite be placed? T2 = 4p2 a3 G mo 86,400s2 = 4p2 a3 (6.67x10-11)(5.979x1024 kg) a3 = 7.54 x1022 m3 a = 4.22x107 m = 26,000 mi At what speed must a geosynchronous satellite be traveling? v2 = G mo a v2 = (6.67x10-11)(5.979x1024 kg) (4.22x107 m) v2 = 9.45 x107 m2/s2 v = 3074 m/s = 17,800 mph ASTRONOMY ORBITAL MECHANICS