19 Dec 1 - Orbital Mechanics

19 Dec 1 - Orbital Mechanics - AOE 2104-Aerospace and Ocean...

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Virginia Tech Space AOE 2104--Aerospace and Ocean Engineering Fall 2009 December 1 2009 Click to edit Master subtitle style AOE 2104 Introduction to Aerospace Engineering Orbital Mechanics
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Virginia Tech Space AOE 2104--Aerospace and Ocean Engineering Fall 2009 December 1 2009 Click to edit Master subtitle style A Brief History of Orbital Mechanics Aristotle (384-322 BC) Ptolemy (87-150 AD) Nicolaus Copernicus (1473-1543) Tycho Brahe (1546-1601) Johannes Kepler (1571-1630) Galileo Galilei (1564-1642) Sir Isaac Newton (1643-1727)
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Virginia Tech Space AOE 2104--Aerospace and Ocean Engineering Fall 2009 December 1 2009 Click to edit Master subtitle style Kepler’s Laws I. The orbit of each planet is an ellipse with the Sun at one focus. II. The line joining the planet to the Sun sweeps out equal areas in equal times. III. The square of the period of a planet’s orbit is proportional to the cube of its mean distance to the sun.
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Virginia Tech Space AOE 2104--Aerospace and Ocean Engineering Fall 2009 December 1 2009 Click to edit Master subtitle style Kepler’s First Two Laws I. The orbit of each planet is an ellipse with the Sun at one focus. II. The line joining the planet to the Sun sweeps out equal areas in equal times.
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Virginia Tech Space AOE 2104--Aerospace and Ocean Engineering Fall 2009 December 1 2009 Click to edit Master subtitle style Kepler’s Third Law III. The square of the period of a planet’s orbit is proportional to the cube of its mean distance to the sun. μ π 3 2 a T = Here T is the period, a is the semimajor axis of the ellipse, and is the gravitational parameter (depends on mass of central body) 2 3 11 sun sun 2 3 5 s km 10 32715 . 1 s km 10 98601 . 3 - - × = = × = = GM GM
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Virginia Tech Space AOE 2104--Aerospace and Ocean Engineering Fall 2009 December 1 2009 Click to edit Master subtitle style Earth Satellite Orbit Periods Orbit Altitude (km) Period (min) LEO 300 90.52 LEO 400 92.56 MEO 3000 150.64 GPS 20232 720 GEO 35786 1436.07 You should be able to do these calculations! Don’t forget to add the radius of the Earth to the altitude to get the orbit radius.
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Virginia Tech Space AOE 2104--Aerospace and Ocean Engineering Fall 2009 December 1 2009 Click to edit Master subtitle style Newton's Laws
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19 Dec 1 - Orbital Mechanics - AOE 2104-Aerospace and Ocean...

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