Two-body and Conic Section

# Two-body and Conic Section - Orbital Mechanics-Introduction...

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JIN KANG Orbital Mechanics -Introduction

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Contents 2 ! Introduction ! Satellite orbit ! LEO, GEO, Molniya, etc. ! Orbital mechanics ! Two body problem ! Conic section ! Characteristics of orbit ! Elliptical orbit
Getting to Orbit 3 ! Throw ball fast enough to match acceleration of gravity, you achieve orbit!

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How Fast Do You Have To Go? ! You want to put a satellite in orbit ! Which direction? ! When? ! How much speed? Starts with Two-Body Problem
Two-Body Problem Derivation Newton’s Gravitation Two-Body Problem Assumption: - Spherical object - Only gravity present - Consider only 2 objects - Earth’s >> satellite mass

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Newton’s Gravitation Law every object in this universe attracts every other object with a force which is directly proportional to their masses and inversely proportional to the square of distance between them " GRAVITY
! Newton’s Second Law ! When force is applied, object accelerates ! Apple drops " acceleration " force present Gravitational force! F = m * a Force = mass * acceleration

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! Force exerted on two body is: ! Proportional to product of two masses ! Inversely proportional to square of distance 2 1 m m F ! 2 1 r F ! m 1 m 2 r
Newton’s Law of Universal Gravitation 2 2 1 r m Gm F " 2 2 11 10 67 . 6 kg m N G # \$ " % Gravitational Constant To go from ‘proportional’ and ‘inversely proportional’ to exact value, need a constant

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Gravity 10 ! Two masses attract each other ! Reduced at square of distance 2 2 11 2 2 1 / 10 67 . 6 kg Nm G R m Gm F g % \$ & "
Application of Gravitation Law 2 2 1 r m Gm F " ! Force felt by object in space ! Gravitational pull from other object ! Perturbations : air friction, electro-magnetic, solar wind, etc.

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Two-body and Conic Section - Orbital Mechanics-Introduction...

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