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Introduction to Satellite Motion. Satellite Motion. Contents: Introduction Kepler’s Laws Kepler Elements. Introduction. Where is the spacecraft? Where is it going? How and why?. Ikonos Imaging Satellite. Satellite Motion. From the beginning…. History Lesson.
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Satellite Motion • Contents: • Introduction • Kepler’s Laws • Kepler Elements
Introduction • Where is the spacecraft? • Where is it going? • How and why?
Satellite Motion • From the beginning…
History Lesson • 270 BC Aristarchus of Samos proposes a sun centred universe. • 140 AD Ptolemy proposes earth centred universe
Copernicus (1473 - 1543) • Explains planetary motion in a sun centred universe • Proposes circular orbits with epicircles
Tycho Brahe (1546 - 1601) • Measured motion of planets to an unprecedented accuracy. • Proposed a model where the planets orbit the sun and the sun orbits the earth.
Johannes Kepler (1571-1630) • From Brahe’s measurements of mars’ motion concluded that mars’ orbit was elliptical with the sun at one focus.
Kepler’s First Law • The planets move in a plane; the orbits described are ellipses with the sun at one focus (1602).
Kepler’s Second Law • The vector from the sun to the planet sweeps equal areas in equal times (the law of areas, 1605).
Kepler’s Third Law • The ratio of the square of the period of revolution of a planet around the sun to the cube of the semi major axis of the ellipse is the same for all planets (1618).
Kepler Elements • Objective: • Define the satellite’s position • Solution: • Define the size and shape of the orbit • Define the orbit in space • Define the satellite’s position in the orbit • Kepler Elements
Orbit Size and Shape • Size: semi major axis, a • Shape: eccentricity, e
Defining the Orbital Plane in Space • Inclination, i • Right Ascension of the ascending node, • Argument of Perigee,
STK Simulation • IPN_Molniya
Inclination, i • Angle between the equatorial plane and the orbital plane
Right Ascension of the Ascending Node, • Angle between the vernal equinox direction and the ascending node.
Argument of Perigee, • Angle between the ascending node and perigee
Defining Satellite’s Position in the Orbit • True anomaly,
Kepler’s Laws • The planets move in a plane; the orbits described are ellipses with the sun at one focus (1602). • The vector from the sun to the planet sweeps equal areas in equal times (the law of areas, 1605). • The ratio of the square of the period of revolution of a planet around the sun to the cube of the semi major axis of the ellipse is the same for all planets (1618).
