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

• 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 Law1. The planets move in a plane; the orbits

described are ellipses with the sun at one focus (1602).

Kepler’s Second Law2. The vector from the sun to the planet

sweeps equal areas in equal times (the law of areas, 1605).

Kepler’s Third Law3. 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).

3

2 aT

Isaac Newton (1642 - 1727)

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

Coordinate System: ECI

Orbit Size and Shape

• Size: semi major axis, a• Shape: eccentricity, e

Defining the Orbital Plane in Space

1. Inclination, i2. Right Ascension of the ascending

node, 3. 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,

And Finally…

Kepler’s Laws1. The planets move in a plane; the orbits

described are ellipses with the sun at one focus (1602).

2. The vector from the sun to the planet sweeps equal areas in equal times (the law of areas, 1605).

3. 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).

Summary of Classical Orbital Elements

Kepler Element Symbol Description

Semi major axis a Size (Energy)

Eccentricity e Shape

Inclination i Tilt of orbital plane with respect to the equator

Right ascension of ascending node

Twist of orbit with respect to the ascending node location

Argument of perigee Location of perigee with respect to the ascending node

True anomaly Location of satellite with respect to perigee