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 Law
1. The planets move in a plane; the orbits
described are ellipses with the sun at one
focus (1602).
Kepler’s Second Law
2. The vector from the sun to the planet
sweeps equal areas in equal times (the law
of areas, 1605).
Kepler’s Third Law
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).
T  2
a3

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, i
2. 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 Laws
1. 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