1. Introduction to Satellite Motion

2. Satellite Motion
Contents:
Introduction
Kepler’s Laws
Kepler Elements

3. Introduction
Where is the spacecraft?
Where is it going?
How and why?

4. Ikonos Imaging Satellite

5. Satellite Motion
From the beginning…

6. History Lesson
270 BC Aristarchus of Samos proposes a sun centred universe.
140 AD Ptolemy proposes earth centred universe

7. Copernicus ( )
Explains planetary motion in a sun centred universe
Proposes circular orbits with epicircles

8. Tycho Brahe ( )
Measured motion of planets to an unprecedented accuracy.
Proposed a model where the planets orbit the sun and the sun orbits the earth.

9. Johannes Kepler ( )
From Brahe’s measurements of mars’ motion concluded that mars’ orbit was elliptical with the sun at one focus.

10. Kepler’s First Law
The planets move in a plane; the orbits described are ellipses with the sun at one focus (1602).

11. Kepler’s Second Law
The vector from the sun to the planet sweeps equal areas in equal times (the law of areas, 1605).

12. 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).

13. Isaac Newton ( )

14. 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

15. Coordinate System: ECI

16. Orbit Size and Shape
Size: semi major axis, a
Shape: eccentricity, e

17. Defining the Orbital Plane in Space
Inclination, i
Right Ascension of the ascending node, 
Argument of Perigee, 

18. STK Simulation
IPN_Molniya

19. Inclination, i
Angle between the equatorial plane and the orbital plane

20. Right Ascension of the Ascending Node, 
Angle between the vernal equinox direction and the ascending node.

21. Argument of Perigee, 
Angle between the ascending node and perigee

22. Defining Satellite’s Position in the Orbit
True anomaly, 

23. And Finally…

24. 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).

25. 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