Orbital_Mechnics_and_Basics_Introduction.ppt

orbital mechanics and orbit perturbations in satellite communications

1. Basic Orbital Mechanics
Dr. Andrew Ketsdever
MAE 5595

2. Conic Sections
EccentricityConic
= 0 Circle
0 - 1 Ellipse
= 1 Parabola
> 1 Hyperbola

3. Elliptical Orbit Geometry

4. Conic Sections
aR
V
22
2

 
R
V
circular



5. Classical Orbital Elements
•Semi-Major Axis, a
–Size
•Eccentricity, e
–Shape
a2


a
c
e
2
2



3
2
a
Period Kepler’s 3
rd
Law

6. Classical Orbital Elements
•Inclination
–Tilt
InclinationOrbit
= 90º Polar
0º or 180ºEquatorial
0º - 90ºPrograde
90º - 180ºRetrograde
h
h
i
Z
cos

7. Classical Orbital Elements
•Right Ascension of
the Ascending Node
(RAAN)
hKn


ˆ
n
n
X
cos
1800 then ,0n If
y

063180 then ,0n If
y 

8. Classical Orbital Elements
•Argument of Perigee
ne
en


cos
1800 then ,0e If
Z  
063180 then ,0e If
Z
 

9. Classical Orbital Elements
•True Anomaly
eR
Re


cos
1800 then 0, )VR( If  

063180 then 0, )VR( If  


10. Computing COEs
•From a R and V vector
–Can compute the 6 COEs
–Also works in reverse (given COEs compute
R and V)
–Example:
sec
km

ˆ
0
ˆ
5.7
ˆ
0
km
ˆ
7500
ˆ
0
ˆ
0
KJIV
KJIR



11. COEs
•a = 7965.1 km
•e = 0.0584
•i = 90º
 = 270º
 = 90º
 = 0º
•Mission: Probably remote sensing or a spy
satellite because it’s in a low, polar orbit.

12. Ground Tracks
Ground Track Slides Courtesy of Major David French

13. COE Determination
Semimajor axis
Δ longitude
ΔN
P =
ΔN
15º / hr


3
a
2P

14. COE Determination
Eccentricity

15. COE Determination
Inclination
i = highest latitude

16. COE Determination
Argument of Perigee
ω = 90º

17. COE Determination
True Anomaly

18. Orbit Examples

19. Molniya

20. Geostationary

21. Geosynchronous

22. e = 0
e = 0
i = 0
Geosynchronous
e = 0.4
 = 180
e = 0.6
 = 90

23. Orbit Prediction
•Kepler’s Problem
–If we know where a satellite (or
planet) is today, where in its orbit will
it be tomorrow?
–Kepler devised a series of
mathematical expressions to solve
this particular problem
•Eccentric Anomaly
•Mean Anomaly
•True Anomaly
II. The line joining the
planet to the Sun
sweeps out equal areas
in equal times as the
planet travels around
the ellipse.
 
               

24. Orbit Prediction
•Kepler defined the
Eccentric Anomaly to
relate elliptical motion
to circular motion
•He also defined Mean
Anomaly to make the
circular motion
constant
•Convert unsteady
elliptical motion into
unsteady circular
motion into steady
circular motion…

25. Orbit Prediction

180or 0 for ME
plane-half same in the always are ,,
 
ME

26. Orbital Prediction
•Given
a = 7000 km
e = 0.05
= 270º
Find the time of flight to 
final
= 50º

27. Orbital Prediction
•n = 0.001078 rad/sec
•E
initial = 272.87º
•E
future = 47.84º
•M
initial = 275.73º
•M
future = 45.72º
•TOF = 2104.58 sec or
35.08 min
3
a
n




cos1
cos
cos
e
e
E



EeEM sin
n
kMM
TOF
if
2
