Bahnmechanik und Missionsplanung

- Direct transformation between multiple reference frames is possible only if none of the frames have a relative rotation. 

- circular reasoning in the def. of Newton's laws.

- Pseudo IRF: e.g. for a short flight neglecting earth's rotation. 

Astronomical event in which the plane of earth's equator passes the center of the sun. Marks the beginning of spring in northern hemisphere. 

--> day as long as the night

--> 23 h 56 min 4,091 sec

The duration of rotation of earth with respect to vernal equinox

- beruht auf scheinbarer Bewegung der Sterne

- Ein Sterntag ist die Dauer, die der Sternenhimmel (genauer: der Frühlingspunkt) für eine ganze scheinbare Umrundung der Erde benötig.

Mean or reference plane about whose axis the instantanious orbit plane of a satellite precesses. Plane perpendicular to a systems mean angular momentum vector.

--> über lange Zeit gemittelte Bahnebene eines Körpers auf einer Umlaufbahn.

- no analytical solution 

- the center of mass of an n-body-problem does not experience an acceleration

- a non-rotating reference frame at the center of mass of all bodies in the universe is the primary IRF

- singularity at collisions

a) Für den Fall n>=3 sind die Bewegunsintegrale nicht mehr algebraisch und somit nicht mit elementaren Funktionen lösbar.

b) - Masse eine der Körper als vernachlässigbar klein annehmen 

- Gleichgewichtsfall lösbar

- für den Fall identischer Massen exisitiert eine Lösung "unendlich"

a)

- the effect of bodies outside the sphere of influence can be neglected

- Force between bodies acts along the line between their positions

- the motion is planar

b) - the oblate-spheroid-shaped region around a celestial body where the primary gravitational influence on an orbiting object is that body

c)

- Satellite orbiting a planet

- planet orbiting a star

- motion of space probe 

Points in an orbital configuration of two large bodies where a smaller body affected only by gravity can maintain a stable position relative to the two large bodies. 

T --> Wahre Anomalie: Winkel zwischen der Verbindungslinie S/C-Fokuspunkt und Perigäum.

E--> Exzentrische Anomalie: Winkel zwischen Perigäum und S/C-Position projiziert auf einen Hilfskreis.

M--> Mitllere Anomalie: Winkel zwischen Perigäum und S/C-Position für konstante Winkelgeschwindigkeit

a--> große Halbachse

e--> Exzentrizität

Flight path angle: Angle between S/C-V-Vektor and local horizontal

Distance where a celestial body, held together only by its own gravity, will disintegrate due to a second celestial body's tidal force exceeding the first body's gravitational self-attraction. 

Data format encoding a list of orbital elements of an earth-orbiting object for a given point in time, the epoch.

--> Elemente werden als Ziffernblöcke in zwei Zeilen dargestellt

--> Tracking-Programme, um Satelliten in Echtzeit zu verfolgen

Ellipse e<1

Parabel e=1

Hyperbel e>1

- i --> Inklination: Neigung der Bahneben

- "GroßOmega" --> right ascension of the ascending note

- "KleinOmega" --> argument of the pericenter

- u=KleinOmega+Theta --> argument of latitude

- perturbations: complex motion of a massive body subject to forces other than the gravitational attraction of a single other massive body

- Bahnstörung: eine Abweichung der tatschächlichen Flugbahn eines Himmelskörpers von der anhand eines Modell berechneten Flugbahn

Ex.: 

- Sun (2nd)

- irragularities of gravitational force --> J2 (1st, earth flattened, oblate spheroid)

- atmosphere

- Solar radiation (2nd)

- relativity (3r)

start at solar minimum --> atmopsheric density is lower

Atmospheric drag causes a circularization of the orbit

Approximation of an interplanetary trajectory, splits the problem into a series of consecutive 2-body-problems

- geosynchronous (orbit period: 1 day)

- geostationary (fixed position with earth)

- repeat (groundtrack repeats after k orbits, j days)

- sun-synchronous (orbit plane fixed with sun)

- Molnija (stable pericenter)

- Lagrange point (fixed with two main bodies)

- frozen (stable pericenter and eccentricity)

- static (fixed with earth and sun)

- interplanetary escape (dealing with 2 spheres of influence)

Under standard assumptions the body travelling along a hyperbolic trajectory will attain at infinity an orbital velocity called "Vinfinit"

Vinfinit=(mhu/(-a))^(1/2)

The view of the horizon without any disturbances (true h=(13*h)^(1/2))

Set of points of distance 1 from a fixed central point where a generalized concept of distance may be used 

The computation of a groundtrack is a dual-axis-spiral problem (for zero-eccentricity satellites)

- Rotation along primary axis must include earth's rotation

- Rotation along secondary axis is orbital motion around orbital pole

1. Newton's three laws of motion

2. Kepler's Law

- needed to enter into heliocentric orbit or into parking orbit around target planet

- Abschätzung des gesamten Deltav, welches für die Mission benötigt wird

- Summe aller Deltav benötigt für Antriebsmanöver während der Mission

- gibt an, wie viel Treibstoff für ein RFZ benötigt wird

- needed for plane changes

- needed to exit from and enter into orbit

can have an effect on both semi-major axis, eccentricity and epoch of the pericenter passage  

- functional requirements: how well it must perform

- operational requirement: how it is to be used

- constraints: what limitations are imposed on the system

- Initial population (random fill)

- Parent selection (random or weighted selection)

- Recombination (random intersection point)

-Mutation (probability)

--> GA is similar to Darwinian evolution in nature

--> Objectives: maximize number of red components in puppet

"Querabweichung"  --> bezeichnet in der Navigation den Abstand zwischen der geplanten Route (gegeben durch zwei Wegpunkte) und der tatsächlichen Position