Chpt. 5:
Describing Orbits
By: Antonio Batiste
5.1 Orbital Elements:
If you’re flying an airplane and the ground
controllers call you on the radio to ask where you
are and where you’re going, you must tell them
six things:
1. Latitude
2. Longitude
3. Altitude
4. Horizontal velocity
5. Heading (I.e. north, south, etc.)
6. Vertical velocity (ascending or descending
Johannes Kepler developed a method for
describing and defining the six orbital
elements.
Classic Orbital Elements (COEs)
•
•
•
•
Orbit’s size
Orbit’s shape
Orbit’s orientation
Spacecraft’s location
Orbit’s size – uses the semimajor axis, a
ε = - μ /2a
ε = specific mechanical energy (km2/s2)
μ = gravitational parameter of the central body
(km3/s2)
a = semimajor axis (km)
Orbit’s shape
– Eccentricity (specifies the shape of an orbit by
looking at the ratio of the distance between the
two foci and the length of the major axis)
e = 2c / 2a
Eccentric Shapes
0<e<1.0
e =1
e > 1.0
ellipse
parabola
hyperbola
NOTE:
e = 0 is a circle
Orbit’s orientation divides into 2 main parts:
Orbit’s plane in space
- Inclination, I
-Right ascension of the ascending node
(swivel), Ω
Orbit within the plane
-Argument of perigee, ω
Orbit’s plane in space
-Inclination, i – describes tilt of the orbital plane
with respect to the fundamental plane
(or equatorial plane) ranges: 0o to 180o degrees
Refer to pg. 158
Fig. 5-5
-Right ascension of the ascending node,
is the angle we measure along the equator
Note:
Right ascension is similar to
longitude except its reference
point is the vernal equinox.
Orbit within the plane
-Line of nodes – the intersection of the orbital plane and the
fundamental plane.
Ascending Node – where the spacecraft goes from below
equator to above equator. (south to north)
Descending Node – when the spacecraft goes from above
equator to below equator. (north to south)
Other Types of Orbits:
Equatorial:
Polar:
0 or 180
90
Direct(Prograde):
0 < i < 90
Indirect
(Retrograde):
90< i <180
-Moves in
direction of
Earth’s rotation.
(ascending
node)
-Moves
against
direction of
Earth’s
rotation.
(ascending
node)
Argument of perigee, ω - the angle along the orbital path between
the ascending node and perigee.
(measure in direction of spacecraft motion)
0o < ω < 360o
True anomaly, v – the angle
along the orbital path from perigee to
the spacecraft’s position vector, R
More types of orbits:
Geostationary orbit – a circular orbit with a period of about 24 hours and
inclination 0o.
(ex: comm. Satellites)
Geosynchronous orbits – inclined orbits with a period of about 24 hours.
Semi-synchronous orbit – has a period of 12 hours.
Sun-synchronous orbits – are retrograde, low-Earth orbits (LEO),
typically inclined 95o to 105o. (ex: remote-sensing)
Molniya orbit – a semi synchronous, eccentric orbit.
(ex; some specific comm. Missions)