Date post: | 22-Dec-2015 |
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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
5.1 Orbital Elements:
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
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:
0 or 180
Direct(Prograde):
0 < i < 90
Polar:
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)