Chpt. 5:Describing Orbits

By: Antonio Batiste

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

e > 1.0

e =10<e<1.0 ellipse

parabola

hyperbola

Eccentric Shapes

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:

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)