Orbit Classification

To discuss the types of closed Earth orbits that are commonly used by spacecraft operators, we need to consider the characteristics of typical orbits that uniquely distinguish one orbit from another. Principally, these distinguishing features are shape, size, and inclination.

Circular orbit Elliptical orbit

- zero eccentricity - moderate eccentricity

Elliptical orbit - high eccentricity

Figure 2.3: Shape is a principal distinguishing characteristic of orbits. The degree of elongation of an orbit is defined by its eccentricity.

Circular orbit Elliptical orbit

- zero eccentricity - moderate eccentricity

Elliptical orbit - high eccentricity

Figure 2.3: Shape is a principal distinguishing characteristic of orbits. The degree of elongation of an orbit is defined by its eccentricity.

For closed orbits, the relevant shapes are circles and ellipses. Of course, some ellipses are more elongated than others, as shown in Figure 2.3, and this degree of elongation is referred to as eccentricity, with high eccentricity orbits being more elongated.

Similarly, size is an easy idea, being defined by the orbit height. More precisely, a circular orbit will be defined by its radius, measured from Earth's center, or by its altitude above Earth's surface, as shown in Figure 2.4a. For elliptical orbits, the overall size of the orbit can be defined in terms of the distance between perigee and apogee (Fig. 2.4b). The perigee and apogee points may also be pinned down by their respective distances from Earth's center or surface.

The third principal characteristic, orbital inclination, essentially defines the orientation of the orbit plane with respect to Earth's equator, as illustrated in Figure 2.5. The orbital inclination is defined as the angle between the orbit plane and the equatorial plane, measured at the ascending node of the orbit. Again in terms of the jargon, a node is simply a

(a) Circular orbit

(b) Elliptical orbit radius

(a) Circular orbit

(b) Elliptical orbit

perigee altitude constant speed variable speed:

- fast at perigee

- slow at apogee altitude perigee constant speed variable speed:

- fast at perigee

- slow at apogee

Figure 2.4: The size of an orbit is a principal characteristic, and this is defined by the orbit's altitude above Earth's surface, or its distance from Earth's center.

Spacecraft

/ / V. Orbital inclination

Earth rotation

Figure 2.5: The angle between the orbit plane and the equatorial plane is called the orbital inclination. This is the third principal distinguishing characteristic of an orbit.

point on the orbit where the spacecraft crosses the equator, and an ascending node is one where the spacecraft is traveling from south to north. Looking at Figure 2.6a, we can see that an orbital inclination of 0 degrees gives an equatorial orbit, that is, one that overflies the equatorial region only. Conversely, an orbital inclination of 90 degrees gives an orbit plane perpendicular to the equatorial plane, as shown in Figure 2.6b. This type of orbit is referred to as a polar orbit. Of course, the orbital inclination may take any value between 0 and 180 degrees; a value of about 45 degrees is illustrated in Figure 2.6c.

Another property of the orbit that is of interest, implied in Figure 2.4, is the orbital speed with which spacecraft move along their orbital path. This is not a principal characteristic, but an attribute that arises as a result of the

Figure 2.6: Orbits of differing orbital inclinations. (a) An equatorial orbit. (b) A polar orbit. (c) An orbit with an inclination of about 45 degrees.

orbit shape and size. The mathematics tells us that in a circular orbit, the spacecraft's speed is dependent on the mass of the central body and the orbit height. Given that we are considering Earth orbits, the mass of the central body, Earth, is of course constant, so the spacecraft's speed then becomes dependent only on the orbit height. A spacecraft in a circular orbit at particular altitude will move at a precisely defined speed. For example, in a 200-km (124-mile) altitude circular orbit, the spacecraft moves at 7.78 km/ sec (4.84 miles/sec), as we have already seen in our discussion earlier of Newton's cannon. This is a low Earth orbit (LEO). The rule is that as the circular orbit height increases, the orbit speed decreases; for example, a spacecraft in a 10,000-km (6200-mile) altitude circular orbit will travel at around 5 km/sec (3 miles/sec).

In an elliptical orbit, the spacecraft speed along its trajectory is slightly more difficult to quantify, as the mathematics are a little more involved. But it can be understood easily in terms of the sharing of the spacecraft's energy between height and speed. As the spacecraft's altitude increases, its energy is sapped by its climb out of the gravity field and it slows down. At the apogee point of an elliptic orbit, the spacecraft speed will be lower than its speed at perigee. We have seen this already, expressed in a rather geometrical (17th century) way by Kepler's second law of planetary motion (see Chapter 1). A good parallel to help remember the variation in speed in elliptical orbits is bike riding on hilly terrain; your speed in the valleys is much higher than when climbing to the high points, for the same reasons of converting height into speed, and vice versa, as you ride.

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