Page 51 - Intro to Space Sciences Spacecraft Applications

Introduction to Space Sciences and Spacecraft Applications
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This value (between 0 and 1) indicates an elliptical orbit and agrees
with the closed orbit indicated by the negative value obtained for the
total energy.

e. Apogee velocity (equation 2-12):
v, = 7.29 Wsec = 26,235 km/hr

f. Perigee velocity (equation 2-13):
vp = 7.95 Msec = 28,628 km/hr

These are appreciable velocities and the velocity difference between
apogee and perigee is also not insignificant!

ORBITAL ELEMENTS

To completely describe the shape and orientation of an orbit around the
earth, six quantities must be specified as shown in Figure 2-6. During the
following discussion keep in mind that, once set, the plane in which an
orbit lies remains inertially fixed in space.
As stated earlier, the eccentricity e and semi-major axis a define the
shape and size, respectively, of the orbit. The orientation ofthe orbital
plane is described by two angles: the inclination i and the longitude of the
ascending node $2. The inclination describes the angle that the orbital plane
makes with a reference plane (chosen to be the plane of the equator for
earth-orbiting satellites). This is the same as the angle between the angular
momentum vector of the orbit h and a coordinate axis perpendicular to the
reference plane (K chosen in the direction of the North Pole) as shown in
Figure 2-6.
The longitude of the ascending node is an angle that describes the rota-
tion of the orbital plane from a line within the reference plane which
points toward an inertially fixed direction (chosen toward the direction of
the vernal equinox, an essentially inertially fixed direction infinitely far
away in space) to the line formed by the intersection of the reference and
orbital planes (line of nodes) on the side where the orbital motion is from
south to north (“ascending” node).
The argument of perigee o describes the orientation of the elliptically-
shaped orbit within the orbital plane. It is measured as the angle from the
line of nodes to the radius of perigee of the orbit.