Page 56 - Intro to Space Sciences Spacecraft Applications

43
Orbital Principles
axis, which can be related to the satellite altitude. For circular orbits
(only), a simple expression gives the number of revolutions per day as:

## Revlday = 16.997 ~ (2 - 19)
(Rri h)li2

Revisit Time

It may be desirable to have a satellite return over a specific point on the
earth's surface periodically for monitoring purposes. It may even be desir-
able to have the satellite pass over the specified point at the same time of
day each visit, or remain in view of a spot indefinitely. Using combina-
tions of the orbital elements and parameters, it is possible to create an
orbit to meet many of these requirements; however, there is no simple way
of describing this process here. Nonetheless, for some simple cases such
as discussed in the following sections, it is possible to see how some of
these requirements can be approached.
Revisit times are mainly dependent on orbital period T which, as we
saw, is a function of the semi-major axis of the orbit. If an orbital period is
established which divides evenly into the period of one sidereal earth rota-
tion (T, = 1 sidereal day = 86,164 sec) such that TJT = n where n is an
integer, then after n orbits (neglecting any perturbations) the ground track
of the orbit will begin to repeat. If n turns out to be unity, then the orbital
period exactly matches the rotational period of the earth and the ground
track repeats itself each orbit. This is known as a geosynchronous orbit.

Example Problem:

The lowest altitude at which a satellite may circle the earth in a
repeating orbit (though its lifetime would be limited due to atmos-
pheric drag) is 262 km. Determine the footprint angle, swath width,
footprint area, angular field of view, maximum time in view, and the
number of revolutions per day. Show that the satellite period is an
integral multiple of the sidereal day.

Solution (using equations 2-14 through 2-19 and equation 2-6):

Cp = 16.15" = 0.28 rad
SW = 3,595.3 km (use radians for Cp in this equation!)