Page 200 - Intro to Space Sciences Spacecraft Applications

Spacecraji Systems
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culates the atmospheric drag on the satellite associated with the precise mis-
sion lifetime (calendar years), which invokes the expected spacecraft envi-
ronment during this lifetime expressed in terms of atmospheric density as a
function of orbit altitude. Atmospheric drag acts in the opposite direction of
the orbital velocity vector and removes energy from the orbit. This reduc-
tion of energy causes the orbital radius to get smaller, leading to further
increases in drag. Acceleration due to drag on a satellite is a function of the
atmospheric density, the satellite cross-sectional area in the direction of
flight (ballistic cross-section), and the satellite mass (in this case the on-
orbit mass). The drag is calculated using the expected environment and the
satellite ballistic cross-section. Various shapes and densities exist from the
distributed modular design architectures to the dense, highly integrated
SMALLSAT designs. This diversity in density and satellite shape results in
an individual determination of the ballistic cross-section of a particular
satellite. These are all known quantities and are used, in turn, to calculate
the Av required to restore the satellite to the prescribed orbit. The remaining
quantity required for this calculation is the Isp or specific impulse of the fuel
that will be used to perform this maneuver. The specific impulse is a mea-
sure of the energy content of the propellant used and how efficiently it is
converted into thrust, or how thrust is produced per time rate of change of
propellant molecular weight. The Isp of the system to be used by the propul-
sion andor orbital maintenance subsystems can be selected by the designer
from a database such as the one shown in Table 8-8.
The orbit modification propulsion subsystem has to provide significantly
more Av than the orbital maintenance subsystem. The propulsion subsystem
must provide the thrust to take the spacecraft from the parking orbit to the
final orbit. The required performance of the system is expressed as a
required Av which is calculated using the principals of orbital mechanics.
Usually only the magnitude of the velocity vector is changed (the condition
when the parking orbit inclination or plane is the same as the final orbit),
but sometimes a plane change is required (the situation for the positioning
of most geosynchronous communications satellites). A design must calcu-
late the Av required for either one of these situations and, using this and the
initial mass of the satellite (m,,) and the Isp of the selected fuel, proceeds to
determine the fuel mass (m,) required to perform the maneuver:

where g is simply the gravitational acceleration.