MISSION PLAN - PDS Small Bodies Node

where:
n *
= thruster pulse frequency (1/s) τ s*
= solar torque (x, y axis) (Nm)
θ s
= z-axis off-sun angle, l *
= effective thruster moment arms
(m),
attitude plan dependent
including effect of thruster cant
I **
= mass moments of inertia (kgm 2 ) db *
= deadband limits (radians)
= solar range (AU)
R ***
These equations decouple the motion in each of the spacecraft axis to facilitate the
modeling process. Notice that the motion about the y axis of the spacecraft is driven
primarily by the influence of the solar torque, while the solar torque components in the
spacecraft z-axis is relatively small and ignored. The degree to which motion about the x
axis is influenced by solar torque is determined by the solar range history of the mission.
Near the sun (R≈Rmin), solar torque is the driving force behind the motion. Far from the
sun (R≈Rmax), the influence of solar torque is minimal and represents steady state or
pure limit cycling.
The thruster pulse frequencies are then combined with the minimum impulse bit and
attitude information to produce an average ACS force and corresponding acceleration.
An average mass flow rate is also calculated to keep track of the change in the mass of
the spacecraft due to the ACS activity. These values are calculated via the following
equations.
"
f = f bit
n T
"
k
"
a = "
f / m
m Ý = f n bit T
Isp acs
g
where:
"
f
"
= ACS force vector (m/s)
a = ACS acceleration vector (m/s 2 )
Ým = mass flow rate (kg/s) Isp acs
= ACS thruster specific impulse (s)
g = gravity at Earth’s surface (m/s 2 "
) k
= unit vector in the direction of
+z axis
Deterministic mass decrements due to deterministic maneuvers and ACS burns are also
included in the trajectory optimization code.
10.1.3 Model Parameters and Characteristics
The attitude schedule and ACS force model parameters used for the data contained herein
are summarized in Tables 10.1-3 and 10.1-4. The resultant total thruster pulse frequency,
mass flow rate, acceleration and acceleration direction are illustrated in Figures 10.1-1
thru 10.1-4.
Table 10.1-3 Spacecraft Attitude Profile - Limit Cycle Model
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