144
A. V. Bogatiy et al.
and defined by SC purpose-oriented task, one can approximately determine the
appropriate type of propulsion system using the diagram in Fig. 11.2.
The diagram in Fig. 11.2 shows that the choice of EPS type for SSC is not an easy
task and it should be made at the stage of preliminary design taking into account the
task to be performed by the spacecraft and the purpose of the propulsion system. Two
typical tasks that can be performed by a low-power electric propulsion system (power
consumption from 10 to 100 W and slightly higher) are considered hereinafter: low
Earth orbit maintenance and attitude control for a spacecraft.
11.3 Low Earth Orbit Maintenance for Small Spacecraft
One of the typical tasks for low-power electric propulsion systems is to maintain a
relatively low circular near-Earth orbit of the spacecraft. The possibility of solving
this problem using APPT was studied in a number of papers.
The aerodynamic drag force F a acting on a spacecraft moving in orbit at a velocity
V is described as [9]:
F a = 1/2 · C d · ρV
2
· S m ,
(11.1)
where ρ is the density of the atmosphere gases (to a first approximation, except for
its fluctuations in solar radiation, it depends only on the orbit altitude h above the
Earth and is regulated by GOST 4401–81 for the International Standard Atmosphere
(ISA)), C d is the aerodynamic drag coefficient (for a free-molecular gas flow that
occurs at densities corresponding to the upper atmosphere (h > 200 km), C d ≈ 2.3)
[9], S m is the midsection area of the spacecraft.
The spacecraft velocity, in the simplest case of a circular orbit with altitude h, is
defined by Eq. 11.2 [9], where G is the gravitational constant, M is the mass of the
Earth, R E is the average radius of the Earth.
V
2
= G · M/(R E + h)
(11.2)
The characteristic velocity V x necessary to maintain a conditional circular orbit
with altitude h during time T is equal to:
V x = F a · T /m,
(11.3)
where m is the spacecraft mass.
Figure 11.3 shows the calculated dependences of the aerodynamic drag force F a
averaged in accordance with ISA and characteristic velocity V x necessary to maintain
circular orbit of a conventional small satellite with mass m = 100 kg and midsection
area of 1 m
2 in the orbit with altitude h for one year (T ≈3.16 × 10
7 s). When
calculating, the aerodynamic drag coefficient was assumed as C d = 2.3.
A. V. Bogatiy et al.
and defined by SC purpose-oriented task, one can approximately determine the
appropriate type of propulsion system using the diagram in Fig. 11.2.
The diagram in Fig. 11.2 shows that the choice of EPS type for SSC is not an easy
task and it should be made at the stage of preliminary design taking into account the
task to be performed by the spacecraft and the purpose of the propulsion system. Two
typical tasks that can be performed by a low-power electric propulsion system (power
consumption from 10 to 100 W and slightly higher) are considered hereinafter: low
Earth orbit maintenance and attitude control for a spacecraft.
11.3 Low Earth Orbit Maintenance for Small Spacecraft
One of the typical tasks for low-power electric propulsion systems is to maintain a
relatively low circular near-Earth orbit of the spacecraft. The possibility of solving
this problem using APPT was studied in a number of papers.
The aerodynamic drag force F a acting on a spacecraft moving in orbit at a velocity
V is described as [9]:
F a = 1/2 · C d · ρV
2
· S m ,
(11.1)
where ρ is the density of the atmosphere gases (to a first approximation, except for
its fluctuations in solar radiation, it depends only on the orbit altitude h above the
Earth and is regulated by GOST 4401–81 for the International Standard Atmosphere
(ISA)), C d is the aerodynamic drag coefficient (for a free-molecular gas flow that
occurs at densities corresponding to the upper atmosphere (h > 200 km), C d ≈ 2.3)
[9], S m is the midsection area of the spacecraft.
The spacecraft velocity, in the simplest case of a circular orbit with altitude h, is
defined by Eq. 11.2 [9], where G is the gravitational constant, M is the mass of the
Earth, R E is the average radius of the Earth.
V
2
= G · M/(R E + h)
(11.2)
The characteristic velocity V x necessary to maintain a conditional circular orbit
with altitude h during time T is equal to:
V x = F a · T /m,
(11.3)
where m is the spacecraft mass.
Figure 11.3 shows the calculated dependences of the aerodynamic drag force F a
averaged in accordance with ISA and characteristic velocity V x necessary to maintain
circular orbit of a conventional small satellite with mass m = 100 kg and midsection
area of 1 m
2 in the orbit with altitude h for one year (T ≈3.16 × 10
7 s). When
calculating, the aerodynamic drag coefficient was assumed as C d = 2.3.