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Solar radiation induced perturbations and control of satellite trajectories Van Der Ha, Jozef Cyrillus
Abstract
The longterm orbital perturbations due to solar radiation forces as well as ways to utilize these effects for corrections in the orbit are investigated. In order to obtain familiarity with relative merits of the formulations and methods relevant to the present objective, the special case of an orbit in the ecliptic plane and a force along the radiation is considered first. The longterm valid analysis is based upon the twovariable expansion method and incorporates the apparent motion of the sun by treating the sun's position as a quasiorbital element. Analytical representations for orbital elements are derived and the perturbations are conveniently summarized in the form of polar plots showing the longterm evolution of the eccentricity vector. While the eccentricity is periodic with period close to one year, the argument of the perigee contains secular terms. The total energy and thus major axis remain conserved in the long run. However, in the course of one year, the effect of the earth's shadow may lead to small secular changes in the major axis thereby modifying the satellite's period. Next, the analysis is extended to orbits of an arbitrary inclination with closedform analytical solutions established in some special cases. An interesting relation between the longterm behavior of the orbital inclination and the inplane perturbations is discovered. Also, more general satellite configurations are studied: e.g., spacecrafts modelled as a plate in an arbitrary fixed orientation with respect to the earth or solar radiation as well as platforms kept fixed to the inertia! space. In all applications a realistic solar radiation force allowing for diffuse and/or specular reflection as well as for reemission of absorbed radiation is considered. In a few cases, the analysis is extended to include arbitrarily shaped satellite bodies modelled by a number of surface components of homogeneous material characteristics. After establishing a comprehensive spectrum of the qualitative and quantitative aspects of solar radiation induced orbital perturbations, the attention is focused on the development of control strategies involving the rotation of solar panels attached to the satellite to manipulate both the direction and magnitude of the resulting force. A few onoff switching strategies are explored and the most effective switching locations for several specific objectives, e.g. maximization of the major axis, are determined. The switching strategies explored here constitute an attractive possibility for orbital corrections. The concept is particularly of interest to modern communications satellite technology since it allows their normal operation to remain unaffected over approximately half the time. Although onoff switching may lead to substantial changes in the major axis, it is not necessarily the best policy when timevarying orientations are also taken into consideration. The optimal control strategy for maximization of the major axis over one revolution is determined by means of the numerical steepestascent iteration procedure, and its effectiveness is compared with that of the switching programs. The solution should prove to be of interest in several future missions including the launching of a solar sail from a geocentric orbit into a heliocentric or escape trajectory. Subsequently, solar radiation effects upon a satellite (usually a solar sail) in a heliocentric orbit are explored. First, the sail is taken in a fixed but arbitrary orientation to the local frame. Using specific initial conditions, exact solutions in the form of conic sections and threedimensional logarithmic spirals are established. For an arbitrary initial orbit, longterm approximate representations of the orbital elements are derived. An effective outofplane spiral transfer trajectory is obtained by reversing the force component normal to the orbit at specified positions. By choosing the appropriate control angles, any point in space can eventually be reached. Finally, timevarying optimal control strategies are explored for increasing the total energy (and angular momentum) during one revolution. While analytical approximate results can be established for nearcircular orbits, in the general case a numerical steepestascent technique is employed. The results are compared with those from the constant sail setting indicating that the latter is a nearoptimal strategy for low eccentricity starting orbits.
Item Metadata
Title 
Solar radiation induced perturbations and control of satellite trajectories

Creator  
Publisher 
University of British Columbia

Date Issued 
1977

Description 
The longterm orbital perturbations due to solar radiation forces as well as ways to utilize these effects for corrections in the orbit are investigated. In order to obtain familiarity with relative merits of the formulations and methods relevant to the present objective, the special case of an orbit in the ecliptic plane and a force along the radiation is considered first. The longterm valid analysis is based upon the twovariable expansion method and incorporates the apparent motion of the sun by treating the sun's position as a quasiorbital element. Analytical representations for orbital elements are derived and the perturbations are conveniently summarized in the form of polar plots showing the longterm evolution of the eccentricity vector. While the eccentricity is periodic with period close to one year, the argument of the perigee contains secular terms. The total energy and thus major axis remain conserved in the long run. However, in the course of one year, the effect of the earth's shadow may lead to small secular changes in the major axis thereby modifying the satellite's period.
Next, the analysis is extended to orbits of an arbitrary inclination with closedform analytical solutions established in some special cases. An interesting relation between the longterm behavior of the orbital inclination
and the inplane perturbations is discovered. Also, more general satellite configurations are studied: e.g., spacecrafts modelled as a plate in an arbitrary fixed orientation with respect to the earth or solar radiation
as well as platforms kept fixed to the inertia! space. In all applications a realistic solar radiation force allowing for diffuse and/or specular reflection as well as for reemission of absorbed radiation is considered. In a few cases, the analysis is extended to include arbitrarily
shaped satellite bodies modelled by a number of surface components of homogeneous material characteristics.
After establishing a comprehensive spectrum of the qualitative and quantitative aspects of solar radiation induced orbital perturbations, the attention is focused on the development of control strategies involving the rotation of solar panels attached to the satellite to manipulate both the direction and magnitude of the resulting force. A few onoff switching strategies are explored and the most effective switching locations for several specific objectives, e.g. maximization of the major axis, are determined.
The switching strategies explored here constitute an attractive possibility for orbital corrections. The concept is particularly of interest
to modern communications satellite technology since it allows their normal operation to remain unaffected over approximately half the time. Although onoff switching may lead to substantial changes in the major axis, it is not necessarily the best policy when timevarying orientations are also taken into consideration. The optimal control strategy for maximization
of the major axis over one revolution is determined by means of the numerical steepestascent iteration procedure, and its effectiveness is compared
with that of the switching programs. The solution should prove to be of interest in several future missions including the launching of a solar sail from a geocentric orbit into a heliocentric or escape trajectory.
Subsequently, solar radiation effects upon a satellite (usually a solar sail) in a heliocentric orbit are explored. First, the sail is taken in a fixed but arbitrary orientation to the local frame. Using specific initial conditions, exact solutions in the form of conic sections and threedimensional logarithmic spirals are established. For an arbitrary
initial orbit, longterm approximate representations of the orbital elements are derived. An effective outofplane spiral transfer trajectory is obtained by reversing the force component normal to the orbit at specified
positions. By choosing the appropriate control angles, any point in space can eventually be reached.
Finally, timevarying optimal control strategies are explored for increasing the total energy (and angular momentum) during one revolution. While analytical approximate results can be established for nearcircular orbits, in the general case a numerical steepestascent technique is employed.
The results are compared with those from the constant sail setting indicating that the latter is a nearoptimal strategy for low eccentricity starting orbits.

Genre  
Type  
Language 
eng

Date Available 
20100223

Provider 
Vancouver : University of British Columbia Library

Rights 
For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.

DOI 
10.14288/1.0081018

URI  
Degree  
Program  
Affiliation  
Degree Grantor 
University of British Columbia

Campus  
Scholarly Level 
Graduate

Aggregated Source Repository 
DSpace

Item Media
Item Citations and Data
Rights
For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.