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Defense Information, Communication, and Space Technology
Published in Anna M. Doro-on, Handbook of Systems Engineering and Risk Management in Control Systems, Communication, Space Technology, Missile, Security and Defense Operations, 2023
True anomaly of a satellite (angle θ) is the angle subtend by the satellite at the focus of its elliptical orbit at any instance between the direction of the perigee and the direction of the satellite, counted positively in the direction of the movement of the satellite (Acharya 2014). It is applied to determine the location of the satellite in its orbit. This is done by defining an angle θ, delineated by the line joining the perigee and the center of the earth with the line joining the satellite and the center of the earth (Figure 5.4c). Further, to get a parameter that varies linearly with time, two further parameters are called the eccentric anomaly and mean anomaly, as follows (Noureldin et al. 2013):
Spaceborne Application of Electronically Scanned Arrays
Published in Arik D. Brown, Electronically Scanned Arrays, 2017
Consider a circle with radius equal to the semimajor axis of the ellipse and concentric with the ellipse. While the true anomaly describes the angular position of the satellite along the ellipse, the eccentric anomaly, E, is the angular position of a point on the circle with equal horizontal displacement from the focus. Figure 5.4 illustrates the relationship between the true anomaly and the eccentric anomaly.
Adaptive kriging-assisted optimization of low-thrust many-revolution transfers to geostationary Earth orbit
Published in Engineering Optimization, 2021
Renhe Shi, Teng Long, Hexi Baoyin, Nianhui Ye, Zhao Wei
The minimum-time low-thrust GEO transfer optimization problem can be generally formulated in Equation (1): where x and u are the state and control variables, respectively; J is the performance index (i.e. the total transfer time ); are the motion equations; and presents the terminal state constraints. The motion equations are established in terms of classical orbital elements combined with the mass–flow rate equation, as shown in Equation (2) (Yang 2001): where n, E and f are the orbit mean motion, eccentric anomaly and true anomaly, respectively; p = a(1− e2) is the latus rectum; u = + f is the argument of latitude; Isp is the specific impulse of the EP system; g0 is the gravitational acceleration at sea level; m is the mass of the spacecraft; T0 is the maximum thrust of the EP system; and F = [FR, FT, FN] are the acceleration components expressed in the RTN coordinate system that is defined in the Appendix. F consists of two parts, i.e. the thrust accelerations provided by the thrusters and the Earth’s oblateness perturbations. In this work, the disturbances caused by the first four zonal harmonics of non-spherical gravitational potential are taken into account (Ghosh et al. 2015). Since the EP system is incapable of operating during eclipses because the solar arrays cannot generate power in the shadow of the Earth, an Earth conical shadow model (Yang 2001) is employed to address the eclipse problem during orbital transfer. It is assumed that T0 = 0 when the satellite enters the shadow of the Earth.