POGO orbits were determined using simple gravity field models up to spherical harmonic degree 7 and order 6, plus three higher order resonance terms (Taylor et al. 1981). Thus, there are two sources contributing to posi- tional error: i) imprecision in determination of actual spot position, through range and range-rate determina- tion; and ii) imprecision in reduction of the data to pro- duce valid orbits, i.e. determination of observations when only timing information was available. Unfortunately, the unprocessed original data are not available any more and we are left only with processed data which are avail- able from the Goddard Space Flight Center (Greenbelt, Maryland, USA). Therefore, a reprocessing of the orbits with BERNESE, using a state-of-the-art gravity field and tidal models, may reduce the position errors and hence increase the data quality. To remove the potential bias from the old **orbit** in an objective way, we radially perturb the orbits according to the maximum radial gradient of |B|, reducing the residual to a magnetic potential field. For more detail about our approach, see the ‘Data compilation’ section.

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Chapter 10 presents the research carried out on the development o f short arc techniques. The motivation for this study is the fact that most o f the applications do not require a precise ephem eiis over a long arc, but only within a limited region. Two new short-arc methods are developed in this study. Both methods are dynamic and involve solving for the 6 initial osculating elem ents. Solving for these 6 elem ents usually leads to ill- conditioned solutions with high correlations between the solved-for parameters. The first method, the so-called "constrained" method, overcom es this problem by applying constraints to the solved-for parameters. These constraints are dependent on station configuration. The second method, called the "Bayesian" method, uses the covariance matrix from a previous "a priori" solution, usually a long arc, in a Bayesian least square schem e to constrain the short arc. These two methods are also compared with the traditional non-dynamic TAR method, whereby corrections to a previous long arc solution, along the three directions, along-track (T), across-track (A) and radial (R), are solved for and applied to obtain a corrected **satellite** track.

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Very few attempts have been executed for generalizing this method from the Keplerian motion to the perturbed motion. As a first try, the Lagrange coefficients have been developed by (Lin & Xin, 2003) by taking into account the Earth’s oblateness. In that research, the Laplace's method of the initial **orbit** determination using the angular observations was developed based on the F and G series. (M. A. Sharifi & Seif, 2011) have developed the Lagrange coefficients from J2 field (the field of the attractive body by considering oblateness) to the gravitational field of an inhomogeneous attracting body (full gravitational field). These coefficients are only restricted to the gravitational field of an attractive body and other perturbations have to be taken into account. In addition to the **satellite** **orbit** propagation and initial **orbit** determination, this method could be utilized to solve various problems such as the 3- body problem (Steffensen, 1956) and N-body problem (Broucke, 1971). As another application, the Lagrange method could represent the continuous solution for the equations of motion over a time-span. It makes the method well suited for problems requiring dense output e.g., ephemeris calculation (Montenbruck, 1992). The method of the Lagrange might be classified as a semi-analytical approach based on the terms of the F and G series that we could approach into analytical solution by using the highest- order series. This new semi-analytical formulation could be used for the **satellite** motion analysis (Sharifi et al., 2013). Recently, the Lagrange coefficients are extended to solve the Stark problem (Pellegrini et al., 2014). In this paper, an attempt is made to represent a formulation to include the non-static forces (non-Earth gravitational and non- gravitational perturbations) into the Lagrange coefficients. Besides, the stability test of the Lagrange method has been carried out and compared with the numerical integrators. To analyze the accuracy of the method, the **orbit** propagated using the Lagrange method was compared with the numerically integrated one.

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Abstract: A very sensitive stage in the lifetime of the spacecraft is during the journey from the launch vehicle parking **orbit** transfer to the final required working **orbit**. In this paper, altitude **orbit** transfer method is introduced taking into account the effect of propulsion system operation on the secular classical orbital elements. Elements taken in the study are the semi- major axis (a), eccentricity (e) and the argument of perigee ().

In order to verify the performance of deep neural network in **satellite** **orbit** prediction, the long short-term memory neural network prediction is carried out based on the actual data of X, Y and Z coordinates of the satellite's geocentric inertial coordinate system. The experimental object was the TacSat2 US scientific imaging **satellite**, launched in December 2006 with orbital height of 413KM × 424KM near-circular **orbit**, and the experiment was performed at UTC time from 12:00:00 on July 1,2007 to October 8, 2017 12:00:00 total of 100 days of data as a learning sample. The 100-day **satellite** orbital X, Y, Z values are calculated by STK (**satellite** Tool Kit) High Precision Orbital Predictor (HPOP) and the learning samples are sampled at 1-minute intervals for the next 20 days. The results of X-axis prediction are partially shown in Figure.3. The error analysis mainly records the maximum absolute error and training time according to the training times. As shown in Table 1.

Abstract. Since Thailand successfully launched the first earth observation **satellite** (Thaichote) in 2008, the Geo-Informatics and Space Technology Development Agency (GISTDA) has started developing an **orbit** analysis tool called “EMERALD” to be used for the current and future mission planned by GISTDA. In this paper, we present the development of a **satellite** **orbit** control maneuver, which is one of the analysis tools, by providing essential parameters for an orbital trajectory analysis and design. The algorithms are developed and programmed in a convenient graphical user interface (GUI). The results can guarantee a mission and design a desired orbital mission by calculating suitable maneuver parameters to correct the ground track (GT) and local solar time (LST) under control window including the transfer **orbit** for the good quality of the mission data. The validation results are in good agreement with Quartz++, which is a flight dynamics software developed by EADS ASTRIUM.

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While, in standard GAs, a chromosome (solution) is rep- resented by a single string of genes all at same unique level, in the presented algorithm a chromosome consists in a matrix containing the information of the values of the genes and, in addiction, their position in the hierarchy of the chromosome. Every gene belongs to a gene class which contains crucial information for collocating it in the rest of the chromosome: data type, children, and bounds (lower LB and upper UB). Particularly, three levels constitute the hierarchical structure. The gene class Ground Station forms the top of the hierarchical structure. The value of this gene indicates the number of different **satellite** passes in which the specific ground station will be used to measure the **satellite** state. In a chromosome, the number of genes of this class is fixes and equal to the number of ground stations in the considered network. However, for a fixed **satellite** **orbit** and tracking window, the number of times the **satellite** falls in the FOV of each tracking station is generally different, depending on

As detailed by [2], various forces influence the attitude motion of a **satellite** and among them we may men- tion circular radiation effect, atmospheric drag, relativistic effect and many others. But the effect of the atmos- pheric drag and the later forces can be neglected and so we have mainly concentrated on aerodynamic and gra- vitational force.

The most challenging problem of navigation in three-axis stabilized geosta- tionary **satellite** is accurate calculation of misalignment angles, deduced by **orbit** measurement error, attitude measurement error, thermal elastic defor- mation, time synchronization error, and so on. Before the **satellite** is launched, the misalignment model must be established and validated. But there were no observation data, which is a non-negligible risk of yielding the greatest returns on investment. On the basis of misalignment modeling using landmarks and stars, which is not available between different organizations and is developed by ourselves, experimental data are constructed to validate the navigation processing flow as well as misalignment calculation accuracy. In the condition of using landmarks, the maximum misalignment calculation errors of roll, pitch, and yaw axis are 2, 2, and 104 micro radians, respectively, without con- sidering the accuracy of image edge detection. While in the condition of using stars, the maximum errors of roll, pitch, and yaw axis are 1, 1, and 3 micro ra- dians, respectively, without considering the accuracy of star center extraction. Results are rather encouraging, which pave the way for high-accuracy image navigation of three-axis stabilized geostationary **satellite**. The misalignment modeling as well as calculation method has been used in the new generation of geostationary meteorological **satellite** in China, FY-4 series, the first **satellite** of which was launched at the end of 2016.

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First, an equation of motion was found for the circular **orbit** scenario. The single equation of motion will describe the behavior of the unknown variable that is 𝜙, the angle of rotation of the **satellite**. Then the state space representation was performed for the equation of motion for use in the ode45 program. Numerical results were then obtained for several cases. The cases investigated for the circular **orbit** are given in the list below:

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The lack of links at the reverse slot limits communication reliability and net- work throughput for a variety of reasons. The main reason for limiting the relia- bility of communication is that the earth’s rotation leads to the rapid movement of the reverse gap coverage area (the equatorial attachment is 1677 km/h). Under such rapid movement, the switching of the **satellite** link near the reverse gap may lead to the delay of real-time communication service. The jitter is too large. The delay jitter in the communication process causes the receiver to compensate for the delay jitter compensation, which increases the packet loss rate and affects the reliability of the communication, and is more likely to bring a bad user expe- rience. The main reason for the reverse gap to limit network throughput is that the bandwidth resources of the link are limited, and there is a throughput limit for a single link. Since the communication across the reverse slot must go to the polar link, and the number of polar links is much smaller than the number of links of non-reverse slot communication, the cross-slot communication is busy, which may cause the polar link load to be too large, which limits the communi- cation throughput.

Restricted Body Problem has important non-linear component. As a result, when we consider the problem, we should take priority for its non-linear identi- ty, and we extend the application of Koopman eigenfunction control to this problem. Restricted Three-Body Problem has deep engineering implications: It can help humans to determine the suitable time for the **satellite** to change its or- bit. Restricted Three-Body Problem has five Lagrange points where the net force is zero. The second Lagrange point is the place where the space telescope James Webb [3] works in. The Lagrange point 4 and point 5 are a suitable place to build Spatial VLBI [4], which guarantees the acceptance of much more informa- tion from the outer space. Classical three-body problem has perplexed scientists for hundreds of years. The typical three-body problem involves 18 first order differential equations. Through use of conservation equations and calculus, the order can be reduced to 6. It has still not been solved because there are not enough conservation quantities to allow for further simplification. In this paper, we consider a restricted three-body model neglecting the force from the smallest body to other larger bodies ( i.e. the **satellite**-earth-moon system or the comet coming into the solar system).

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the study, performances of two nonlinear estimators are compared for the localization of a spacecraft. It is as- sumed that range measurements are not available, and the localization problem is tackled on the basis of an- gle-only measurements. A dynamic model of the space- craft accounting for several perturbing effects, such as Earth and Moon gravitational field asymmetry and errors associated with the Moon ephemerides, is employed. The measurement process is based on elevation and azimuth of Moon and Earth with respect to the spacecraft refer- ence system. Position and velocity of the spacecraft are estimated using both the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). The behaviour of the filters is compared on two sample missions: Earth-to-Moon transfer and geostationary **orbit** raising.

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In this paper, the motion of an axi-symmetric **satellite** under the effect of a radiating body in the presence of air drag is studied. An energy-like integral for the problem has been evaluated using a Taylor expansion for the ve- locity around the initial value of the polar angel. The convergence of the integral is guaranteed by the assump- tion that the derivative

From this initial analysis the paper presents families of long-lived orbits for swarms of ‟smart dust‟ devices. The conditions for long-lived orbits are identified in the **orbit** element phase-space and numerical integration of the secular variation of orbital elements is used to characterize their long-term evolution. Different families of orbits are presented. In those regions of the phase-space where the effect of atmospheric drag is negligible, equilibrium orbits can be found under the effect of solar radiation only, where the condition of Sun-synchronous apse-line precession is achieved passively, without any propellant mass consumption. If the initial condition is in a certain region around the equilibrium solution set, the long-term evolution follows a librational motion, progressively decaying due to the non-conservative effect of atmospheric drag. Asymmetry in solar radiation pressure due to eclipses leads to modulation of the **orbit** energy, and families of orbits can be found where the energy gain due to solar radiation pressure balances the energy dissipation due to drag. It is therefore shown that the exploitation of the natural effects of solar radiation pressure and atmospheric drag provides a means of enabling long-lived orbits for future „smart dust‟ devices and ensures the final re-entry of the devices so that they do not constitute future space debris.

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dierences. It would be better to uniformly distribute the dierences over the interval. In other words, the v-shaped pattern of the dierences is changed in such a way that the maximum deviation of the two orbits should be minimized to a great extent. This **orbit** is usually called the best-tting reference **orbit** in the sense of the least squares of **orbit** deviations. An **orbit** could be described by a dynamic process a linear dierential equation of the rst order as:

Abstract--In order to evaluate the integrity of a **satellite** transponder, it is necessary to measure its characteristics (i.e. frequency response) and the characteristics of its high power amplifier (HPA), such as sensitivity and saturated output power. Since these properties are subject to aging and the **satellite** itself suffers from the vibration shocks during launch hence performance of these components have to be monitored to guarantee that they still meet the initial specifications. **Satellite** in-**orbit** testing is a very necessary task in order to be able to predict possible malfunctioning of the transponders.

In this work the **satellite**‟s **orbit** is set at LEO that is a distance between 160 kilometers and 2,000 kilometers above the Earth‟s surface. Its mission is specified to be a nadir pointing mission meaning one of the axes will point toward the Earth. The other two axes will be normal to the orbital plane and towards the **satellite**‟s orbital motion respectively. This work will specifically look into a gravity gradient stabilized **satellite** which is a passive system as well as magnetic attitude system which is an active system.

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The manoeuvring case considers a **satellite** in the same **orbit** as above, but equipped with the MIT TILE propulsion system capable of producing a total ∆V of 120m/s. The **satellite** is tasked to begin manoeuvring after the second flyover identified above at 1.433 days from mission start, with the aim of reducing the time to the next flyover from 12.5 days. The analytical method is used to identify the shortest flyovers possible using up to 120m/s ∆V. The results of this are presented in Figure 4 where the flyover time is calculated for ∆V values ranging from 0m/s to 120m/s in 1m/s increments. Time here is measured from the beginning of the manoeuvre, that is, from viewing instance two. These results show that the minimum achievable flyover time for a ∆V <120m/s is 3.623 days, or 86.96 hours, achieved with a ∆V of 36m/s. However, it is of note that a very similar time of flyover can be achieved using a lower ∆V. For example, a flyover time of 87.02 hours is achievable with 21m/s ∆V. This is clear from the solutions shown in Figure 4, however as the solution space is discontinuous such insights may be difficult to gain through numerical methods alone. For the case study being considered, the use of 21m/s ∆V gives an 87 hour manoeuvre time and a potential decrease in flyover time of almost 9 days when compared with the non-manoeuvring case.

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The initial condition (13) provides an initial guess for an almost periodic **orbit** with nonlinearities and eccentricity perturbations. In this case the initial uncontrolled **orbit** (for an initial 20 km relative distance) has a large drift of 0.2439 km and an average drift of 0.6908 km per **orbit** over 10 orbits, see Figure 10 (ii). In this case the average drift increases with longer mission times. Applying TDFC to the system (12) in the same way as for the case without the eccentricity perturbation yields the trajectory shown in Figure 10 (i) Figure 10 (ii) illustrates the TDFC-controlled **orbit**. It can be seen that the initial **orbit** has the same drift as before of 0.2439 km, but an average drift of 0.0145 km per **orbit** over 20 orbits. Therefore, in the uncontrolled case the average drift per **orbit** increases with mission length whereas the average drift per **orbit** is decreasing in the controlled case. The average ∆V over 20 orbits is 15.016 m/s per **orbit**.

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