Summary Formation-Flying Interferometry in Geocentric Orbits A Preliminary Study arxiv.org
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The study examines the use of formation-flying interferometry in geocentric orbits, highlighting the significance of accounting for perturbations and eclipse effects when selecting suitable orbits for different formation sizes.
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Key Points
- Formation-flying interferometry in geocentric orbits is investigated for its feasibility and potential.
- Small-perturbation regions tend to appear in higher-altitude and shorter-separation regions in geocentric orbits.
- Candidate orbits are identified for different formation sizes, including high Earth orbit for a gravitational-wave telescope and middle Earth orbit for an astronomical interferometer.
- Control approaches are analyzed to compensate for relative fictitious perturbations in orbital motion.
- Analytical models are developed for various perturbation sources to better understand and mitigate perturbations in formation-flying interferometry.
- Geocentric orbits show potential for various types of formation-flying interferometry, with guidelines provided for finding candidate orbits and control approaches.
- The study emphasizes the importance of considering specific mission requirements and selecting the appropriate orbit to ensure a small-disturbance environment and desired observation conditions.
- A mathematical framework is provided for analyzing formation-flying interferometry in geocentric orbits, with a focus on orbital elements and variations in satellite motion.
Summaries
26 word summary
This study analyzes formation-flying interferometry in geocentric orbits, identifying candidate orbits for different formation sizes and emphasizing the importance of considering perturbation sources and eclipse effects.
93 word summary
This study investigates formation-flying interferometry in geocentric orbits, analyzing the impact of perturbation sources. Small-perturbation regions are more likely at higher altitudes and shorter separations. Candidate orbits are identified for different formation sizes, including a high Earth orbit for a triangular laser-interferometric gravitational-wave telescope and a middle Earth orbit for a linear astronomical interferometer. A low Earth orbit with a separation of approximately 0.1 km may be suitable for experiments. The study also develops analytical models for perturbed orbital motion and emphasizes the importance of considering eclipse effects in orbit design and planning.
134 word summary
This study explores the feasibility of formation-flying interferometry in geocentric orbits, focusing on the effects of various perturbation sources. The results show that small-perturbation regions are more likely to occur in higher-altitude and shorter-separation regions. Candidate orbits are identified for different formation sizes, including a high Earth orbit for a triangular laser-interferometric gravitational-wave telescope and a middle Earth orbit for a linear astronomical interferometer. A low Earth orbit with a separation of approximately 0.1 km may be suitable for experimental purposes. The study also examines the effects of perturbed orbital motion on control accelerations and develops analytical models for each perturbation source. Geocentric orbits demonstrate potential for formation-flying interferometry, and the study provides guidance for orbit selection and control approaches. The importance of accounting for eclipse effects in orbit design and planning is emphasized.
487 word summary
This study investigates the feasibility of formation-flying interferometry in geocentric orbits, specifically focusing on the effects of various perturbation sources. The aim is to demonstrate the potential of geocentric orbits for this type of interferometry due to their economic accessibility and flight-proven technologies. Perturbations such as CW nonlinearity, Earth's J2 and J3 gravity potentials, lunisolar gravity, atmospheric drag, and solar radiation pressure on spacecraft motions in Earth orbits are analyzed.
The results indicate that small-perturbation regions are more likely to occur in higher-altitude and shorter-separation regions in geocentric orbits. Candidate orbits are identified for different formation sizes, including a high Earth orbit for a triangular laser-interferometric gravitational-wave telescope and a middle Earth orbit for a linear astronomical interferometer. A low Earth orbit with a separation of approximately 0.1 km may be suitable for experimental purposes.
The study also examines the effects of perturbed orbital motion on control accelerations to compensate for relative fictitious perturbations. It is found that compensating for relative perturbations can lead to more efficient control, except in the secular and long-periodic parts of the term with (.)n^2r^r.
Analytical models are developed for each perturbation source, providing insights into the magnitude and period of perturbing accelerations. This allows for better understanding and mitigation of perturbations in formation-flying interferometry.
Geocentric orbits demonstrate potential for various types of formation-flying interferometry. The study offers guidance for identifying candidate orbits and control approaches to mitigate perturbations. Perturbing accelerations are categorized into four types, and the study discusses the control approach for each type based on its characteristics. Small-disturbance regions are identified in high Earth orbits and middle Earth orbits, with larger disturbance magnitudes in low Earth orbits.
Factors contributing the most to control magnitudes are discussed, and an orbit selection approach based on these factors is presented. The semi-major axis characterizes absolute perturbations, while the semi-major axis and formation size characterize relative perturbations.
This study demonstrates that geocentric orbits can be utilized for various types of formation-flying interferometry missions. Mission requirements and appropriate orbit selection are crucial to ensure a small-disturbance environment and achieve desired observation conditions.
Mathematical equations and expressions are provided to describe orbital elements and variations in satellite motion. Constants and coefficients are introduced to simplify the expressions, and orbital elements for near-circular satellite motion are provided.
Osculating orbital elements are calculated by computing secular orbital elements, long-periodic variations using the secular orbital elements, and short-periodic variations using both secular and long-periodic orbital elements.
Eclipse effects of the Earth on selected orbits are examined, emphasizing the importance of accounting for eclipse effects in orbit design and planning. A figure illustrating the annual duration of eclipses per orbit for different types of orbits is presented.
Overall, this preliminary study offers a mathematical framework for analyzing formation-flying interferometry in geocentric orbits. It highlights the orbital elements and variations in satellite motion that need to be considered for such missions and emphasizes the importance of accounting for eclipse effects.
497 word summary
This study examines the feasibility of formation-flying interferometry in geocentric orbits, focusing on various perturbation sources. The goal is to demonstrate the potential of geocentric orbits for this type of interferometry due to their economic accessibility and flight-proven technologies. The study analyzes the effects of perturbations such as CW nonlinearity, Earth's J2 and J3 gravity potentials, lunisolar gravity, atmospheric drag, and solar radiation pressure on spacecraft motions in Earth orbits.
The results show that small-perturbation regions tend to appear in higher-altitude and shorter-separation regions in geocentric orbits. Candidate orbits are identified for different formation sizes, including a high Earth orbit for a triangular laser-interferometric gravitational-wave telescope and a middle Earth orbit for a linear astronomical interferometer. A low Earth orbit with a separation of approximately 0.1 km may be suitable for experimental purposes.
The study also analyzes the effects of perturbed orbital motion on control accelerations to compensate for relative fictitious perturbations. It is found that compensating for relative perturbations can lead to more efficient control, except in the secular and long-periodic parts of the term with (.)n^2r^r.
Analytical models are developed for each perturbation source, providing insights into the magnitude and period of perturbing accelerations. This allows for better understanding and mitigation of perturbations in formation-flying interferometry.
Overall, geocentric orbits show potential for various types of formation-flying interferometry. The study provides a guideline for finding candidate orbits and control approaches to mitigate perturbations.
The study categorizes perturbing accelerations into four types and discusses the control approach for each type based on its characteristics. Small-disturbance regions are identified in high Earth orbits and middle Earth orbits, with larger disturbance magnitudes in low Earth orbits.
The study also discusses the factors that contribute the most to control magnitudes and the orbit selection approach based on these factors. The semi-major axis characterizes absolute perturbations, while the semi-major axis and formation size characterize relative perturbations.
This study demonstrates that geocentric orbits can be used for various types of formation-flying interferometry missions. However, it is important to consider mission requirements and select the appropriate orbit to ensure a small-disturbance environment and achieve desired observation conditions.
The study presents mathematical equations and expressions to describe orbital elements and variations in satellite motion. It introduces constants and coefficients to simplify the expressions and provides orbital elements for near-circular satellite motion.
The study calculates osculating orbital elements by computing secular orbital elements, long-periodic variations using the secular orbital elements, and short-periodic variations using both secular and long-periodic orbital elements.
The study also examines the eclipse effects of the Earth on selected orbits, presenting a figure illustrating the annual duration of eclipses per orbit for different types of orbits. It emphasizes the importance of accounting for eclipse effects in orbit design and planning.
Overall, this preliminary study provides a mathematical framework for analyzing formation-flying interferometry in geocentric orbits. It highlights the orbital elements and variations in satellite motion that need to be considered for such missions and emphasizes the importance of accounting for eclipse effects.
813 word summary
This study investigates the feasibility of formation-flying interferometry in geocentric orbits with various perturbation sources. The goal is to demonstrate the potential of using geocentric orbits for formation-flying interferometry, which offers economic accessibility and flight-proven technologies tailored for Earth orbits. The study focuses on analyzing spacecraft motions in Earth orbits subjected to perturbations, such as CW nonlinearity, Earth's J2 and J3 gravity potentials, lunisolar gravity, atmospheric drag, and solar radiation pressure.
The results show that small-perturbation regions tend to appear in higher-altitude and shorter-separation regions in geocentric orbits. Candidate orbits are identified for different formation sizes, such as a high Earth orbit for a triangular laser-interferometric gravitational-wave telescope and a middle Earth orbit for a linear astronomical interferometer. A low Earth orbit with a separation of approximately 0.1 km may be suitable for experimental purposes.
The study also analyzes the effects of perturbed orbital motion on control accelerations to compensate for relative fictitious perturbations. It is found that most terms to compensate for relative fictitious perturbations include common terms of the absolute physical perturbations multiplied by small factors, indicating that compensating for relative perturbations can lead to more efficient control. However, there are exceptions in the secular and long-periodic parts of the term with (.)n^2r^r, where compensating absolute perturbations may be more efficient.
Analytical models are developed for each perturbation source, including CW nonlinearity, Earth's J2 and J3 gravity potentials, lunisolar gravity, atmospheric drag, and solar radiation pressure. These models provide insights into the magnitude and period of perturbing accelerations, allowing for better understanding and mitigation of perturbations in formation-flying interferometry.
Overall, geocentric orbits show potential for various types of formation-flying interferometry. The study provides a guideline for finding candidate orbits and control approaches to mitigate perturbations. This information will be useful for future applications of formation-flying interferometry in geocentric orbits.
This study focuses on the feasibility of formation-flying interferometry in geocentric orbits. The perturbing accelerations that need to be mitigated by precise control are categorized into four types: absolute physical acceleration, relative physical acceleration, relative fictitious acceleration due to the perturbed orbital motion of the chief, and relative fictitious acceleration due to the perturbed motion of the reference formation. The control approach for each type of perturbation depends on its characteristics.
The study reveals that there are small-disturbance regions in high Earth orbits and middle Earth orbits. In a high Earth orbit, a small-disturbance region of less than 10^-7 m/s^2 was identified for a laser-interferometric gravitational-wave telescope with a size of 100 km. In a middle Earth orbit, a small-disturbance region of less than 10^-7 m/s^2 was identified for a linear astronomical interferometer with a size of 0.5 km. However, the low Earth orbit (LEO) has larger disturbance magnitudes, although a relatively small acceleration of 10^-6.5 to 10^-6 m/s^2 can be attained in LEO at an altitude higher than 500 km and a separation of approximately 0.1 km.
The study also discusses the orbit selection approach based on the factors that contribute the most to the control magnitudes. The semi-major axis characterizes the absolute perturbations, while the semi-major axis and formation size characterize the relative perturbations. The control magnitudes against the absolute perturbations decrease with an increase in the semi-major axis, while those against the relative perturbations increase linearly with the formation size for certain perturbations.
Overall, this study demonstrates that geocentric orbits can be used for various types of formation-flying interferometry missions. However, it is important to consider the specific mission requirements and select the appropriate orbit to ensure a small-disturbance environment and achieve the desired observation conditions.
This preliminary study explores the concept of formation-flying interferometry in geocentric orbits. The study presents mathematical equations and expressions to describe the orbital elements and variations in satellite motion. The study introduces constants and coefficients to simplify the expressions. The orbital elements for near-circular satellite motion are provided, including the semi-major axis, eccentricity, inclination, and longitude of the ascending node. The study also discusses the secular and short-periodic variations in these orbital elements.
To calculate the osculating orbital elements, the study first computes the secular orbital elements. Then, it calculates the long-periodic variation using the secular orbital elements, and the short-periodic variation using both the secular and long-periodic orbital elements.
In Appendix D, the study examines the eclipse effects of the Earth on selected orbits. It presents a figure illustrating the annual duration of eclipses per orbit for different types of orbits. The durations were computed assuming circular orbits and considering perturbed or unperturbed motion depending on the altitude of the orbit. The study only takes into account the effects of the Earth's umbra.
Overall, this preliminary study provides a mathematical framework for analyzing formation-flying interferometry in geocentric orbits. It highlights the orbital elements and variations in satellite motion that need to be considered for such missions. The study also emphasizes the importance of accounting for eclipse effects in orbit design and planning.