Orbital Mechanics

Descrizione principi di funzionamento endoreattori ibridi, principali parametri caratteristici di dimensionamento, configurazioni moderne in via di sviluppo, tipologie di combustibili, additivi e ossidanti.
Confronto prestazionale in una manovra di Hohmann con endoreattori liquidi, utilizzando il programma NASA CEA (Combustion Equilibrium Analysis).

Co-Author:
Barberi Spirito Daniele
Bassissi Enrico

This document was created in hopes for a safer, more prosperous future of aeronautics. This document seeks to present an otherwise highly complex topic in the framework of game theory, economic or otherwise with players being governing entities as well as agencies within countries.

Spacecraft Dynamics and Control: The Embedded Model Control Approach provides a uniform and systematic way of approaching space engineering control problems from the standpoint of model based control, using state-space equations as the key paradigm for simulation, design and implementation. The book introduces the Embedded Model Control methodology for the design and implementation of attitude and orbit control systems. The logic architecture is organized around the embedded model of the spacecraft and its surrounding environment. The model is compelled to include disturbance dynamics as a repository of the uncertainty that the control law must reject to meet attitude and orbit requirements within the uncertainty class. The source of the real-time uncertainty estimation/prediction is the model error signal, as it encodes the residual discrepancies between spacecraft measurements and model output. The embedded model and the uncertainty estimation feedback (noise estimator in the book) constitute the state predictor feeding the control law. Asymptotic pole placement (exploiting the asymptotes of closed-loop transfer functions) is the way to design and tune feedback loops around the embedded model (state predictor, control law, reference generator). The design versus the uncertainty class is driven by analytic stability and performance inequalities. The method is applied to solve several attitude and orbit control problems. Key features  The book begins with an extensive introduction to attitude geometry and algebra and ends with the core themes: state-space dynamics and Embedded Model Control.  Orbital mechanics, attitude kinematics and dynamics, and environmental perturbations are treated giving emphasis to state-space formulation, disturbance dynamics, state feedback and prediction, closed-loop stability.  Sensors and actuators are treated giving emphasis to measurement errors, command distribution and dynamics. Numerical tables are included and their data employed for numerical simulations.  Orbit and attitude control problems of the European GOCE mission are the inspiration of numerical exercises and simulations.  The suite of the attitude control modes of a GOCE-like mission is designed and simulated around the so-called mission state predictor.  Solved and unsolved exercises are included within the text-and not separated at the end of chapters-for better understanding, training and hands-on applications.  Simulated results and their graphical plots are developed through MATLAB/Simulink code. Readership Researchers and practitioners in the field of control engineering, aerospace engineering, mechanical engineering, and applied mathematics. The detailed exposition of fundamental topics may benefit students and young practitioners.

The concept of a space elevator dates back to Tsilokovsky, but they are not commonly considered in near-term plans for space exploration, perhaps because a terrestrial elevator would not be possible without considerable improvements in tether material. A Lunar Space Elevator (LSE), however, can be built with current technology using commercially available tether polymers. This paper considers missions leading to infrastructure capable of shortening the time, lowering the cost and enhancing the capabilities of robotic and human explorers. These missions use planetary scale tethers, strings many thousands of kilometers long stabilized either by rotation or by gravitational gradients. These systems promise major reduction in transport costs versus chemical rockets, in a rapid timeframe, for a modest investment. Science will thus benefit as well as commercial activities.

Electric propulsion is currently seen as a key enabling technology for space debris removal missions aimed at deorbiting multiple debris targets. This paper develops an autonomous onboard orbit control strategy tailored to these missions. The control problem is divided into four stages, involving a sequence of low-thrust orbital transfer and rendezvous maneuvers. A feedback control law is derived for each maneuvering stage, by exploiting Lyapunov-based and model predictive control techniques. The proposed design is able to account for mission-specific performance and safety requirements, while satisfying on-off constraints inherent to the propulsion technology. Simulation case studies of a multidebris removal mission demonstrate the effectiveness of the proposed control strategy, and support the viability of electric propulsion for such type of missions.

Space missions in the past were focused on traditional large costly satellites, but are now transitioning to smaller satellites. These satellites include nano-satellites, which is the object of this thesis, becoming one of the most exciting, diverse and fast paced satellites of today. In this study, CubeSats were investigated, focusing on double unit and triple unit CubeSats and deployment effects on CubeSat systems. The deployment effects on CubeSats depend on numerous uncertainties. However, with assumptions for some parameters, analyses can give approximate results. There are also some uncertainties for orbit perturbations such as atmospheric drag, earth gravity and solar radiation pressure which were briefly clarified. The objectives of this thesis are minimizing the risk of collision between CubeSats and deployer and gaining knowledge to optimize the lifetime of CubeSats. To accomplish these objectives specifications of these CubeSats were given and orbital elements were explained. Moreover, each scenario for the cases described reference CubeSats and simulation parameters are briefly explained. Afterwards, with the assumed parameters, some simulations performed. There are two main parts for simulations which are deployment effects to lifetime of CubeSats and collision risks for CubeSats deployment. To accomplish these simulations the two part divided for each part has 2 cases. These cases are altitude effects and ejection time for lifetime prediction part, direction difference and multiple ejection cases for obtaining collision risks part. Deployment altitude effects were explored with taking ballistic coefficient, atmospheric drag, and gravity effects into account. By using STK Lifetime Tool, lifetime for all CubeSats were calculated. Ejection time for CubeSats were changed to observe the effects on them. Solar activity effects are also considered and explained briefly. Deployment directions and multiple ejection cases were investigated with several simulations and some of them are shown. By the help of these simulations, the risk pie for CubeSats deployments were obtained. This thesis proposes knowledge for optimizing lifetime and proper deployment directions which are less risky against collision between CubeSats and deployer. The performed simulations also give some deployment system constraints.

This document details the procedure of calculation of orbital perturbation due to gravitational harmonics by simulation of various orbits at different altitudes and inclinations to the earth's equatorial plane. The orbits were first simulated and data of position and velocity was collected. The data was then analysed by another program to calculate the perturbations. Runge – Kutta fourth order method was used to simulate the orbits. The orbits were assumed to start from the perigee position which lied on the longitudinal plane containing the point of vernal equinox. The perturbations obtained were analysed w.r.t inclination of orbits and eccentricity of the orbits. The order of magnitude of the perturbations obtained were analysed w.r.t altitude. The earth was assumed to be symmetrical in all other terms.

The report gives a practical understanding of basic Orbital Mechanics. In this report, a step by step approach is used for computing and visualising a satellite in orbit with reference to a station on earth. For this purpose a pragmetic explanation is given on how to convert from one coordinate system to other and how to derive the position and velocity of a satellite in an orbit. The software used for computation and plotting is Matlab.

Spacecraft collision avoidance procedures have become an essential part of satellite operations. Complex and constantly updated estimates of the collision risk between orbiting objects inform the various operators who can then plan risk mitigation measures. Such measures could be aided by the development of suitable machine learning models predicting, for example, the evolution of the collision risk in time. In an attempt to study this opportunity, the European Space Agency released, in October 2019, a large curated dataset containing information about close approach events, in the form of Conjunction Data Messages (CDMs), collected from 2015 to 2019. This dataset was used in the Spacecraft Collision Avoidance Challenge, a machine learning competition where participants had to build models to predict the final collision risk between orbiting objects. This paper describes the design and results of the competition and discusses the challenges and lessons learned when applying machine ...

This document outlines the solution of the assignment problem given in 'Introduction to Space Flight Mechanics' by Dr Ramanann. The document contains MATLAB code for solving the Kepler's equation
and plotting the graph between the eccentric anomaly and Mean anomaly. Newton Raphson method was used for solving the Kepler equation. The graph was plotted for 6 different eccentricity values. For two given state vectors the orbital elements were obtained. The variation of eccentric anomaly is explained at the end.

Variations in gravitational forces on the surface of natural satellites cause orbits to lose rotational angular momentum. A tetrahedron joined by springs is introduced to allow these differentials to distort the shape of a satellite. A dashpot (damper) is used to dissipate energy through tension in the springs as a result of these tidal bulges. We manage to predict the time-scale of tidal locking to within one order of magnitude.

We present here a simple and novel proposal for the modulation and rhythm of ice ages and interglacials during the late Pleistocene. While the standard Milankovitch-precession theory fails to explain the long intervals between interglacials, these can be accounted for by a novel forcing and feedback system involving CO2, dust and albedo. During the glacial period, the high albedo of the northern ice sheets drives down global temperatures and CO2 concentrations, despite subsequent precessional forcing maxima. Over the following millennia CO2 is sequestered in the oceans and atmospheric concentrations eventually reach a critical minima of about 200 ppm, which causes a die-back of temperate and boreal forests and grasslands, especially at high altitude. The ensuing soil erosion generates dust storms, resulting in increased dust deposition and lower albedo on the northern ice sheets. As northern hemisphere insolation increases during the next Milankovitch cycle, the dust-laden ice-sheets absorb considerably more insolation and undergo rapid melting, which forces the climate into an interglacial period. The proposed mechanism is simple, robust, and comprehensive in its scope, and its key elements are well supported by empirical evidence.

As the spacefaring community is well aware, the increasingly rapid proliferation of man-made objects in space, whether active satellites or debris, threatens the safe and secure operation of spacecraft and requires that we change the way we conduct business in space. The introduction of appropriate protocols and procedures to regulate the use of space is predicated on the availability of quantifiable and timely information regarding the behavior of resident space objects (RSO): the basis of space domain awareness (SDA). Yet despite five decades of space operations, and a growing global dependence on the services provided by space-based platforms, the population of Earth orbiting space objects is still neither rigorously nor comprehensively quantified, and the behaviors of these objects, whether directed by human agency or governed by interaction with the space environment, are inadequately characterized. Key goals of advanced SDA are to develop a capability to predict RSO behavior, extending SDA beyond its present paradigm of catalog maintenance and forensic analysis, and to arrive at a comprehensive physical understanding of all of the inputs that affect the motion of RSOs. Solutions to these problems require multidisciplinary engagement that combines space surveillance data with other information, including space object databases and space environmental data, to help decision-making processes predict, detect, and quantify threatening and hazardous space domain activity. 1.0 INTRODUCTION This document presents an introductory overview of space surveillance, tracking, and information fusion for SDA. A relevant activity is the NATO Science and Technology Organization's Task Group (SCI-279-TG) is addressing the technical considerations for enabling a NATO-Centric Space Domain Common Operating Picture (COP). The impetus for this effort is the growing dependence by NATO and its member nations on space capabilities to achieve its mission responsibilities as well as the growing role that space, as an operational domain in its own right, is playing in matters concerning global security. NATO has recognized this important reality and increased the Alliance's collective attention on ensuring NATO operations maximize their leverage of space while ensuring the space capabilities provided by its member nations are preserved to the maximum extent possible. A critical element of ensuring the availability and efficacy of these space capabilities is the availability of a common operational perspective or picture of the space domain throughout the Alliance and its partners. The presumption is that NATO forces will be more efficient, protected and successful in their future missions if a common operational perspective can be achieved across all operational domains in which NATO must operate; air, land, sea, cyber AND space. The corollary is, without a common Alliance perspective of the space domain,

Space missions in the past were focused on traditional large costly satellites, but are transitioning to smaller satellites. Nowadays, humankind have the technology of landing a comet and try to make manned flight to Mars. These satellites include
nano-satellites, which is the object of this thesis, becoming one of the most exciting, diverse and fast paced satellites of today. 1U Cubesat is traditionally 10x10x10 cm cubic satellite that weights 1 kg. They are currently used in many countries and
educational institutions as technology demonstration and an easy access to space. The QB50 project is an initiative of the von Karman Institute to operate a network of 50 CubeSats to conduct in-situ, multi-point and long duration measurements in the lower thermosphere between 380 and 90 km. In this study, one of the participant of QB50 project, double unit CubeSat of Istanbul Technical University and Turkish Air Force Academy, namely BeEagleSat were investigated, focusing on orbital mission analysis. Starting with the known values and restriction of the project, simulations have been carried out in order to obtain the orbital analysis the satellite will would perform. Because of the atmospheric drag, the altitude of the satellites will gradually decrease. Additionally, perturbations in the orbit, comparatives with other models and simulations with different parameters were studied. By the help of assumptions for some parameters, analyses can give approximate results. There are also some uncertainties for orbit perturbations such as atmospheric drag, Earth gravity and solar radiation pressure which were briefly clarified. Before launch the primary work to do would be the analysis of the orbit the satellite would perform. In this way, the STK (Systems Tool Kit) software is used to perform this analysis. Deployment altitude effects were explored with taking ballistic coefficient, atmospheric drag, and gravity effects into account. By using STK Lifetime Tool, lifetime for all CubeSats were calculated. Solar activity effects are also considered and explained briefly. Definition of CubeSats, QB50 project and mission characteristic of BeEagleSat is the introduction part of this work. Afterwards, the architecture of BeEagleSat with the payloads and individual subsystems are briefly explained. Then, mission phases of the CubeSat which are mostly related with the ADCS subsystem are shown. In order to give a pre knowledge of surveyed analyses, orbital elements and orbital perturbations are shown with necessary calculations. Finally, simulations are done by predicting lifetime, calculating sunlight and coverage ability of BeEagleSat. This thesis proposes knowledge of the orbital limits and forecasted results of BeEagleSat and can be implemented to other CubeSats especially for another QB50 CubeSat.

A Lunar Space Elevator [LSE] can be built today from existing commercial polymers; manufactured, launched and deployed for less than $2B. A prototype weighing 48 tons with 100 kg payload can be launched by 3 Falcon-Heavy's, and will pay for itself in 53 sample return cycles within one month. It reduces the cost of soft landing on the Moon at least threefold, and sample return cost at least ninefold. Many benefits would arise. A near side LSE can enable valuable science mission, as well as mine valuable resources and ship to market in cislunar space, LEO and Earth's surface. A far-side LSE can facilitate construction and operation of a super sensitive radio astronomy facility shielded from terrestrial interference by the Moon. The LSE would facilitate substantial acceleration of human expansion beyond LEO.

The libration point orbits in the Sun-Earth/Moon system are formed by concurrent gravitational influences by various celestial bodies, originating in a nonlinear dynamical regime. Coupled with the unstable nature of the orbit, the impact of any perturbations are expected to increase rapidly. The feasibility of a flow-based, Cauchy-Green tensor control strategy for station-keeping is examined. An orbit consistent with the mission objectives is selected for examination. The station-keeping process is stochastic, thus Gaussian random errors are introduced for simulation. The evolution of a velocity perturbation over time is monitored, beyond which the attainable state in the accessible region nearest to the target state is employed as a feedback to compute the necessary full, three-component corrective maneuver. The application and appropriateness of single axis control maneuvers for orbit maintenance are also evaluated. The selection procedure for certain parameters such as tolerances and weighting values are developed to incorporate the available dynamical information, yielding a versatile and straightforward strategy. Weighting matrices within the target point approach are effective in influencing the station-keeping costs as well as size and direction of maneuvers. Moreover, selection of appropriate tolerance values in the application of the Cauchy-Green tensor exploits the dominant stretching direction of the perturbation magnitude to inform the maneuver construction process. The work is demonstrated in the context of the upcoming Aditya-1 mission to a Sun-Earth/Moon L1 halo orbit for solar observations and the James Webb Telescope to a Sun-Earth/Moon L2 halo orbit for astronomy.

This paper develops the ontology of space objects for theoretical and computational ontology applied to the space (astronautical/astronomical) domain. It follows “An ontological architecture for Orbital Debris Data” (Rovetto, 2015) and “Preliminaries of a Space Situational Awareness Ontology” (Rovetto, Kelso, 2016). Important considerations for developing a space object ontology, or more broadly, a space domain ontology are presented. The main category term ‘Space Object’ is analyzed from a philosophical perspective, and the ontological commitments of legal definitions for artificial space objects are also discussed. Space object taxonomies are offered and space object terms are defined. Part of the taxonomy of my Space Object Ontology (SOO), a computational ontology under-development using Protege ontology editor, is introduced. Given the narrow scope of an SOO, it serves as a part or module of a broader Space Situational Awareness Ontology, or alternatively an Orbital Space Environment Ontology (Rovetto, 2016).

In this technical report, I describe the details of the code that I had written to fit a curve for a set of observational data points using the Givens Rotation method of performing QR factorization. This document is structured in a manner where I first describe what Givens Rotation is, then the complete sequence of how I used Givens Rotation to find the R factor and, finally, how I use the R factor to fit a curve that matches the measured data points.

The orbits of interest for potential missions are stable or nearly stable to maintain long-term presence for conducting scientific studies and to reduce the possibility of rapid departure. Near Rectilinear Halo Orbits (NRHOs) offer such stable or nearly stable orbits that are defined as part of the L1 and L2 halo orbit families in the circular restricted three-body problem. Within the Earth-Moon regime, the L1 and L2 NRHOs are proposed as long-horizon trajectories for cislunar exploration missions, including NASA’s upcoming Gateway mission. These stable or nearly stable orbits do not possess well-distinguished unstable and stable manifold structures. As a consequence, existing tools for stationkeeping and transfer trajectory design that exploit such underlying manifold structures are not reliable for orbits that are linearly stable. The current investigation focuses on leveraging stretching direction as an alternative for visualizing the flow of perturbations in the neighborhood of a reference trajectory. The information supplemented by the stretching directions are utilized to investigate the impact of maneuvers for two contrasting applications; the stationkeeping problem, where the goal is to maintain a spacecraft near a reference trajectory for a long period of time, and the transfer trajectory design application, where rapid departure and/or insertion is of concern.

Particularly, for the stationkeeping problem, a spacecraft incurs continuous deviations due to unmodeled forces and orbit determination errors in the complex multi-body dynamical regime. The flow dynamics in the region, using stretching directions, are utilized to identify appropriate maneuver and target locations to support a long lasting presence for the spacecraft near the desired path. The investigation reflects the impact of various factors on maneuver cost and boundedness. For orbits that are particularly sensitive to epoch time and possess distinct characteristics in the higher-fidelity ephemeris model compared to their CR3BP counterpart, an additional feedback control is applied for appropriate phasing. The effect of constraining maneuvers in a particular direction is also investigated for the 9:2 synodic resonant southern L2 NRHO, the current baseline for the Gateway mission. The stationkeeping strategy is applied to a range of L1 and L2 NRHOs, and validated in the higher-fidelity ephemeris model.

For missions with potential human presence, a rapid transfer between orbits of interest is a priority. The magnitude of the state variations along the maximum stretching direction is expected to grow rapidly and, therefore, offers information to depart from the orbit. Similarly, the maximum stretching in reverse time, enables arrival with a minimal maneuver magnitude. The impact of maneuvers in such sensitive directions is investigated. Further, enabling transfer design options to connect between two stable orbits. The transfer design strategy developed in this investigation is not restricted to a particular orbit but applicable to a broad range of stable and nearly stable orbits in the cislunar space, including the Distant Retrograde Orbit (DROs) and the Low Lunar Orbits (LLO) that are considered for potential missions. Examples for transfers linking a southern and a northern NRHO, a southern NRHO to a planar DRO, and a southern NRHO to a planar LLO are demonstrated.

This is a presentation that discusses the simulation of a projectile (potentially a rocket) being fired from the Earth with some initial velocity and directed towards the Moon. It explores the use of different iterative methods to model the differential equations governing the trajectory, particularly Euler's method, the classical fourth-order Runge-Kutta method, and Mat-lab's built-in function for differential equations, ode45.

There are two main sections of the presentation. Slides 1 through 8 and the final two slides (slides 20 and 21). Slides 1 through 8 contain a video showing a Mat-lab program simulating the motion of the projectile when governed by Euler's method and the fourth-order Runge-Kutta method when a fixed time step is used. It also contains the assumptions necessary for creating the model and provides an intuition of some of the Math behind the Mat-lab programs hopefully understandable for someone with less of a background in math. A picture of a simulation of the path of the projectile when governed by Euler's method, the Runge-Kutta method, and ode45 when a "distance-step" is used is also shown. Slides 20 and 21 contain the acknowledgments and links to the Mat-lab programs used to create the presentation.

The other section (slides 9 through 19) contain the derivation of orbital equations and the math used in setting up Euler's method, the Runge-Kutta method, and ode45. The math required to understand the derivations and the implementation of the numerical methods requires a basic understanding of vector algebra and some knowledge in differential equations & the numerical methods used for differential equations.

This presentation was created for BCCC's Math Awareness Week Events.

The aim of this research is to investigate how to track the QB50 cubesats when they are
deployed from the rocket launchers. Also the use of the ground station in Von Karman
Institute to track, identify and distinguish the signals for each of the 50 cubesats of the
QB50 constellation is examined in this research.
Cubesats, due to their small size and weight, are low cost platforms to place in orbit. In
parallel to this, cubesats are becoming more powerful everyday with very promising future
from earth observation to telecommunications.
Cubesat tracking and signal analysis is a crucial milestone in the cubesats constellation.
The deployment of multiple cubesats from a rocket at an interval of about 30-60 seconds,
creates a cloud of multiple cubesats orbiting close to each other. The process of tracking
an individual cubesat and distinguish each signal is a complex process. Thus a research
in the antennas, tracking system, orbital mechanics, electromagnetics, software and
general ground station assembly is needed.
Furthermore to track the cubesats exact orbital elements for a satellite are needed. Orbital
elements or two line elements are also very hard to be generated at the early stages of
deployment. NORAD the organization who is generating the two line elements for all
space objects, is able to generate accurate two line elements for the cubesats after one
month of deployment.
As a conclusion to this research two methods are presented to track the QB50
constellation. The first is aiming to use the existing antennas and devices at VKI and the
second is presenting a more sophisticated mini radar like system with a parabolic antenna
which can be used alone or in a combination with the existing system. Also for future
cubesats constellations a proposed system of time flags and time measuring is proposed.

The orbital debris problem presents an opportunity for international cooperation toward the mutually beneficial goals of orbital debris prevention, mitigation, remediation, and improved space situational awareness (SSA). Achieving these goals requires sharing orbital debris and other SSA data. Toward this, I present an ontological architecture for the orbital debris and related domains, taking steps in the creation of an orbital debris ontology. The purpose of the ontology is to capture general scientific domain knowledge; formally represent the entities within the domain; form, structure, and standardize (where needed) orbital and SSA terminology; and foster semantic interoperability and data-exchange. In doing so I hope to offer a scientifically accurate ontological representation of the orbital domain; contribute to research in astroinformatics, space ontology, and space data management; and improve spaceflight safety by providing a means to capture and communicate information associated with space debris.

Destination: 700 km LEO - 200 km LLO
Micro Ion Thruster Optimization
Low Thrust Continuous Spiral Orbit Approach
R3BP and GEO Launch is the next step
3U/6U/12U Satellite Designs
Primary Cost Estimation
Basic Thruster Optimization:
    Initial Mass, Burn Time vs. Thrust

Objects in Low-Earth Orbits (LEO) and Highly Elliptical Orbits (HEO) are subject to decay and re-entry into the atmosphere due mainly to the drag force. While being this process the best solution to avoid the proliferation of debris in space and to ensure the future sustainability of space activities, it implies a certain amount of risk as many of these reentries are done in an uncontrolled manner.
In order to have a better insight on the objects reentering the Earth’s atmosphere, in short and middle term, and on the risk posed by these re-entries, CNES has developed a tool named OPERA (Outil de PrEvision des dates des Rentrées Atmosphèriques non contrôlées).
This paper will concentrate on the prediction of the in-orbit lifetime of a space object, based on publicly available TLE (Two Line Elements sets) data, as it has been implemented in OPERA.
To this purpose, several operations are needed prior to the computation of the residual in-orbit lifetime of such object, by the propagation of its orbital position up to re-entry.
These operations include the pre-processing of the TLE data by filtering their outliers and detecting maneuvers, as only non-maneuverable objects are considered for the analysis, the preliminary estimation of objects area-to-mass ratio and the final estimation of the orbits based on a weighted least-squares algorithm taking the TLE states as input pseudo-observations. Additionally, the accuracy (estimation error) of the results obtained for known past reentries will be presented.

Implementation of a numerical method for targeting both the transfer orbit and Trojan orbit around the triangular points in the Sun-Earth system. This method generates end-to-end trajectories from a low Earth parking orbit at a 200-km altitude and 28.5 degrees inclination, using a high fidelity model allowing for injection velocity corrections at the parking orbit. Either the position or velocity at arrival in the Trojan orbit around L5 can be targeted. During the injection velocity correction, we use the classical and hyperbolic elements to target the desired orientation and radius of periapsis.