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UC3M Analysis of Orbital Relay Stations for Orbital Energy

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UC3M Analysis of Orbital Relay Stations for Orbital Energy Analysis of Orbital Relay Stations for Orbital Energy Accumulation Author: Juan José García Ortiz Tutor: Mario Merino Martínez University Carlos III Madrid NANOSTAR consortium 1 Analysis of Orbital Relay Stations for Orbital Energy Accumulation BSc Aerospace Engineering Abstract Space activities and attainability are constrained nowadays due to the high cost of rocketry employed put payloads in orbit. This study aims to design, analyze and optimize a network of orbital relay stations that can act as orbital energy accumulators to support other space missions. The sustainability of such network lies in a balance between payloads being orbited and deorbited. To test the viability of the proposed network, simulated missions are implemented in a programming environment in a way that can reproduce numerically the behaviour of the network in missions of increasing complexity. The design optimization of such missions is then performed assisted with a built-in genetic algorithm. The results gathered prove that the energetic balance can be achieved providing an operation with minimal degradation. Proper mission design and station orbit spacing are key in defining suitable design conditions that yield the best case performance and the genetic algorithm is applicable to reduce the losses in off-design operating conditions. 1 Analysis of Orbital Relay Stations for Orbital Energy Accumulation BSc Aerospace Engineering Contents 1 Introduction 3 1.1 Proposed study and design objectives . .4 2 State of the art 5 3 Model and numerical implementation 7 3.1 Mathematical model and assumptions . .7 3.2 Problem variables . .7 3.3 Cowell orbital propagator . .8 3.4 Targeting method: Lambert algorithm . .9 3.5 Payload-station operations: Attachment and ejection . 11 4 Single Payload Missions 12 4.1 Direct Mission definition . 12 4.1.1 Objective . 13 4.1.2 Code structure and algorithm design . 13 4.1.3 Output and post-process . 15 4.1.4 Remarks on mission design . 17 4.1.5 Sensitivity analysis from non-Hohmann scenarios . 18 4.1.6 Limitations on station operation . 21 4.2 Wait and flight time estimator . 23 4.2.1 Objective . 23 4.2.2 Code structure and algorithm design . 23 4.2.3 Output and post-process . 24 4.2.4 Station spacing . 26 4.2.5 Multi-payload coupling . 28 5 Multi-payload Mission Design 29 5.1 Objective . 29 5.2 Code structure and algorithm design . 29 5.3 Output and post-process . 32 6 Mission analysis and optimization 38 6.1 Introduction to genetic algorithms . 38 6.2 Problem definition . 39 6.3 Problem bounding . 39 6.4 Optimized cases . 41 7 Conclusion 50 Appendices 51 2 Analysis of Orbital Relay Stations for Orbital Energy Accumulation BSc Aerospace Engineering 1 Introduction Means of transport on Earth are frequently, if not always, supported by ground infrastructure (roads, highways, airports, sea ports and railways among others). Space transport is popularly known to be expensive and challenging in many ways. In a similar way to air and ground transportation, space infrastructure may help overcome many of these challenges and hopefully cheapen the operations at least in the vicinity of planet Earth. The present study is devoted to the analysis and optimization of a network of space stations so that they may serve as orbital energy accumulators. Such energy will be employed to perform orbit transfers of payloads without the use of propellant. The stations, which may serve other purposes besides payload transferring, are reduced to black boxes that receive, store and eject payloads on demand. These operations will of course have an impact on the station orbit itself. One of the objectives of this project is to assess that impact as well as study how to reduce it. The proposed layout is complex and has many details to consider, the following points fall under the scope of this study: • The implementation in a programming environment of the relay station network with trajectory propagation capabilities. • Complete this programming model with payload transfer missions of one or more payload exchanges with increasing complexity. • Asses the impact of the payload operation on the station orbit and normal trajectory. • Study how different parameters affect this impact and determine possible ways to minimize it. Other considerations regarding station design, station orbit correction, station and payload orbital insertion or economical analysis of the network cost and maintenance are beyond the scope of the present study. If accomplished, this network would allow the transmission of any kind of material between different orbits of our planet. The payloads may serve as supplies for the operation of the stations, to place smaller scale objects into orbit and, in general, to enable motion between orbits of items that lack a proper propulsion system in an economical way. It constitutes a fairly complex optimization problem that motivates this report. Interesting particular applications include the orbital placement of nanosatellites, which are meant themselves to be inexpensive devices, have difficulties implementing propulsion systems in their constrained allowable weight. This network of relay stations would reduce the propulsive requirements to just a launch into a low altitude parking orbit. The orbit raising propulsion would be replaced with a set of transfers between the stations of the network. Additionally, since the operation of this network is restricted to the Earth gravity influence only, the generalization to a Earth-moon system would also have interesting application. Such generalization would require the introduction of three body problem considerations that are beyond the scope of this study. If accomplished, the generalized network would grant access to a cheap and reliable way of supply transfer between Earth and moon stations as well as grant easy access to the L2 Lagrange point. All in all, the socioeconomic impact this system would have if performed would imply a cheapening and simplification of the access to all layers of orbits within the cislunar regime. This would broaden the impact of space activities in life on Earth and open new possibilities in regards of scientific research and attainability of the space around Earth. 3 Analysis of Orbital Relay Stations for Orbital Energy Accumulation BSc Aerospace Engineering 1.1 Proposed study and design objectives The objective is to implement in a programming environment a system of stations that are able to perform payloads transactions among themselves without the use of propellant. The stations will use part of their mechanical orbital energy to launch payload towards another station. Such an operation will cause the station lose part of its energy and change its linear momentum. Assess the impact of this transactions on the orbit of the stations is one of the main concerns of this study. A succession of several payload transactions may be defined, constituting a mission. Missions may include one or more payloads and aim to make them visit several stations in a predetermined sequence. Along this report, missions of increasing complexity will be considered with different implementation in code. To implement the specific algorithms for each mission, several tools are at our disposal and will be detailed in section 3. In general, some assumptions regarding the modelling of the missions are considered: • Both stations and payloads follow an ideal two body problem motion around the Earth (orbital parameter µ = 3:986 × 105km3s−2) • Payload exchanges are impulsive instantaneous manoeuvres in which linear momentum of the payload + station system is preserved. • The station network is defined by initial conditions (in terms of their Classical Orbital Elements) and they are assumed to be in orbit already. • Payloads start attached to a certain station at t = 0. • Payload and station mass is assumed constant and defined as an input. Each payload operation is defined by: • Initial station • Target station • Waiting time in initial station • Time of flight after ejection until arrival at target station. • Payload number (if more than one payload is being considered). One or more of this parameters may be not directly an input but instead product of an estimation that attempts to optimize the operation of the network (for example, adjusting the time of flight to make close-to-Hohmann transfers [1]). In the following chapters we will go through the state of the art of space infrastructure and payload transfer systems (section 2), the theoretical basis and the preliminary tools to model it in a programming environment (section 3). Section 4 is devoted to the missions that can only process one payload at a time and chapter 5 to the more complete versions with multiple payloads and varied mission profiles. To conclude, the performance of the more advanced missions will be optimized in section 6. The code employed and developed for this project is published in GitHub repository at: https://github.com/JuanJoseGarciaOrtiz/Analysis-of-Orbital-Relay-Stations 4 Analysis of Orbital Relay Stations for Orbital Energy Accumulation BSc Aerospace Engineering 2 State of the art Space transportation has since its beginning been approached using rocket engineering. The lack of material medium in space requires a self-contained propulsion system. In this way, rockets store both fuel and oxidizer and achieve a high velocity jet exhaust to propel a spacecraft. The mixture of fuel and oxidizer is called propellant and corresponds to a large fraction of the mass at launch of modern spacecraft. This technology was first proposed for space applications by Konstantin E. Tsiolkovsky. Tsiolkovsky also developed the famous rocket equation, first published in his work Exploration of the Universe with Reaction Machines [2], that relates the ∆V and the propellant mass fraction required with the specific impulse Isp (see equation 1). mfull mpropellant ∆V = Isp log = Isp log 1 + (1) mempty mempty Some refinements have cheapened the propellant cost through the years. Improvements in nozzle and combustion technology provide a higher Isp granting more ∆V for the same mass fraction.
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