Mars is expected to become a focal point of exploration (human and robotic) in the coming century, with a very likely need for a robust space infrastructure. Be it communication and navigation satellite constellations or scientific missions in low Mars orbits (LMO) and Areosynchronous orbits (ASO), every individual satellite will have a definitive period of operation after which it becomes derelict. At the end-of-life (EOL) the satellite shall be proactively dealt with in a sustainable manner to protect our access to the space environment of Mars and opportunities to use this. Clearly, impacting Mars or escaping Mars’ gravity are no viable options. This paper aims at identifying graveyard orbit solutions in circummartian space for future Mars space debris. Orbital stability for a period of 200 years is studied for Martian orbits using the symplectic integration technique. Extensive validations are performed and propagation and integration settings are tuned to suit a variety of configurations. A plethora of candidate graveyard orbit solutions are found and presented for orbits in the ASO and LMO regimes. For example, it is found that transferring an ASO satellite to 400 km below the nominal orbit altitude would ensure a stability margin of ±25 km for at least 200 years. Multiple orbital geometry characteristics (combinations of semi-major axis, inclination, right ascension of ascending node), satellite geometries (various values of area-to-mass ratio) and uncertainties are studied to produce a comprehensive analysis of long-term stability of potential graveyard orbits around Mars, making them attractive for such purposes. The protected zones are found to be safe from debris even for an uncertainty in initial eccentricity of 0.01 and variations in cross-sectional area due to uncontrolled tumbling. The overall objective of this paper is to make designers of future missions to Mars aware of the EOL aspects and include this in their mission design proposals at an early stage already.

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This research investigates the performance of a space-based laser system to remove debris objects with size smaller than 10 cm. The laser system is placed in a 800 km Sun Synchronous Orbit and consists of a 20 kW laser that shoots 300 J energy pulses with a repetition frequency of 66.66 Hz. The system is able to detect and track debris objects in situ using a 2.0 m mirror from 800 km distance. From a distance of about 500 km, the laser fluence on the targets is sufficiently high to trigger ablation, which decelerates the debris objects and reduces their lifetime. The feasibility of the concept is tested in scenarios where the laser system targets the debris objects from a different orbiting altitude and from varying azimuth angles. For many geometries, the laser is capable of significantly reducing the lifetime of the debris object. Extrapolating to longer periods of operation, the laser can be expected to provide a significant reduction of the population of small debris objects in LEO.

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Due to ever increasing accessibility, recent years have seen a fast growing number of launches to space, especially to Sun-synchronous orbit. The spent rocket parts, and eventually non-functioning payloads of these launches remain in orbit. It is well established that this accumulation of space debris over time is quickly making this the most severe threat to future spaceflight operations. To address this, international guidelines have been established including a maximum of 25-year remaining orbital lifetime after end of operational life. This paper evaluates if Sun-synchronous satellites adhere to this guideline. To determine the compliance, the operational status of satellites with orbital control capabilities is established using a maneuver detection algorithm. For satellites without this capability, a model is created based on mass and design lifetime. The remaining orbital lifetime is determined using semi-analytic propagation. The results reveal that compliance was poor in the past, with 20 to 40% prior to 2014, but has increased to 95% in 2018. Satellites with a mass lower than 10 kg have a compliance of 86% compared to 35% for heavier satellites. Analysis shows that compliance is mostly a result of choosing an operational orbit with a sufficient natural decay, and less due to altitude lowering maneuvers near end-of-life. The relative popularity of SSO may demand re-evaluation of current guidelines to sustain future operations in these valuable orbits.

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Inspired by the Keplerian Map and the Flyby Map, a Gravity Assist Mapping using Gaussian Process Regression for the fully spatial Circular Restricted Three-Body Problem is developed. A mapping function for quantifying the flyby effects over one orbital period is defined. The Gaussian Process Regression model is established by proper mean and covariance functions. The model learns the dynamics of flyby's from training samples, which are generated by numerical propagation. To improve the efficiency of this method, a new criterion is proposed to determine the optimal size of the training dataset. We discuss its robustness to show the quality of practical usage. The influence of different input elements on the flyby effects is studied. The accuracy and efficiency of the proposed model have been investigated for different energy levels, ranging from representative high- to low-energy cases. It shows improvements over the Kick Map, an independent semi-analytical method available in literature. The accuracy and efficiency of predicting the variation of the semi-major axis are improved by factors of 3.3, and 1.27×10⁴, respectively.

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We develop a Gravity Assist Mapping to quantify the effects of a flyby in a two-dimensional circular restricted three-body situation based on Gaussian Process Regression (GPR). This work is inspired by the Keplerian Map and Flyby Map. The flyby is allowed to occur anywhere above 300 km altitude at the Earth in the system of Sun-(Earth+Moon)-spacecraft, whereas the Keplerian map is typically restricted to the cases outside the Hill sphere only. The performance of the GPR model and the influence of training samples (number and distribution) on the quality of the prediction of post-flyby orbital states are investigated. The information provided by this training set is used to optimize the hyper-parameters in the GPR model. The trained model can make predictions of the post-flyby state of an object with an arbitrary initial condition and is demonstrated to be efficient and accurate when evaluated against the results of numerical integration. The method can be attractive for space mission design.

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This paper presents the theory for linear cotangential transfers and safe orbits for elliptic orbit rendezvous. Expressions for the transfer angle and the required ΔV’s are derived. Singularities in the algorithm can occur if the two orbits intersect. Alternative maneuvers for such singular cases are developed. The linear cotangential transfer algorithm is compared with the nonlinear cotangential transfer and the algorithm is found to be very similar. The development of the linear cotangential transfer leads to a new set of relative orbital elements that are well suited for defining safe trajectories. The characteristics of safe trajectories are discussed and a linear safety checking algorithm is developed. Finally, the combination of the cotangential transfers and safe orbits is used to define safe rendezvous trajectories for elliptical orbit rendezvous.

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Verified interval orbit propagation provides mathematically guaranteed solutions of satellite position and velocity over time. These verified solutions are useful for conjunction analysis and other space-situational-awareness activities. Unfortunately, verified methods suffer from overestimation and explosive interval growth, limiting the possible propagation time and thus their applicability. Different orbital-element state models have been shown to increase the maximum propagation time to a degree, but at the expense of significant overestimation introduced by the state transformations. This paper proposes the Dromo state model for verified integration. Dromo is a regularized variation-of-parameter formulation of the perturbed two-body equations of motion. Taylor models are implemented for both integration and transformation. Moreover, a technique is developed for dealing with time uncertainty resulting from verified regularized propagation. Dromo significantly prolongs the maximum forecasting window, producing verified trajectories of days up to weeks in duration for the low Earth orbit regime. A sensitivity analysis of the integrator settings identifies combinations that produce stable and computationally efficient solutions. A sensitivity study of the orbital parameters shows that the method is applicable to a large orbital regime, especially for low Earth orbit regions that contain high densities of space debris.

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GTO objects can potentially collide with operative satellites in LEO and GEO protected regions. Internationally accepted debris mitigation guidelines require that these objects exit these protected regions within 25 years, e.g. by re-entering and burning up in Earth's atmosphere. In this paper, an inventory of the GTO debris generated from Ariane 5 launches in the period 2012–2017 is provided, and it is expected that none of these objects will re-enter within 25 years. For future launches, natural perturbations can be exploited to increase compliance with mitigation guidelines without the use of extra propellant or complex de-orbiting systems, which is attractive from an economic point of view. The lifetime of GTO objects is very sensitive to initial conditions and some environmental and body-related parameters, mainly due to the effect of solar gravity on the perigee altitude. As a consequence, the lifetime of a specific GTO object cannot be predicted accurately, but its probability of re-entering in less than 25 years can be estimated with proper accuracy by following a statistical approach. By propagating the orbits of over 800,000 simulated Ariane 5 GTO objects, it was found that the launch time leading to the highest probability of compliance with debris mitigation guidelines for GEO launches from Kourou corresponds to about 2 PM local time, regardless of the date of launch, which leads to compliance rates ranging from 60 to 100%. Current practice is to launch at around 5–9 PM, so a change in procedures would be required in order to reach a higher degree of compliance with debris mitigation guidelines, which was predicted to be on average below 20% for the objects generated in the period 2012–2017.@en

The Lunar Meteoroid Impact Observer (LUMIO) is one of the four projects selected within ESA’s SysNova competition to develop a small satellite or scientific and technology demonstration purposes to be deployed by a mothership around the Moon. Themission utilizes a 12U form-factor CubeSat which carries the LUMIO-Cam, an optical instrument capable of detecting light flashes in the visible spectrum to continuously monitor and process the meteoroids impacts. In this chapter, we will describe the mission concept and focus on the performance of a novel navigation concept using Moon images taken as byproduct of the LUMIOCam operations. This new approach will considerably limit the operations burden on ground, aiming at autonomous orbit-attitude navigation and control. Furthermore, an efficient and autonomous strategy for collection, processing, categorization, and storage of payload data is also described to cope with the limited contact time and downlink bandwidth. Since all communications have to go via a lunar orbiter, all commands and telemetry/data will have to be forwarded to/from the mothership. This will prevent quasi-real-time operations and will be the first time for CubeSats as they have never flown without a direct link to Earth. This chapter was derived from a paper the authors delivered at the SpaceOps 2018 conference.

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Satellite reentry predictions are used to determine the time and location of impacts of decaying objects. These predictions are complicatedby uncertainties in the initial state and environment models, and the complex evolution of the attitude. Typically, the aerodynamic and error propagation are done in a simplistic fashion. Full six-degrees-of-freedom modeling and attitude control is proposed for studying the historic reentry case of the Gravity Field and Steady-State Ocean Circulation Explorer satellite. Improved error modeling and estimation of the initial state and atmospheric density are introduced for both Global Positioning System and two-line elements states. A sensitivity analysis is performed to identify the driving parameters for several models and epochs. The predictions are compared against Tracking And Impact Predictions, and predictions by the European Space Agency Space Debris Office. The performed predictions are consistently closer to the true decay epoch for several starting epochs, while providing narrower windows than other predictions with higher confidence.

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At present, tracking data for planetary missions largely consists of radio observables: range-rate (Doppler), range and angular position (VLBI/Δ DOR). Future planetary missions may use Interplanetary Laser Ranging (ILR) as a tracking observable. Two-way ILR will provide range data that are about 2 orders of magnitude more accurate than radio-based range data. ILR does not produce Doppler data, however. In this article, we compare the relative strength of radio Doppler and laser range data for the retrieval of parameters of interest in planetary missions, to clarify and quantify the science case of ILR, with a focus on geodetic observables. We first provide an overview of the near-term attainable quality of ILR, in terms of both the realization of the observable and the models used to process the measurements. Subsequently, we analyse the sensitivity of radio Doppler and laser range measurements in representative mission scenarios for parameters of interest. We use both an analytical approximation and numerical analyses of the relative sensitivity of ILR and radio Doppler observables for more general cases. We show that mm-precise range normal points are feasible for ILR, but mm-level accuracy and stability in the full analysis chain are unlikely to be attained, due to a combination of instrumental and model errors. We find that ILR has the potential for superior performance in observing signatures in the data with a characteristic period of greater than 0.33–1.65 hours (assuming 2–10 mm uncertainty for range and 10 μ m/s at 60 s for Doppler). This indicates that Doppler tracking will typically remain the method of choice for gravity field determination and spacecraft orbit determination in planetary missions. ILR data will be able to supplement the orbiter tracking data used for the estimation of parameters with a once-per-orbit signal. Laser ranging data, however, are shown to have a significant advantage for the retrieval of rotational and tidal characteristics from landers. Similarly, laser ranging data will be superior for the construction of planetary ephemerides and the improvement of solar system tests of gravitation, both for orbiter and for lander missions.

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The Lunar Meteoroid Impact Observer (LUMIO) is a CubeSat mission to observe, quantify, and characterize the meteoroid impacts by detecting their flashes on the lunar farside. LUMIO is one of the two winners of ESA’s LUCE (Lunar CubeSat for Exploration) SYSNOVA competition, and as such it is being considered by ESA for implementation in the near future. The mission utilizes a CubeSat that carries the LUMIO-Cam, an optical instrument capable of detecting light flashes in the visible spectrum. On-board data processing is implemented to minimize data downlink, while still retaining relevant scientific data. The mission implements a sophisticated orbit design: LUMIO is placed on a halo orbit about Earth–Moon L2 where permanent full-disk observation of the lunar farside is made. This prevents background noise due to Earthshine, and permits obtaining highquality scientific products. Innovative full-disk optical autonomous navigation is proposed, and its performances are assessed and quantified. The spacecraft is a 12U form-factor CubeSat, with 22 kg mass. Novel on-board micro-propulsion system for orbital control, de-tumbling, and reaction wheel desaturation is used. Steady solar power generation is achieved with solar array drive assembly and eclipse-free orbit. @en

The Lunar Meteoroid Impact Observer (LUMIO) is a mission designed to observe, quantify, and characterize the meteoroid impacts by detecting their flashes on the lunar farside. Earth-based lunar observations are restricted by weather, geometric, and illumination conditions, while a lunar orbiter can improve the detection rate of lunar meteoroid impact flashes, as it would allow for longer monitoring periods. This paper presents the scientific mission of LUMIO, designed for the ESA SysNova LUCE competition, that resulted as the ex-aequo winner in the competition. LUMIO, a 12U CubeSat weighting approximately 20 kg, is expected to be deployed into a quasi-polar selenocentric orbit by a mother spacecraft, which also acts as communication relay. From a lunar high-inclination orbit, LUMIO will autonomously determine its trajectory to reach the Moon–Earth L2 point and perform the cruise phase. From the operative orbit, LUMIO will observe the lunar farside. When the lunar disk illumination is less than 50%, LUMIO autonomously performs the scientific task without direct coordination from Earth. Fully autonomous operations will include science, communication, and navigation. A similar concept can be re-used for a wide variety of future missions. The scientific mission will also be possible thanks to an innovative on-board data processing system, capable of drastically reducing the information to transmit to Earth. The camera, designed to capture the flashes and measure their intensity is, in fact, capable of generating 2.6 TB/day while only approximately 1 MB/day will need to be transmitted to Earth. Impact identification will be autonomous and only relevant information will be transmitted. A study at the ESA/ESTEC concurrent design facility has shown evidence of feasibility and that a CubeSat orbiting along an Earth–Moon L2 quasi-halo orbit is expected to bring a relevant contribution to lunar science and innovation to space exploration.@en

The Earth–Moon system is constantly being bombarded by a significant number of meteoroids with different sizes and velocities. Observation of the lunar surface impacts will enable characterization of the lunar meteoroid flux, which is similar to that of the Earth, and provide more detailed information on meteoroid size, velocity, temporal and spatial distribution. The Lunar Meteoroid Impacts Observer (LUMIO) is a CubeSat mission at Earth–Moon L2 to observe, quantify, and characterise these meteoroid impacts by detecting their flashes on the lunar farside. LUMIO is one of the two winners of ESA’s LUCE (Lunar CubeSat for Exploration) SysNova competition, and as such is being considered by ESA for implementation in the near future. This paper will present the design of the LUMIO spacecraft that will host the payload to capture the meteoroid flashes. Key system specifications, trade-offs and consequent design iterations are presented. The final design yields a feasible spacecraft budget and a configuration that enables the LUMIO mission to be realized by 2023. The spacecraft is a 12U form-factor CubeSat, with a mass of less than 22 kg. A zero-redundancy and COTS based approach has been adopted for the spacecraft design. A strong emphasis has been placed on realizing high onboard autonomy. A novel and autonomous navigation strategy that uses optical observations of the Earth and the Moon is proposed for navigation around the Moon and beyond. The payload and navigation are the key drivers of the pointing requirements. Pointing requirements are achieved through reaction wheels, IMUs, star trackers, and fine sun sensors. A hybrid micro-propulsion system is included for orbital control, de-tumbling, and reaction wheel desaturation. Steady solar power availability is ensured with a one-axis solar array drive assembly in combination with an innovative attitude algorithm. Communication with Earth is through the Lunar Orbiter with a low-bandwidth UHF link, which places high constraints on the data throughput. An onboard payload data processor has been designed that compresses the science data to a fraction of the raw data with no loss of information. The paper will conclude with the key findings of a concurrent design review of the LUMIO spacecraft design that was performed at ESA/ESTEC’s Concurrent Design Facility (CDF). The major design changes are outlined along with a summary and discussion of the iterated design.@en

The operational use of satellite systems has been increasing due to technological advances and the reduced costs of satellites and their launching. As such it has become more relevant to determine how to better use these new capabilities which is reflected in an increase in application studies in this area. This work focuses on the problem of developing the scheduling of a constellation of satellites and associated ground stations to monitor different types of locations (targets) with different priorities for a given planning horizon. In order to address this problem we will propose a new model that considers explicitly the operational requirements of Brazilian relevant scenarios for a given planning horizon and target priority list. The methodology to be developed to solve this model will also be discussed.@en

The Lunar Meteoroid Impacts Observer (LUMIO) is one of the four projects selected within ESA’s SysNova competition to develop a small satellite for scientific and technology demonstration purposes to be deployed by a mother ship around the Moon. The mission utilizes a 12U form-factor CubeSat which carries the LUMIO-Cam, an optical instrument capable of detecting light flashes in the visible spectrum to continuously monitor and process the meteoroids impacts. In this paper, we will describe the mission concept and focus on the performance of a novel navigation concept using Moon images taken as byproduct of the LUMIO-Cam operations. This new approach will considerably limit the operations burden on ground, aiming at autonomous orbit-attitude navigation and control. Furthermore, an efficient and autonomous strategy for collection, processing, categorization, and storage of payload data is also described to cope with the limited contact time and downlink bandwidth. Since all communications have to go via a Lunar Orbiter (mothership), all commands and telemetry/data will have to be forwarded to/from the mother ship. This will prevent quasi-real time operations and will be the first time for CubeSats as they have never flown so far from Earth. @en

Using a gravitational field truncated at the 4th degree and order, the 1:1 ground-track resonance is studied. To address the main properties of this resonance, a 1-degree of freedom (1-DOF) system is firstly studied. Equilibrium points (EPs), stability and resonance width are obtained. Different from previous studies, the inclusion of non-spherical terms higher than degree and order 2 introduces new phenomena. For a further study about this resonance, a 2-DOF model which includes a main resonance term (the 1-DOF system) and a perturbing resonance term is studied. With the aid of Poincaré sections, the generation of chaos in the phase space is studied in detail by addressing the overlap process of these two resonances with arbitrary combinations of eccentricity (e) and inclination (i). Retrograde orbits, near circular orbits and near polar orbits are found to have better stability against the perturbation of the second resonance. The situations of complete chaos are estimated in the e- i plane. By applying the maximum Lyapunov Characteristic Exponent (LCE), chaos is characterized quantitatively and similar conclusions can be achieved. This study is applied to three asteroids 1996 HW1, Vesta and Betulia, but the conclusions are not restricted to them.

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A laser-enhanced solar sail is a solar sail that is not solely propelled by solar radiation but additionally by a laser beam that illuminates the sail. This way, the propulsive acceleration of the sail results from the combined action of the solar and the laser radiation pressure onto the sail. The potential source of the laser beam is a laser satellite that coverts solar power (in the inner solar system) or nuclear power (in the outer solar system) into laser power. Such a laser satellite (or many of them) can orbit anywhere in the solar system and its optimal orbit (or their optimal orbits) for a given mission is a subject for future research. This contribution provides the model for an ideal laser-enhanced solar sail and investigates how a laser can enhance the thrusting capability of such a sail. The term ”ideal” means that the solar sail is assumed to be perfectly reflecting and that the laser beam is assumed to have a constant areal power density over the whole sail area. Since a laser beam has a limited divergence, it can provide radiation pressure at much larger solar distances and increase the radiation pressure force into the desired direction. Therefore, laser-enhanced solar sails may make missions feasible, that would otherwise have prohibitively long flight times, e.g. rendezvous missions in the outer solar system. This contribution will also analyze exemplary mission scenarios and present optimial trajectories without laying too much emphasis on the design and operations of the laser satellites. If the mission studies conclude that laser-enhanced solar sails would have advantages with respect to ”traditional” solar sails, a detailed study of the laser satellites and the whole system architecture would be the second next step @en

Two-Line Elements (TLEs) resulting from the Space Surveillance Network (SSN) are often the only available source for many Space Situational Awareness (SSA) activities such as conjunction analyses and re-entry predictions. The network consists of many different radar and optical stations, contributing in either a dedicated, collateral and contributing fashion. For low-Earth orbit radar stations are primarily employed. Radar station can be further distinct into phased-array and mechanically steered radars. Uncertainties in TLEs are primarily a product of sensor capabilities, model deficiencies, network geometry and configuration, and orbit determination setup. The aim of the paper is to separate and analyse the individual contributions and identify potential areas of improvement. Specifically, the configuration and geometry of the network is investigated. Only the LEO satellites are considered. Further, although mechanically steered radars are generally much more accurate, only phased-array radar stations, capable of tracking many object, are considered. The SSN is simulated as a collection of present and hypothetical dedicated and collateral radar stations. An investigation into the current state of the SSN is performed. The location and coverage of each station is accurately estimated and modelled. Range and range-rate measurements are generated for several setups over a number of revolutions. Noise is introduced to individual observations to account for sensor capabilities (e.g. power and resolution) and secondary disturbances. Lastly, observations are edited out to account for sensor availability, viewing conditions, and other limitations. TLEs are estimated from the simulated measurements using Simplified General Perturbations (SGP4) model. GOCE during its re-entry phase is used as the reference satellite. During this final phase the thruster was switched off. GPS derived orbits are considered as truth for assessing TLE accuracy. The optimal number of measurement and passes are investigated to achieve the best state estimates. The resulting simulated TLEs are compared against actual historical TLE estimates. Several network configuration consisting of different combinations of stations are investigated, including historical, present, proposed and hypothetical scenarios. Individual sensors are shown to be the primary factor in the overall accuracy of the initial state. Sensor accuracy, however, is difficult to improve, due to the associated cost and trade-off between accuracy and capacity. The network itself is found to be underrepresented in large regions of the world. The new proposed space fence, with sites in the Marshall Islands and Western Australia, improves the geometry and overall accuracy significantly. @en

TLEs are important for many Space Situational Awareness (SSA) studies, because of their widespread availability. For many objects such as rocket bodies, stages, and defunct satellites TLEs present the only source of orbital states. Despite their importance, TLEs suffer from some major drawbacks: they are of limited accuracy (especially compared to GPS/TIRA), are often mistagged, miss manoeuvres, and lack covariance information. Although the TLEs are openly available, their observations and corresponding covariance are not. The proper understanding and subsequent modeling and estimation of these uncertainties is paramount for previously mentioned SSA activities. The aim of the paper is to present uncertainty models and estimation techniques, focusing on improving re-entry predictions using TLEs of low-earth orbit (LEO) satellites. Only the uncertainties in the initial translational state and deficiencies in atmospheric density and spacecraft aerodynamic modeling are considered. GOCE, during its re-entry phase, is used as the reference object for this study. Probability distributions are presented for modeling uncertainties in the translational and rotational state, and atmospheric density. A new robust weighted differencing method for estimating the uncertainty of TLEs is introduced. For GOCE during the period of investigation, two types of TLEs are present, namely of the classic and enhanced type. The latter TLEs are obtained from pseudo observations derived from a numerical higher-order fit and propagation. The proposed method is validated using GPS orbit solutions. Moreover, the estimation of the ballistic coefficient through retrofitting is discussed and executed for both TLE types. The obtained estimates of the uncertainty in the initial translational state and atmospheric density are applied to re-entry time predictions of GOCE. Specifically, decay time distributions are obtained using six degree-of-freedom statistical re-entry simulations. The effects of the different environment and spacecraft models is investigated, especially the proper modeling of the attitude control that was present almost entirely throughout re-entry. Moreover, GPS and TLE-derived translational-state inputs are compared. The developed methods and findings are then applied to re-entry predictions of several Delta-K rocket bodies. Enhanced TLEs are shown to have a reduced uncertainty and improved forward propagation stability compared to the older classic type. In fact, enhanced TLEs states are found to be most accurate after their associated epoch, due to the inclusion of propagated pseudo measurements. The ballistic coefficient of enhanced TLEs is found to differ from classic TLEs and is shown to be consistent with retrofit estimates of the ballistic coefficient. This suggests that the coefficient is obtained directly from the numerical fitting process, rather than co-estimated with the mean elements of the TLE themselves, as is the case for classic TLEs. This finding positively affects re-entry predictions. The attitude control and atmospheric density bias are the two major factors on the mean decay epoch. While the atmospheric density uncertainty is by far the most important factor in the decay-time uncertainty. The uncertainty in initial state is shown to have only minor influence on the final decay-time distributions, despite GPS being up to four orders of magnitude more accurate than TLEs. This illustrates the importance of improving atmospheric density modeling for re-entry predictions. @en