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To settle the question of the nature of the interstellar object 1I/'Oumuamua requires in-situ observations via a spacecraft, as the object is already out of range of existing telescopes. Most previous proposals for reaching 1I/'Oumuamua using near-term technologies are based on the Solar Oberth Manoeuvre (SOM), as trajectories without the SOM are generally significantly inferior in terms of lower mission duration and higher total velocity requirement. While the SOM allows huge velocity gains, it is also technically challenging and thereby increases programmatic and mission-related risks. In this paper, we identify an alternative route to the interstellar object 1I/'Oumuamua, based on a launch in 2028, which does not require a SOM but has a similar performance as missions with a SOM. It instead employs a Jupiter Oberth Manoeuvre (JOM) with a total time of flight of around 26 years or so. The efficacy of this trajectory is a result of it significantly reducing the $\Delta$V to Jupiter by exploiting the VEEGA sequence. The total $\Delta$V of the trajectory is 15.8 $kms^{-1}$ and the corresponding payload mass is 115 kg for a SLS Block 1B or 241 kg for a Block 2. A further advantage of the JOM is that the arrival speed relative to 1I/'Oumuamua is approximately 18 $kms^{-1}$, much lower than the equivalent for the SOM of around 30 $kms^{-1}$., Comment: 6 pages, 3 figures, 4 tables

We relate the known Oberth effect and the nonrelativistic analogue of the Penrose process. When a particle decays to two fragments, we derive the conditions on the angles under which debris can come out for such a process to occur. We also consider the decay and the Oberth effect in the relativistic case, when a particle moves in the background of the Schwarzschild black hole. This models the process when a rocket ejects fuel. Different scenarios are analyzed depending on what data are fixed. The efficiency of the process is found, in particular, near the horizon and for a photon rocket (when the ejected particle is massless). We prove directly that the most efficient process occurs when fuel is ejected along the rocket trajectory. When this occurs on the horizon, the efficiency reaches 100% for a photon rocket. We compare in two ways how a rocket can reverse its direction of motion to a black hole near the event horizon by restoring the initial energy-to-mass ratio: (i) by a single ejection or (ii) in the two-step process when it stops and moves back afterwards. For a nonphotonic rocket, in case (ii) a larger mass can be taken out from the vicinity of a horizon. For a photonic one, there is no difference between (i) and (ii) in this respect. We also consider briefly the scenario when a rocket hangs over a black hole due to continuous ejection of fuel. Then, the fuel mass decays exponentially with the proper time., Comment: 29 pages, matches published version

A highly reflective sail provides a way to propel a spacecraft out of the solar system using solar radiation pressure. The closer the spacecraft is to the Sun when it starts its outward journey, the larger the radiation pressure and so the larger the final velocity. For a spacecraft starting on the Earth's orbit, closer proximity can be achieved via a retrograde impulse from a rocket engine. The sail is then deployed at the closest approach to the Sun. Employing the so-called Oberth effect, a second, prograde, impulse at closest approach will raise the final velocity further. Here I investigate how a fixed total impulse ({\Delta}v) can best be distributed in this procedure to maximize the sail's velocity at infinity. Once {\Delta}v exceeds a threshold that depends on the lightness number of the sail (a measure of its sun-induced acceleration), the best strategy is to use all of the {\Delta}v in the retrograde impulse to dive as close as possible to the Sun. Below the threshold the best strategy is to use all of the {\Delta}v in the prograde impulse and thus not to dive at all. Although larger velocities can be achieved with multi-stage impulsive transfers, this study shows some interesting and perhaps counter-intuitive consequences of combining impulses with solar sails., Comment: 10 pages, accepted to the American Journal of Physics

Any missions to catch 1I/'Oumuamua have the daunting challenge of generating higher hyperbolic excess speeds than the interstellar object's own, i.e. $>$ 26.3 $kms^{-1}$ with respect to the Sun. To accomplish this task using chemical propulsion, previous papers have investigated a Solar Oberth manoeuvre and alternatively a Jupiter Oberth, these options requiring a thrust from the chemical rocket at perihelion/perijove respectively, points at which the available velocity increment ($\Delta V$) results in maximum augmentation of the kinetic energy of the spacecraft. In this paper we unravel the specifics of a mission requiring a JOM or optionally a passive Jupiter encounter, i.e. with no thrust, the latter having so far not been addressed by Project Lyra. Whereas the previous papers were feasibility studies, this paper delves into what would be achievable with a Jupiter encounter (without any preceding gravitational assists from the inner planets), using currently available off-the-shelf solid and liquid rocket stages and assuming the NASA Space Launch System Block 2 can be deployed. Optimal Launch dates are found to lie in the years 2030, 2031 and 2032 with resulting mission durations of around 30-40 years, depending on the particular number and combination of stages exploited. Payload masses to 'Oumuamua of 860kg can readily be accomplished with a duration of 43 or so years, assuming a Centaur D and STAR 48B combination, the latter booster being ignited at perijove. On the other hand if two Centaur Ds are utilised instead of just one, retaining the STAR 48BV for the JOM, 35 years are evinced for the same mass. Furthermore, for lower payloads of $\sim{100}$kg, the flight duration can be cut accordingly to 31 years, with the additional benefit of requiring no burn at Jupiter.

Planet 9 is an hypothetical object in the outer Solar system, which is as yet undiscovered. It has been speculated that it may be a terrestrial planet or gas/ice giant, or perhaps even a primordial black hole (or dark matter condensate). State-of-the-art models indicate that the semimajor axis of Planet 9 is $\sim 400$ AU. If the location of Planet 9 were to be confirmed and pinpointed in the future, this object constitutes an interesting target for a future space mission to characterize it further. In this paper, we describe various mission architectures for reaching Planet 9 based on a combination of chemical propulsion and flyby maneuvers, as well as more advanced options (with a $\sim 100$ kg spacecraft payload) such as nuclear thermal propulsion (NTP) and laser sails. The ensuing mission duration for solid chemical propellant ranges from 45 years to 75 years, depending on the distance from the Sun for the Solar Oberth maneuver. NTP can achieve flight times of about 40 years with only a Jupiter Oberth maneuver whereas, in contrast, laser sails might engender timescales as little as 7 years. We conclude that Planet 9 is close to the transition point where chemical propulsion approaches its performance limits, and alternative advanced propulsion systems (e.g., NTP and laser sails) apparently become more attractive.

In October 2017, the first interstellar object within our solar system was discovered. Today designated 1I/'Oumuamua, it shows characteristics that have never before been observed in a celestial body. Due to these characteristics, an in-situ investigation of 1I would be of extraordinary scientific value. Previous studies have demonstrated that a mission to 1I/'Oumuamua is feasible using current and near-term technologies however with an anticipated launch date of 2020-2021, this is too soon to be realistic. This paper aims at addressing the question of the feasibility of a mission to 1I/'Oumuamua in 2024 and beyond. Using the OITS trajectory simulation tool, various scenarios are analyzed, including a powered Jupiter flyby and Solar Oberth maneuver, a Jupiter powered flyby, and more complex flyby schemes including a Mars and Venus flyby. With a powered Jupiter flyby and Solar Oberth maneuver, we identify a trajectory to 1I/'Oumuamua with a launch date in 2033, a total velocity increment of 18.2 km/s, and arrival at 1I/'Oumuamua in 2048. With an additional deep space maneuver before the powered Jupiter flyby, a trajectory with a launch date in 2030, a total velocity increment of 15.3 km/s, and an arrival at 1I/'Oumuamua in 2052 were identified. Both launch dates would provide over a decade for spacecraft development, in contrast to the previously identified 2020-2021 launch dates. Furthermore, the distance from the Sun at the Oberth burn is at 5 Solar radii. This results in heat flux values, which are of the same order of magnitude as for the Parker Solar Probe. We conclude that a mission to 1I/'Oumuamua is feasible, using existing and near-term technologies and there is sufficient time for developing such a mission.

In preceding papers, Project Lyra has covered many possible trajectory options available to a spacecraft bound for 1I/Oumuamua, including Solar Oberth manoeuvres, Passive Jupiter encounters, Jupiter Oberths, Double Jupiter Gravitational Assists, etc. Because feasibility was the key driver for this analysis, the important question of which launcher to exploit was largely skirted in favour of adopting the most powerful options as being sufficient, though these launchers are clearly not necessary, there being alternative less capable candidates which could be utilised instead. In this paper the various launch options available to Project Lyra are addressed to allow a general overview of their capabilities. It is found that the SpaceX Super-Heavy Starship would be a game-changer for Project Lyra, especially in the context of refuelling in LEO, and furthermore a SpaceX Falcon Heavy Expendable could also be utilised. Other launchers are considered, including Ariane 6 and the future Chinese Long March 9. The importance of the V infinity Leveraging Manoeuvre (VILM) in permitting less capable launchers to nevertheless deliver a payload to Oumuamua is elaborated

This paper explicates the concept of an Intermediate Point (IP), its incorporation as a node along an interplanetary trajectory, and how it permits the determination and optimization of trajectories to interstellar objects (ISOs). IPs can be used to model Solar Oberth Manoeuvres (SOM) as well as Vinfnity Leveraging Manoeuvres (VLM). The SOM has been established theoretically as an important mechanism by which rapid exit from the solar system and intercept of ISOs can both be achieved; the VLM has been demonstrated practically as a method of reducing overall mission Delta-V as well as the Characteristic Energy, C3, at launch. Thus via these two applications, the feasibility of missions to interstellar objects (ISOs) such as 1I/Oumuamua can be analysed. The interplanetary trajectory optimizer tool exploited for this analysis, OITS, permits IP selection as an encounter option along the interplanetary trajectory in question. OITS adopts the assumption of impulsive thrust at discrete points along the trajectory, an assumption which is generally valid for high thrust propulsion scenarios, like chemical or nuclear thermal for instance.

The first interstellar object to be discovered, 1I/'Oumuamua, exhibited various unusual properties as it was tracked on its passage through the inner solar system in 2017/2018. In terms of the potential scientific return, a spacecraft mission to intercept and study it in situ would be invaluable. As an extension to previous Project Lyra studies, this paper elaborates an alternative mission to 1I/'Oumuamua, this time also requiring a Jupiter Oberth Manoeuvre (JOM) to accelerate the spacecraft towards its destination. The difference is in the combination of planetary flybys exploited to get to Jupiter, which includes a Mars encounter before proceeding to Jupiter. The trajectory identified is inferior to previous finds in terms of higher $\Delta V$ requirement (15.6 $kms^{-1}$), longer flight duration (29 years) and less mission preparation time (launch 2026), however it benefits from a feature absent from previous JOM candidates, in that there is little or no $\Delta V$ en route to Jupiter (i.e. a free ride) which means the spacecraft need not carry a liquid propellant stage. This is marginally offset by the higher $\Delta V$ needed at Jupiter, requiring either 2 or 3 staged solid rocket motors. As an example, a Falcon Heavy Expendable with a CASTOR 30B booster followed by a STAR 48B can deliver 102kg to 1I/'Oumuamua by the year 2059. Other scenarios with shorter flight durations and higher payload masses are possible.

Current research focuses on designing fast trajectories to the trans-Neptunian object (TNO) (90377) Sedna to study the surface and composition from a close range. Studying Sedna from a close distance can provide unique data about the Solar System evolution process including protoplanetary disc and related mechanisms. The trajectories to Sedna are determined considering flight time and the total characteristic velocity (${\Delta}V$) constraints. The time of flight for the analysis was limited to 20 years. The direct flight, the use of gravity assist manoeuvres near Venus, the Earth and the giant planets Jupiter and Neptune, and the flight with the Oberth manoeuvre near the Sun are considered. It is demonstrated that the use of flight scheme with ${\Delta}VEGA$ (${\Delta}V$ and Earth Gravity Assist manoeuvre) and Jupiter-Neptune gravity assist leads to the lowest cost of ${\Delta}V$=6.13 km/s for launch in 2041. The maximum payload for schemes with ${\Delta}$VEGA manoeuvre is 500 kg using Soyuz 2.1.b, 2,000 kg using Proton-M and Delta IV Heavy and exceeds $12,000$ kg using SLS. For schemes with only Jupiter gravity assist, payload mass is twice less than for ones with ${\Delta}$VEGA manoeuvre. As a possible expansion of the mission to Sedna, it is proposed to send a small spacecraft to another TNO during the primary flight to Sedna. Five TNOs suitable for this scenario are found, three extreme TNOs 2012 VP113, (541132) Lele\=ak\=uhonua (former 2015 TG387), 2013 SY99) and two classical Kuiper Belt objects: (90482) Orcus, (20000) Varuna., Comment: Acta Astronautica (2021)

The first definite interstellar object observed in our solar system was discovered in October of 2017 and was subsequently designated 1I/'Oumuamua. In addition to its extrasolar origin, observations and analysis of this object indicate some unusual features which can only be explained by in-situ exploration. For this purpose, various spacecraft intercept missions have been proposed. Their propulsion schemes have been chemical, exploiting a Jupiter and Solar Oberth Maneuver (mission duration of 22 years) and also using Earth-based lasers to propel laser sails (1-2 years), both with launch dates in 2030. For the former, mission durations are quite prolonged and for the latter, the necessary laser infrastructure may not be in place by 2030. In this study Nuclear Thermal Propulsion (NTP) is examined which has yet to materialise as far as real missions are concerned, but due to its research and development in the NASA Rover/NERVA programs, actually has a higher TRL than laser propulsion. Various solid reactor core options are studied, using either engines directly derived from the NASA programs, or more advanced options, like a proposed particle bed NTP system. With specific impulses at least twice those of chemical rockets, NTP opens the opportunity for much higher {\Delta}V budgets, allowing simpler and more direct, time-saving trajectories to be exploited. For example a spacecraft with an upgraded NERVA/Pewee-class NTP travelling along an Earth-Jupiter-1I trajectory, would reach 1I/'Oumuamua within 14 years of a launch in 2031. The payload mass to 1I/'Oumuamua would be around 2.5metric tonnes, but even larger masses and shorter mission durations can be achieved with some of the more advanced NTP options studied. In all 4 different proposed NTP systems and 5 different trajectory scenarios are examined.

Discovered in October 2017, the interstellar object designated 1I/'Oumuamua was the first such object to be observed travelling through our solar system. 1I/'Oumuamua has other characteristics never seen before in a celestial body and in-situ observations and measurements would be of extraordinary scientific value. Previous studies have demonstrated the viability of spacecraft trajectories to 'Oumuamua using chemical propulsion with a Solar Oberth burn at a perihelion as low as a few solar radii. In addition to chemical propulsion, there is also the possibility of missions involving light sails accelerated by the radiation pressure of a laser beam from a laser located on Earth. Based on a scaled-down Breakthrough Starshot beaming infrastructure, interplanetary missions and missions to the outer solar system have been proposed using lower sailcraft speeds of 0.001c relaxing the laser power requirements (3-30 GW for 1-100 kg spacecraft) and various other mission constraints. This paper uses the OITS trajectory simulation tool, which assumes an impulsive $\Delta$V increment, to analyze the trajectories which might be followed by a sailcraft to 'Oumuamua, with a launch in the year 2030 and assuming it has already been accelerated to a maximum speed of 300km/s (approx. 0.001c) by the laser. A minimum flight duration of 440 days for a launch in July 2030 is found. The intercept would take place beyond 82 AU. We conclude that the possibility of launching a large number of spacecraft and reaching 1I much faster than chemical propulsion would circumvent several disadvantages of previously proposed mission architectures.

States of particles with negative energies are considered for the nonrelativistic and relativistic cases. In nonrelativistic case it is shown that the decays close to the attracting center can lead to the situation similar to the Penrose effect for rotating black hole when the energy of one of the fragments is larger than the energy of the initial body. This is known as the Oberth effect in the theory of the rocket movement. The realizations of the Penrose effect in the non-relativistic case in collisions near the attracting body and in the evaporation of stars from star clusters are indicated. In relativistic case similar to the well known Penrose process in the ergosphere of the rotating black hole it is shown that the same situation as in ergosphere of the black hole occurs in rotating coordinate system in Minkowski space-time out of the static limit due to existence of negative energies. In relativistic cases differently from the nonrelativistic ones the mass of the fragment can be larger than the mass of the decaying body. Negative energies for particles are possible in relativistic case in cosmology of the expanding space when the coordinate system is used with nondiagonal term in metrical tensor of the space-time. Friedmann metrics for three cases: open, close and quasieuclidian, are analyzed. The De Sitter space-time is shortly discussed., Comment: 10 pages

In August 2019, a second interstellar object 2I/Borisov was discovered 2 years after the discovery of the first known interstellar object, 1I/'Oumuamua. Can we send a spacecraft to this object, using existing technologies? In this paper we assess the technical feasibility of a near-term mission to 2I/Borisov. We apply the Optimum Interplanetary Trajectory Software (OITS) tool to generate trajectories to 2I/Borisov. As results, we get the minimal $\Delta V$ trajectory with a launch date in July 2018. For this trajectory, a Falcon Heavy launcher could have hauled an 8 ton spacecraft to 2I/Borisov. For a later launch date, results for a combined powered Jupiter flyby with a Solar Oberth maneuver are presented. For a launch in 2027, we could reach 2I/Borisov in 2052, using the Space Launch System (SLS), up-scaled Parker probe heat shield technology, and solid propulsion engines. Using a SLS a spacecraft with a mass of 765 kg could be sent to 2I/Borisov. A Falcon Heavy could deliver 202 kg to 2I/Borisov. Arrival times sooner than 2052 can potentially be achieved but with higher $\Delta V$ requirements and lower spacecraft payload masses. 2I/Borisov's discovery shortly after the discovery of 1I/'Oumuamua implies that the next interstellar object might be discovered in the near future. The feasibility of a mission to both, 1I/'Oumuamua and 2I/Borisov using existing technologies indicates that missions to at least some future interstellar objects are feasible as well., Comment: 25 pages 5 figures

The first definitely interstellar object 1I/'Oumuamua (previously A/2017 U1) observed in our solar system provides the opportunity to directly study material from other star systems. Can such objects be intercepted? The challenge of reaching the object within a reasonable timeframe is formidable due to its high heliocentric hyperbolic excess velocity of about 26 km/s; much faster than any vehicle yet launched. This paper presents a high-level analysis of potential near-term options for a mission to 1I/'Oumuamua and potential similar objects. Launching a spacecraft to 1I/'Oumuamua in a reasonable timeframe of 5-10 years requires a hyperbolic solar system excess velocity between 33 to 76 km/s for mission durations between 30 to 5 years. Different mission durations and their velocity requirements are explored with respect to the launch date, assuming direct impulsive transfer to the intercept trajectory. For missions using a powered Jupiter flyby combined with a solar Oberth maneuver using solid rocket boosters and Parker Solar Probe heat shield technology, a Falcon Heavy-class launcher would be able to launch a spacecraft of dozens of kilograms towards 1I/'Oumuamua, if launched in 2021. An additional Saturn flyby would allow for the launch of a New Horizons-class spacecraft. Further technology options are outlined, ranging from electric propulsion, and more advanced options such as laser electric propulsion, and solar and laser sails. To maximize science return decelerating the spacecraft at 'Oumuamua is highly desirable, due to the minimal science return from a hyper-velocity encounter. Electric and magnetic sails could be used for this purpose. It is concluded that although reaching the object is challenging, there seem to be feasible options based on current and near-term technology.