Article

# Fast reconnaissance missions to the outer solar system utilizing energy derived from the gravitational field of Jupiter

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## Abstract

Contrary to popular belief, indirect ballistic trajectories involving close approach to one or more intermediate planets need not require longer flight duration than is characteristic of direct transfer orbits. In fact, significant reduction of both required flight time and launch energy results if efficient use is made of the energy which can be gained during a midcourse planetary encounter. From the point of view of a passing space vehicle, the intermediate planet appears as a field of force moving relative to the inertial heliocentric coordinate system. Thus, work is done on the spacecraft, and its heliocentric energy may be increased or decreased depending upon the geometric details of the encounter. This paper describes the application of energy derived in this fashion, utilizing gravitational perturbations from Jupiter, for reduction of required launch energy and flight duration for exploratory missions to all of the outer planets of the solar system. The latter half of the next decade abounds in interesting multiple planet apportunities due to the similar heliocentric longitudes of the major planets during this time period. Trajectories to Saturn, Uranus, Neptune, and Pluto using the midcourse energy boost from Jupiter are best initiated in the years 1978, 1979, 1979, and 1977 respectively. Flight time reduction ranges from one half the required direct trajectory duration for Earth-Jupiter-Saturn Missions to as much as 85% of the direct transfer time for Pluto flights via Jupiter. Many multiple-target trajectories are also possible. Of particular interest is the 1978 Earth-Jupiter-Saturn-Uranus-Neptune "grand tour" opportunity which would make possible close-up observation of all planets of the outer solar system (with the exception of Pluto) in a single flight.

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... Several missions used this idea to save fuel in their maneuvers. The Voyager mission visited several planets of the Solar System gaining energy from successive close approaches [1][2][3][4]. Other applications of this maneuver are available in the literature, like: the use of Swing-Bys in the inner Solar System to send a spacecraft to the giant planets [5] or even to the Sun [6]; the use of Venus in a trip to Mars [7,8]; studies to make a three-dimensional close approach to Jupiter to change the orbital plane of the spacecraft [9]; use of one [10] or two [11] passages by the Moon to increase the energy of the spacecraft; the use of multiple passages by the secondary body to find trajectories linking the primaries [12] or the Lagrangian points [13,14]. ...
... It is the angle formed by the line of the periapsis (line linking the center of Jupiter to the point of the closest approach of the trajectory) and the line connecting the two primaries (Sun-Jupiter). In the rotating system of reference this line is also the horizontal axis; (b) , the Jacobian constant, expressed by (4). Although this is no longer constant after the inclusion of the atmospheric drag, this parameter is usually used to identify Swing-By trajectories. ...
Article
The present paper has the goal of studying the changes of the orbital parameters of each individual element of a cloud of particles that makes a close approach with the Earth. Clouds of particles are formed when natural or man-made bodies explode for some reason. After an explosion like that, the center of mass of the cloud follows the same orbit of the body that generated the explosion, but the individual particles have different trajectories. The cloud is specified by a distribution of semi-major axis and eccentricity of their particles. This cloud is assumed to pass close to the Earth, making a close approach that modifies the trajectory of every particle that belongs to the cloud. The present paper makes simulations based in the “Patched-Conics” model to obtain the new trajectories of each particle. Then, it is possible to map the new distribution of the Keplerian elements of the particles that constituted the cloud, using the previous distribution as initial conditions. These information are important when planning satellite missions having a spacecraft passing close to a cloud of this type, because it is possible to obtain values for the density and amplitude of the cloud, so finding the risks of collision and the possible maneuvers that need to be made in the spacecraft to avoid the collisions.
... In the sixties of the past century [22,8] the aerospace engineer G. A. Flandro devised an ingenious proposal for a spacecraft to extract energy from the gravitational field of a planet using a gravity assist or flyby manoeuver. In his idea the planet is seen as a field of force moving relative to the inertial heliocentric or barycentric coordinate system so it can transfer a certain amount of kinetic energy to the passing spacecraft with respect to that inertial system. ...
... Flandro also foresaw the fact that all major planets from Jupiter to Neptune would be almost aligned on the same side of the Sun during the decades of the seventies and the eighties allowing for the design of a "grand tour" project in which a spacecraft should successively explore Jupiter, Saturn, Uranus and Neptune in a period of twelve years [22]. This project was effectively carried out by the Voyager 1 and Voyager 2 missions launched on September, 5th and August, 20th, 1977, respectively [16]. ...
Article
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Gravity assist manoeuvres are one of the most succesful techniques in astrodynamics. In these trajectories the spacecraft comes very close to the surface of the Earth, or other Solar system planets or moons, and, as a consequence, it experiences the effect of atmospheric friction by the outer layers of the Earth’s atmosphere or ionosphere. In this paper we analyze a standard atmospheric model to estimate the density profile during the two Galileo flybys, the NEAR and the Juno flyby. We show that, even allowing for a margin of uncertainty in the spacecraft cross-section and the drag coefficient, the observed mm/sec anomalous velocity decrease during the second Galileo flyby of December, 8th, 1992 cannot be attributed only to atmospheric friction. On the other hand, for perigees on the border between the termosphere and the exosphere the friction only accounts for a fraction of a millimeter per second in the final asymptotic velocity.
... Methods based on analytic solutions are a typical example: the patched-conic technique, for instance, was extensively used during the conception of the planetary Grand Tour that took the Voyager spacecraft out of the Solar System. 1,2 Despite ignoring all sources of perturbations the solution was sufficiently close to the actual trajectory for initializing the detailed design phase. ...
... 9 When combined with Eqs. (2)(3) it follows the system ...
Conference Paper
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The family of generalized logarithmic spirals including a control parameter is extended to the three-dimensional case. The in-plane motion is decoupled from the out-of-plane motion in such a way that the integrals of motion found in the planar problem are still preserved in the three-dimensional case. Designing a low-thrust orbit transfer decomposes in two stages: first, orbits are projected on a reference plane and the planar transfer is solved with a generalized logarithmic spiral. Second , the out-of-plane component of the motion is included in order to target the final orbit. The projection of the three-dimensional transfer orbit on the reference plane is a generalized logarithmic spiral. Arbitrary shape-based laws for the 3D motion can be considered. This paper explores a polynomial and a Fourier series shaping method, together with a polynomial steering law. A fictitious low-thrust sample return mission to Ceres is designed to show the versatility of the method.
... Several missions used this idea to save fuel in their maneuvers. The Voyager mission visited several planets of the Solar System gaining energy from successive close approaches [1][2][3][4]. Other applications of this maneuver are available in the literature, like: the use of Swing-Bys in the inner Solar System to send a spacecraft to the giant planets [5] or even to the Sun [6]; the use of Venus in a trip to Mars [7,8]; studies to make a three-dimensional close approach to Jupiter to change the orbital plane of the spacecraft [9]; use of one [10] or two [11] passages by the Moon to increase the energy of the spacecraft; the use of multiple passages by the secondary body to find trajectories linking the primaries [12] or the Lagrangian points [13,14]. ...
... It is the angle formed by the line of the periapsis (line linking the center of Jupiter to the point of the closest approach of the trajectory) and the line connecting the two primaries (Sun-Jupiter). In the rotating system of reference this line is also the horizontal axis; (b) , the Jacobian constant, expressed by (4). Although this is no longer constant after the inclusion of the atmospheric drag, this parameter is usually used to identify Swing-By trajectories. ...
Article
The goal of this research is to study close approaches between a planet, which is assumed to have an atmosphere, and a cloud of particles. This cloud of particles is formed during the passage of a spacecraft by the atmosphere, due to its explosion. The complete system is formed by two main bodies (the Sun and the planet), that are assumed to stay in circular orbits around their center of mass, and the spacecraft, that is then transformed in a cloud of particles. This spacecraft is moving under the gravitational attractions of the two main bodies when it makes a close approach with the planet in such a position that it passes inside the atmosphere of the planet and then is transformed in a cloud of particles. The motion is assumed to be planar for the spacecraft and all the particles and the dynamics is given by the well-known planar restricted circular three-body problem plus atmospheric drag. For the simulations shown here the planet Jupiter is used as the body for the close approach, but the method works well for any planet. The initial conditions for the spacecraft and the particles of the cloud are specified at the periapsis, because it is assumed that the fragmentation of the spacecraft occurs at this point.
... Voyager 2 also visited Uranus and Neptune, and is expected to leave the solar system by 2016. 1 The mission design took advantage of a rare planetary alignment that permitted the orbiters to sequentially reach the outer planets. 2 Cassini-Huygens mission to Saturn is another example of gravity-assist trajectories; to reach Saturn, the spacecraft performed three planetary flybys about Venus, the Earth and Jupiter. 3 In its way to comet 67P/Churyumov-Gerasimenko, the Rosetta spacecraft benefitted from a series of gravity assist maneuvers. Launched in March, 2004 it performed three geocentric flybys, one about Mars, and about asteroids 2867 Steins and 21 Lutetia. ...
... The different definitions of norm in the Euclidean and the Minkowskian vector space provide two different expressions for the osculating eccentricity e, given in Eqs. (2) and (3). But the eccentricity of the orbit has a clear physical meaning and it is possible to assume that both definitions of norm yield the same physical quantity. ...
Conference Paper
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A more adequate description of perturbed hyperbolic orbits is found in the geometry underlying Minkowski space-time. Hypercomplex numbers appear naturally when describing vectors, rotations, and metrics in this geometry. The solution to the unperturbed hyperbolic motion is well known in terms of hyperbolic functions and the hyperbolic anomaly. From this, a general solution is derived through the Variation of Parameters technique. Hyperbolic geometry leads to a more coherent formulation. The evolution of the eccentricity vector is described by means of its components on the Minkowski plane. The orbital plane is defined in the inertial reference using quaternions, treated as particular instances of hypercomplex numbers. The performance of the proposed formulation is evaluated for integrating flyby trajectories of NEAR, Cassini, and Rosetta spacecraft. Improvements in accuracy have been observed in these cases, with no penalties on the computational time.
... While the inner planets were reachable using existing launch vehicles at the time, getting spacecraft to the outer solar system required the gravity assist technique. Even with gravity assist, missions to Uranus and Neptune at 19 AU and 30 AU respectively would still take multiple decades.Fortuitously, it was discovered in the 1960s that a rare planetary alignment that occurs only once every 176 years would allow a single spacecraft to visit the four giant planets if it launched in the late 1970s[ 170 ]. Leveraging gravity assists at Jupiter, Saturn and Uranus would enable the spacecraft to reach Neptune in just 12 years. ...
Thesis
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Aerocapture offers a near propellantless and quick method of orbit insertion at atmosphere bearing planetary destinations. Compared to conventional propulsive insertion, the primary advantage of using aerocapture is the savings in propellant mass which could be used to accommodate more useful payload. To protect the spacecraft from the aerodynamic heating during the maneuver, the spacecraft must be enclosed in a protective aeroshell or deployable drag device which also provides aerodynamic control authority to target the desired conditions at atmospheric exit. For inner planets such as Mars and Venus, aerocapture offers a very attractive option for inserting small satellites or constellations into very low circular orbits such as those used for imaging or radar observations. The large amount of propellant required for orbit insertion at outer planets such as Uranus and Neptune severely limits the useful payload mass that can delivered to orbit as well as the achievable flight time. For outer planet missions, aerocapture opens up an entirely new class of short time of flight trajectories which are infeasible with propulsive insertion. A systems framework for rapid conceptual design of aerocapture missions considering the interdependencies between various elements such as interplanetary trajectory and vehicle control performance for aerocapture is presented. The framework provides a step-by-step procedure to formulate an aerocapture mission starting from a set of mission objectives. At the core of the framework is the aerocapture feasibility chart", a graphical method to visualize the various constraints arising from control authority requirement, peak deceleration, stagnation-point peak heat rate, and total heat load as a function of vehicle aerodynamic performance and interplanetary arrival conditions. Aerocapture feasibility charts have been compiled for all atmosphere-bearing Solar System destinations for both lift and drag modulation control techniques. The framework is illustrated by its application to conceptual design of a Venus small satellite mission and a Flagship-class Neptune mission using heritage blunt-body aeroshells. The framework is implemented in the Aerocapture Mission Analysis Tool (AMAT), a free and open-source Python package, to enable scientists and mission designers perform rapid conceptual design of aerocapture missions. AMAT can also be used for rapid Entry, Descent, and Landing (EDL) studies for atmospheric probes and landers at any atmosphere-bearing destination.
... According to Flandro [27], Ehricke made presentations in the Space Technology course at UCLA, showing in full detail his ideas on gravity-assists. He also mentioned that Ehricke's works were the first seeds for his later work that led to the Voyager missions [26]. With the work of Ehricke in 1957 [21], the theory needed to the design of gravity-assists was available in the astrodynamics literature. ...
Article
The gravity-assist manoeuvre is a technique in which a spacecraft changes its orbital energy and angular momentum by a close-approach with a celestial body. The result is a great reduction in the use of fuel and flight time. Several interplanetary missions have applied it for this reason, like the famous Voyagers, Mariner, or Galileo. The astronomers knew the mechanics behind such concept for at least two centuries by noting the change in the orbits of the comets after passing close to Jupiter. The introduction of this phenomenon to spaceflight was a very successful story and motivated many claims that the proposal of the gravity-assist manoeuvres occurred in the early 60s. However, the idea of using such mechanism for interplanetary spaceflight can be traced back to the 20s. The dispute of being the first to have this idea contributed to throw shadow on these early pioneers. In that sense, the present paper has the goal of discussing some aspects related to the history of this manoeuvre in the pre-spaceflight era, trying to show some of the major steps made in its early history. It covers from the first studies found on this topic and goes up to the beginning of the space age, with the launching of the Sputnik satellite. This time period is chosen to bring light to these early works in which the astronomical phenomenon is introduced in the astronautics. Their importance is highlighted by putting these works under their historical context, as it shows how some of them were far ahead of their time. Among these, the work of Tsander, made in mid-20s, is outstanding.
... The discovery of gravityassists in 1961 made the solar system instantly accessible with available launchers [30]. This disruptive paradigm change from a mostly inaccessible solar system requiring huge nuclear-electric spaceships [31][32] to the Voyager missions firmly established the combination of chemical propulsion with gravity-assists in solar system exploration [33][34][35][36][37][38] from Earth [39][40][41]. Fitting space probes into existing fairings advanced electronics and miniaturization. ...
Conference Paper
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... T Theoretically, the aerodynamic shape of waveriders is able to generate high Lift-to-Drag ratio (L/D) (comparing with traditional spacecraft geometries), with maximum values of L/D around 9.0, during the AGAM [2]. One difference between the GAM and the AGAM is that the GAM has been studied in detail and has been applied in missions like Voyager, Messenger and recently during the BepiColombo´s Earth fly-by (April, 2020) [5][6][7][8][9][10][11][12][13][14][15][16]. ...
Article
Thse powered aero-gravity-assist is an orbital maneuver that combines three basic components: a gravity-assist with a passage by the atmosphere of the planet during the close approach and the application of an impulse during this passage. The mathematical model used to simulate the trajectories is the Restricted Three-Body Problem including the terms coming from the aerodynamic forces. The present paper uses this type of maneuver considering that the trajectory of the spacecraft is in the ecliptic plane and the presence of the atmospheric Drag and Lift forces. The maneuver in the ecliptic plane can be done due to technologies that provides spacecraft with high values for the Lift to Drag ratio. The main advantage is that this maneuver allows the modification of the semi-major axis of the orbit of the spacecraft using the gravity of the planet and, at the same time, to change the inclination, using the high Lift that is perpendicular to the ecliptic plane. So, it is a combined maneuver that changes two important orbital parameters at the same time. The Lift is applied orthogonal to the initial orbital plane to generate an inclination change in the trajectory of the spacecraft, which is a very expensive maneuvers when made using propulsion systems. The Lift to Drag ratio used in the present paper goes up to 9.0, because there are vehicles, like waveriders, designed to have these values. When the spacecraft is passing by the periapsis of its orbit, an instantaneous impulse is applied to increase or decrease the variation of energy given by the aero-gravity-assist maneuver. The planets Venus and Mars are selected to be the bodies for the maneuver, due to their atmospheric density and strategic location in the Solar System to provide possible uses for future missions. Results coming from numerical simulations show the maximum changes in the inclination obtained by the maneuvers, as a function of the approach angle and direction of the impulse; the Lift to Drag ratio and the ballistic coefficient. In the case of Mars, inclination changes can be larger than 13°, and for Venus larger than 21°. The energy and inclination variations are shown for several selected orbits. The powered aero-gravity-assist maneuver generates inclination changes that are higher than the ones obtained from the powered maneuver and/or the aero-gravity maneuver.
... Since then, the maneuver is extensively applied in interplanetary missions. Early missions, such as Pioneer 10 and 11 (Carlson and Judge, 1974;Fimmel et al., 1980;Fimmel, 1977), Mariner 10 (Dunne and Burgess, 1978) and Voyager 1 and 2 (Kohlhase and Penzo, 1977;Flandro, 1966) showed the potential and feasibility of this technique. This enabled the great number of interplanetary missions in the decades to come, such as Galileo (Diehl and Nock, 1979), Cassini-Huygens (Hansen et al., 2004), Messenger (Mcnutt et al., 2004(Mcnutt et al., , 2006, Rosetta (Hechler, 1997), New Horizons (Guo and Farquhar, 2008), and many others. ...
Article
The gravity assist is a maneuver greatly applied to space missions, with the main goal of giving or removing energy of a spacecraft through a passage near a celestial body. The patched-conics approximation is the first approximation that is usually considered in the mission planning. It gives a good accuracy in the majority of the situations. However, when using the Moon for the close approach, the results have a tendency to diverge from a more complete three body dynamics. This is due to the large mass of the Moon compared to the Earth. In that sense, the goal of the present paper is to study the errors given by the patched-conics approximation in a lunar gravity assist maneuver. To find those errors we compare the results coming from this approximation with the equivalent results obtained from the circular restricted three body problem and the bi-circular restricted four body problem for a same periselenium condition. This comparison is made in the orbital elements before the maneuver and the C 3 of the spacecraft after the maneuver under the three models considered. Different values for the initial conditions of the spacecraft are used to obtain general conclusions about the behavior of the errors involved. We conclude that there is a tendency to a better agreement between the patched-conics and the three body problem for retrograde transfer orbits. We also find that the effects of the Sun in the maneuver needs to be included only in more accurate steps of the mission.
... The description of this type of maneuver can be seen in several publications, like [1]- [7]. Applications of this maneuver are also widely available, like in studies of transfer orbits to/from the Lagrangian points [8]- [11]; in the description of real missions that used this concept, like in [12]- [18]. Also variations of this problem is studied, like using the combination of impulsive maneuvers with the close approach [19], the presence of an atmosphere of the planet during the passage [20], elliptical orbits for the main bodies [21], the simultaneous passage of a group of particles instead of a single one [22]- [24], the combination with multiobjective optimization [25] or in the scattering of comets by a planet [26]. ...
Article
Full-text available
: The present paper has the goal of studying the changes of the orbital parameters considering a fragment that makes a close approach with the Saturn.Successive swing-by maneuvers with the planet was performed to determine the trajectory. It is also assumed the presence of only two massive bodies (Sun and Saturn) that are in circular and planar orbits. Those derivations are based in the “patched-conics” approximation, which means that a series of keplerian orbits are assumed for the debris. It is then searched for geometries of the swing-by maneuvers that cause a series of passages by the planet. Those orbits have to be resonant with the motion of Saturn. After deriving the equations they are verified using the Tisserand’s Criterion, which is a rule that must be followed by the keplerian elements before and after a swing-by. It is necessary to verify if the orbits are physically possible, having in mind that the periapsis of the orbits around the Sun needs to be above its surface, as well as the closest approach with Saturn needs to be above the surface of the planet.
... Some examples are: Casalino and Colasurdo (2002), Brophy and Noca (1998), and Sukhanov and Prado (2001). Other type of applications considers the use of chaos, like in Macau (2000) and Macau and Grebogi (2006); swing-by techniques (Flandro 1966;Dunham and Davis 1985;Farquhard and Dunham 1981;Prado 2007;Gomes and Prado, 2008;DeMelo et al. 2009;Gomes et al. 2013); and even gravitational capture (Belbruno and Miller 1993;Kluever and Pierson 1994;Neto and Prado 1998;Machuy et al. 2007). There are also other researches looking for specific types of missions, like Carvalho et al. (2010), D'Amario et al. (1982, Farquhar et al. (1985), Gomes and Domingos (2015), Salazar et al. (2012Salazar et al. ( , 2014Salazar et al. ( , 2015a, and Sanchez et al. 2014. ...
Article
Aerospace engineering is a relatively new topic in engineering. It deals with several aspects of activities related to space. It includes Astrodynamics, which is a field that studies the motion of spacecraft, like guidance and control, which studies different forms to guide the motion of a spacecraft, etc. All those fields started from the Celestial Mechanics, one of the first topics studied in Astronomy. The first studies had the goal to record and explain the motions of the stars, with special attention given to the motion of some “irregular” stars, which showed later to be planets. Considering the advances in the technology, those earlier studies generated the space activities that are well known nowadays. Different topics, like orbital and attitude maneuvers and determination of spacecrafts, mission design, etc. are covered. The present Focus Issue publishes several papers related to aerospace engineering in general and can be useful for further studies and planning of space missions.
... 38] from Earth[39][40][41]. The need to fit space probes into the fairings of existing launch vehicles also advanced electronics design[42][43][44] and relegated nuclear power sources to small size and the outer solar system. ...
Conference Paper
Full-text available
... He developed an interplanetary free-fall trajectory design method and the tools to study the trajectories for identified line-ups of the planets [23][24][25]. Using these tools, following the leads already placed in [23,26], and equipped with a new high-quality planetary ephemeris extended beyond 1980 [27], Flandro singled out the 'Grand Tour' trajectories around the 1977 launch window, in particular the one to be flown by Voyager 2 to all the gas giants taking advantage of a planetary line-up occurring only every ≈175 years in this quality [28]. ...
Article
Space capabilities play a crucial role in ensuring human security. One of the threats coming from space is the possible damage to our assets by an asteroid or comet impact. As demonstrated by the object entering the Earth's atmosphere over Chelyabinsk, Russia, in February 2013, the threat of an asteroid or comet impact is a real and global issue demanding development of an international response. Addressing such a hazard, by first identifying those objects that pose a threat to enable planning a corresponding mitigation campaign, require international coordination. The United Nations Member States, especially those with capabilities to engage in a possible planetary defence mission, already share a number of common activities in this field. This paper outlines the progress made in the implementation of recommendations for an international response to the NEO impact threat, as agreed under the auspices of the United Nations (UN) Committee on the Peaceful Uses of Outer Space (COPUOS) and welcomed by the UN General Assembly in its resolution 68/75 of December 2013. The recommendations provide for a coordinated international response to a possible NEO threat. They aim at ensuring international information-sharing in discovering, monitoring and physically characterizing potentially hazardous NEOs with a view that all countries, in particular developing countries with limited capacity in predicting and mitigating a NEO impact, are aware of potential threats. They emphasize the need for an effective emergency response and disaster management in the event of a discovered NEO impact threat. The International Asteroid Warning Network (IAWN) and the Space Mission Planning Advisory Group (SMPAG), which are the two entities established in 2014 as a result of the UN-endorsed recommendations, are important mechanisms at the global level for strengthening the coordination in the area of planetary defence. The United Nations Office for Outer Space Affairs (UNOOSA) acts as secretariat to SMPAG and works with both IAWN and SMPAG in addressing this global issue. In the event of a credible impact prediction, warnings would be issued by the IAWN, the SMPAG would propose mitigation options and implementation plans for consideration to the Member States. The goal is the global protection of the eco-system, of human beings and their properties on Earth, and of the civilization of humankind from a devastating asteroid impact. The current paper outlines the work of the IAWN and the SMPAG towards a road-map for planetary defence at the global level, including agreements on initial criteria and thresholds for impact threat response actions, consideration of mitigation mission types and technologies and mapping of threat scenarios to mission types as well as developing a plan for action in case a credible threat is discovered. The paper also reflects on how to convey information about the NEO impact warnings and associated impact probabilities to the public and governmental decision-makers as part of the agreed communications guidelines, which are another important pillar in the work of the IAWN.
... There are also several studies in the literature that combine low thrust, gravity assist and three body problem (Casalino et al. 1999b;Mc-Conaghy et al. 2003;Okutsu et al. 2006;Santos et al. 2008;Pourtakdoust and Sayanjali 2014;Zotos 2015;Qian et al. 2016). Regarding practical applications, Flandro (1966) projected the Voyager missions, which were sent to explore the outer planets of the solar system. The Swing-By maneuver was also applied to the missions Galileo (D'Amario et al. 1981Byrnes and D'Amario 1982), Mariner 10 (Dunne and Burgess 1978), Messenger (McNutt et al. 2004, 2006Grard and Mercury 2006) and LCROSS, which made a close approach to the Moon (LCROSS 2009). ...
Article
Full-text available
Analytical equations describing the velocity and energy variation of a spacecraft in a Powered Swing-By maneuver in an elliptic system are presented. The spacecraft motion is limited to the orbital plane of the primaries. In addition to gravity, the spacecraft suffers the effect of an impulsive maneuver applied when it passes by the periapsis of its orbit around the secondary body of the system. This impulsive maneuver is defined by its magnitude $$\delta V$$ and the angle that defines the direction of the impulse with respect to the velocity of the spacecraft ($$\alpha$$). The maneuver occurs in a system of main bodies that are in elliptical orbits, where the velocity of the secondary body varies according to its position in the orbit following the rules of an elliptical orbit. The equations are dependent on this velocity. The study is done using the “patched-conics approximation”, which is a method of simplifying the calculations of the trajectory of a spacecraft traveling around more than one celestial body. Solutions for the velocity and energy variations as a function of the parameters that define the maneuver are presented. An analysis of the efficiency of the powered Swing-By maneuver is also made, comparing it with the pure gravity Swing-by maneuver with the addition of an impulse applied outside the sphere of influence of the secondary body. After a general study, the techniques developed here are applied to the systems Sun-Mercury and Sun-Mars, which are real and important systems with large eccentricity. This problem is highly nonlinear and the dynamics very complex, but very reach in applications.
... He developed an interplanetary free-fall trajectory design method and the tools to study the trajectories for identified line-ups of the planets [23] [24] [25]. Using these tools, following the leads already placed in [23] [26], and equipped with a new high-quality planetary ephemeris extended beyond 1980 [27], Flandro singled out the 'Grand Tour' trajectories around the 1977 launch window, in particular the one to be flown by Voyager 2 to all the gas giants taking advantage of a planetary line-up occurring only every ≈175 years in this quality [28]. Provided one puts enough effort in finding such planetary line-ups and is patient enough to await their occurrence, tours to any combination of all the planets are possible starting from the ones easiest to reach, Venus [23] or Earth itself [29] [30] [31]. ...
Article
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Any effort which intends to physically interact with specific asteroids requires understanding at least of the composition and multi-scale structure of the surface layers, sometimes also of the interior. Therefore, it is necessary first to characterize each target object sufficiently by a precursor mission to design the mission which then interacts with the object. In small solar system body (SSSB) science missions, this trend towards landing and sample-return missions is most apparent. It also has led to much interest in MASCOT-like landing modules and instrument carriers. They integrate at the instrument level to their mothership and by their size are compatible even with small interplanetary missions. The DLR-ESTEC Gossamer Roadmap NEA Science Working Groups‘ studies identified Multiple NEA Rendezvous (MNR) as one of the space science missions only feasible with solar sail propulsion. Parallel studies of Solar Polar Orbiter (SPO) and Displaced L1 (DL1) space weather early warning missions studies outlined very lightweight sailcraft and the use of separable payload modules for operations close to Earth as well as the ability to access any inclination and a wide range of heliocentric distances. These and many other studies outline the unique capability of solar sails to provide access to all SSSB, at least within the orbit of Jupiter. Since the original MNR study, significant progress has been made to explore the performance envelope of near-term solar sails for multiple NEA rendezvous. However, although it is comparatively easy for solar sails to reach and rendezvous with objects in any inclination and in the complete range of semi-major axis and eccentricity relevant to NEOs and PHOs, it remains notoriously difficult for sailcraft to interact physically with a SSSB target object as e.g. the Hayabusa missions do. The German Aerospace Center, DLR, recently brought the Gossamer solar sail deployment technology to qualification status in the Gossamer-1 project. Development of closely related technologies is continued for very large deployable membrane-based photovoltaic arrays in the GoSolAr project. We expand the philosophy of the Gossamer solar sail concept of efficient multiple sub-spacecraft integration to also include landers for one-way in-situ investigations and sample-return missions. These are equally useful for planetary defence scenarios, SSSB science and NEO utilization. We outline the technological concept used to complete such missions and the synergetic integration and operation of sail and lander. We similarly extend the philosophy of MASCOT and use its characteristic features as well as the concept of Constraints-Driven Engineering for a wider range of operations.
... One of the first was made by Minovitch (1961), followed by Clarke (1962), Niehoff (1966), Hollister and Prussing (1966), Deerwester (1966), Diehl and Myers (1987), and Qi and Xu (2015), among others. In terms of practical applications, considering missions that used this type of maneuver, Flandro (1966) designed the Voyager missions, which were later sent to the outer planets. The gravity assist was also applied to the mission Galileo, which was sent to Jupiter (D'Amario et al. 1981Byrnes and D'Amario 1982), Mariner 10 and the Messenger missions sent to Mercury (Dunne and Burgess 1978;McNutt et al. 2004McNutt et al. , 2006Grard 2006); and LCROSS, which was launched in 2009 and, after five days from launching, made a swing-by around the Moon with the goal of entering a polar orbit around the Moon (NASA 2009). ...
Article
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The objective of the present paper is to derive a set of analytical equations that describe a swing-by maneuver realized in a system of primaries that are in elliptical orbits. The goal is to calculate the variations of energy, velocity and angular momentum as a function of the usual basic parameters that describe the swing-by maneuver, as done before for the case of circular orbits. In elliptical orbits the velocity of the secondary body is no longer constant, as in the circular case, but it varies with the position of the secondary body in its orbit. As a consequence, the variations of energy, velocity and angular momentum become functions of the magnitude and the angle between the velocity vector of the secondary body and the line connecting the primaries. The “patched-conics” approach is used to obtain these equations. The configurations that result in maximum gains and losses of energy for the spacecraft are shown next, and a comparison between the results obtained using the analytical equations and numerical simulations are made to validate the method developed here.
... A key step towards interplanetary space exploration was achieved by the theoretical work of Minovitch [34,33] and Flandro [23]. In the early sixties of the past century these authors proposed the use of the gravitational assist manoeuvre to increase the energy of spacecraft in the Solar System barycenter, allowing for fast reconnaissance missions to the outer planets from Jupiter to Neptune [19]. ...
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In the last decades there have been an increasing interest in improving the accuracy of spacecraft navigation and trajectory data. In the course of this plan some anomalies have been found that cannot, in principle, be explained in the context of the most accurate orbital models including all known effects from classical dynamics and general relativity. Of particular interest for its puzzling nature, and the lack of any accepted explanation for the moment, is the flyby anomaly discovered in some spacecraft flybys of the Earth over the course of twenty years. This anomaly manifest itself as the impossibility of matching the pre and post-encounter Doppler tracking and ranging data within a single orbit but, on the contrary, a difference of a few mm$/$s in the asymptotic velocities is required to perform the fitting. Nevertheless, no dedicated missions have been carried out to elucidate the origin of this phenomenon with the objective either of revising our understanding of gravity or to improve the accuracy of spacecraft Doppler tracking by revealing a conventional origin. With the occasion of the Juno mission arrival at Jupiter and the close flybys of this planet, that are currently been performed, we have developed an orbital model suited to the time window close to the perijove. This model shows that an anomalous acceleration of a few mm$/$s$^2$ is also present in this case. The chance for overlooked conventional or possible unconventional explanations is discussed.
... The literature is very reach in topics related to this field, starting from basic impulsive maneuvers (Roth 1967;Prussing 1970Prussing , 1969Eckel 1963;Smith 1959;Bender 1962;Jin and Melton 1991;Jezewski and Mittleman 1982;Hoelker and Silber Hoelker and Silber;Shternfeld 1959;Gross and Prussing 1974;Eckel 1982;Prussing and Chiu 1986;Ting 1960;Walton et al. 1975). Then, it goes to orbital maneuvers based in low thrust (Casalino and Colasurdo 2002;Casalino et al. 1999;Brophy and Noca 1998;Zee 1963;Lion and Handelsman 1968;Prado 2007, 2008;Macau 2000;Macau and Grebogi 2006), swing-by techniques (Flandro 1966;Marsh 1988;Farquhard and Dunham 1981;Prado and Broucke 1995;Prado 2007;Gomes et al. 2013;DeMelo et al. 2009), and even gravitational capture (Belbruno and Miller 1993;Pierson and Kluever 1994;Neto and Prado 1998). It covers also some more applied concepts, like searches for specific orbits (Chiaradia et al. 2003;Carvalho et al. 2010;Araujo et al. 2012;Domingos et al. 2008;D'Amario et al. 1982;Farquhar et al. 1985;Gomes and Domingos 2015;Salazar et al. 2015aSalazar et al. , b, 2014Salazar et al. , 2012Gomes et al. 2007). ...
Article
Studies related to Celestial Mechanics started long ago, and it is one of the oldest fields in Astronomy. It started to try to explain the motions of the stars in the sky, in particular the irregular motion of some of those of then, which were really the planets of the Solar System. In the 20th century, with the arrival of the “Space Age”, many applications related to the motion of artificial spacecrafts appeared. This new field was called “Astrodynamics”, to designate the use of Celestial Mechanics in man-made objects. Several aspects, like orbit determination, maneuvers to change the orbit of the spacecraft, etc., are covered by this topic. The present Focus Issue in Celestial Mechanics publishes a list of papers in topics related to applications in Celestial Mechanics to both situations: natural and artificial satellites.
... As described by Dowling et al. (1991), one of the first studies about the use of swing-bys in spacecraft applications can be found in Minovich (1961). Based on this work, Flandro (1966) studied sequence of swing-by maneuvers in the outer planets of the Solar system, which would be the basis for the Voyager missions, one of the most important projects that used this technique. Other applications are shown in Sohn (1964), Sohn (1966) and Hollister and Prussing (1966), all of them proposing the use of a swing-by in Venus to send a spacecraft to Mars. ...
Article
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The swing-by maneuver is a technique used to change the energy of a spacecraft by using a close approach in a celestial body. This procedure was used many times in real missions. Usually, the first approach to design this type of mission is based on the “patched-conics” model, which splits the maneuver into three “two-body dynamics.” This approach causes an error in the estimation of the energy variations, which depends on the geometry of the maneuver and the system of primaries considered. Therefore, the goal of the present paper is to study the errors caused by this approximation. The comparison of the results are made with the trajectories obtained using the more realistic restricted three-body problem, assumed here to be the “real values” for the maneuver. The results shown here describe the effects of each parameter involved in the swing-by. Some examples using bodies in the solar system are used in this part of the paper. The study is then generalized to cover different mass parameters, and its influence is analyzed to give an idea of the amount of the error expected for a given system of primaries. The results presented here may help in estimating errors in the preliminary mission analysis using the “patched-conics” approach.
... There are many publications in topics related to Swing-Bys [5,6]. The Voyager mission was one of the first and most famous mission using this concept [7,8]. Byrnes and D'Amario [9] studied the Galileo mission that was sent to Jupiter. ...
Article
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The present paper studies the effects of a powered Swing-By maneuver, considering the particular and important situations where there are energy gains for the spacecraft. The objective is to map the energy variations obtained from this maneuver as a function of the three parameters that identify the pure gravity Swing-By with a fixed mass ratio (angle of approach, periapsis distance and velocity at periapsis) and the three parameters that define the impulsive maneuver (direction, magnitude and the point where the impulse is applied). The mathematical model used here is the version of the restricted three-body problem that includes the Lemaître regularization, to increase the accuracy of the numerical integrations. It is developed and implemented by an algorithm that obtains the energy variation of the spacecraft with respect to the largest primary of the system in a maneuver where the impulse is applied inside the sphere of influence of the secondary body, during the passage of the spacecraft. The point of application of the impulse is a free parameter, as well as the direction of the impulse. The results make a complete map of the possibilities, including the maximum gains of energy, but also showing alternatives that can be used considering particularities of the mission.
... A description of the works developed by Minovitch is available in Dowling et al. (1991Dowling et al. ( , 1992. Regarding practical applications, Flandro (1966) designed the Voyager missions, based in the equations developed by Minovitch. After that, Swing-Bys in the large planets of the Solar System were used to get energy to help the spacecrafts to reach their goals. ...
Article
The present paper studies the powered Swing-By maneuver when performed in an elliptical system of primaries. It means that there is a spacecraft travelling in a system governed by the gravity fields of two bodies that are in elliptical orbits around their center of mass. The paper particularly analyzes the effects of the parameters relative to the Swing-By (Vinf-,rp,ψ), the orbit of the secondary body around the primary one (e,ν) and the elements that specify the impulse applied (δV,α) to the spacecraft. The impulse is applied when the spacecraft passes by the periapsis of its orbit around the body, where it performs the Swing-By, with different magnitudes and directions. The inclusion of the orbital eccentricity of the primaries in this problem makes it closer to reality, considering that there are many known systems with eccentricities different from zero. In particular, there are several moons in the Solar System which orbits are not circular, as well as some smaller bodies, like the dwarf planet Haumea and its moons, which have eccentricities of 0.25 or even larger. The behavior of the energy variation of the spacecraft is shown in details, as well as the cases where captures and collisions occur. The results show the conditions that optimize this maneuver, according to some given parameters, and how much can be obtained in terms of gains or losses of energy using the best conditions found by the algorithm developed here.
... This study is very important, because the results are very much dependent on the particular system of primaries. Several studies are available in the literature on this topic, in terms of practical missions or theoretical results, like the ones presented in D' Amario et al. (1982), Farquhar and Dunham (1981), Flandro (1966), Helton et al. (2002), Longuski and Williams (1991), Strange and Longuski (2002), Petropoulos and Longuski (2000), Petropoulos et al. (1999), Striepe and Braun (1981), Prado (2008, 2010), Sukhanov et al. (2010), Sukhanov and Prado (2004), Swenson (1991), Broucke (1995a, b, 1996), Prado (2005Prado ( , 2007, Machuy et al. (2007). ...
Article
The objective of the present paper is to study orbital maneuvers to perform a mission to a triple asteroid. First, a genetic algorithm is used to find multi-impulsive maneuvers to go from the Earth to the asteroid, with minimum fuel consumption. After that, swing-by maneuvers with the two smaller bodies of the triple system are simulated and mapped to show the possible gains of energy that can be accomplished with the use of this technique. This study is made using the “patched conics approximation” and the “restricted three-body problem”, to determine the accuracy of the approximated model. The system of asteroids 2001SN$$_{263}$$ is used as an example for the calculations.
... The technique of gravity-assist maneuvers has been studied by several authors. In the decade of the 60's, Flandro [1] considered a mission to the exterior solar system using the concept of gravity-assist maneuvers with Jupiter, Saturn, and Uranus. This type of trajectory was used by the Voyagers 1 and 2. Hollister and Prussing [2] considered a Mars transfer through Venus, analyzing the advantages of an impulsive maneuver during the close approach with Venus. ...
Article
The gravitational capture was initially used to understand the capture of planetary satellites. However, in the 90's decade, this phenomenon was applied in spacecraft trajectories. Belbruno and Miller studied missions in the Earth-Moon system that uses this technique to save fuel during the insertion of the spacecraft in its final orbit around the Moon. Using a parameter defined as twice the two-body energy of the planet-particle system, Yamakawa also studied the gravitational capture in the Earth-Moon system. In the present paper, this technique is used to study a mission that goes to the Neptune system and perform a gravitational capture in the satellite Triton. The results show direct and retrograde trajectories, for different values of the initial conditions.
... Some results in this problem are available in (Yamakawa, 1992) and (Vieira Neto, and Prado, 1998). Regarding applications of the swing-by maneuver, some examples are: the study of missions to the satellites of the giant planets (D'Amario, Byrnes, and Stanford, 1982); new missions to Neptune (Swenson, 1992) and Pluto (Weinstein, 1992); the study of the Earth's environment (Farquhar, and Dunham, 1981;Farquhar, Muhonen, and Church, 1985); fast reconnaissance missions of the solar system (Flandro, 1966;Carvell, 1986); and transfers between hyperbolic asymptotes (Gobetz 1963;Walton 1975). The present paper comes in the sequence of the literature and numerical simulations are made in the three-dimensional restricted three-body problem, with the primary goal of studying the behavior of the inclination in this maneuver. ...
Article
In the present paper the swing-by maneuvers are studied under the model given by the three-dimensional circular restricted three-body problem. A numerical algorithm to study this problem is build and used to generate several results. The main goal is to study the variation of the inclination in the trajectory of a spacecraft that performs this maneuver. The results shows that: i) for the planar maneuvers the variation in inclination can assume only the values ± 180° and 0°; ii) for the polar maneuver, or for maneuvers with angle of approach α = 0° or 180°, the variation in inclination is zero. The effects of an out-of-plane component for the velocity at periapsis in the variation of the inclination, energy and angular momentum of the spacecraft are also described in details. This research has applications to design interplanetary missions.
... The close approach modifies the velocity, energy and angular momentum of a spacecraft or particle (Gobetz, 1963;Walton et al., 1975;Broucke, 1988). There are many important applications very well known, like the Voyagers I and II that used successive close encounters with the giant planets to make a long journey to the outer Solar System (Flandro, 1966). In astronomy, this phenomenon is used to explain the capture and escape of comets to/from the inner Solar System. ...
Article
This paper studies the effects of a close approach between a planet and a cloud of particles. It is assumed that the maneuver is planar and that the particles that belong to the cloud have a uniform distribution of semi-major axis and eccentricity around a nominal value and a given amplitude (so, the semi-major axes are in the interval a ±Δa and the eccentricities are in the interval e ±Δ e). The main goal is to study the distribution of those two orbital elements after the close approach. In particular, we will measure the amplitude and area (in the plane a-e) of the distribution of the orbital elements. Two solutions are considered for the maneuver, to take into account the possibility that the particles crosses the line Sun-Jupiter between the primaries (with rotation of the velocity vector in the clockwise sense) or not (with rotation of the velocity vector in the counter-clockwise sense). For the numerical simulations shown here, the planet Jupiter is used.
... There is a large number of missions that used this technique. A well-known mission was the Voyager spacecraft that traveled to the giant planets of the Solar System using a series of close approaches (Minovich 1961;Flandro 1966) to complete its mission. Later, some other options to visit those same planets and/or their moons were considered, and they can be found in several references (D'Amario et al. 1982;Strange and Longuski 2002;McConaghy et al. 2003;Okutsu et al. 2006;Helton et al. 2002). ...
Article
A maneuver called “Aero-Gravity Assisted” is known in the literature to increase the energy gains given by a close approach between a spacecraft and a planet using the atmosphere of the planet. In a sequence of studies related to this problem, the present paper studies close approaches between a spacecraft and the Earth, in situations where the passage is close enough to the surface of the Earth such that the spacecraft crosses its atmosphere. The dynamical model considers the atmosphere of the Earth, in terms of drag and lift, the gravitational fields of the Earth and the Sun, assumed to be points of mass, and the spacecraft. The Earth and the Sun are assumed to be in circular coplanar orbits around their common center of mass. The equations of motion are the ones given by the circular planar restricted three-body problem with the addition of the forces generated by the atmospheric drag and lift. The primary objective is to map the variations of energy of the orbits of the spacecraft due to this close approach. The results show how the atmosphere affects the trajectory of the spacecraft, generating situations where the variation of energy changes sign with respect to the gravity part of the maneuver or where they have a zero net result, based in the equilibrium between atmospheric and gravity forces. This result opens the possibility of changing only the eccentricity of the orbit, keeping fixed its semi-major axis.
... The technique of gravity-assist maneuvers has been studied by several authors. In the decade of the 60's, Flandro [1] considered a mission to the exterior solar system using the concept of gravity-assist maneuvers with Jupiter, Saturn, and Uranus. This type of trajectory was used by the Voyagers 1 and 2. Hollister and Prussing [2] considered a Mars transfer through Venus, analyzing the advantages of an impulsive maneuver during the close approach with Venus. ...
Article
Gravity assist is a proven technique in interplanetary exploration, as exemplified by the missions Voyager, Galileo, and Cassini. In the present paper, based in this well-known technique, an algorithm is developed to optimize missions to the outer planets. Then, this algorithm is applied to a mission to Neptune for the mid-term (2008-2020). The following schemes are analyzed: Earth-Jupiter-Neptune, Earth-Venus-Earth-Jupiter-Neptune, Earth-Venus-Earth- Jupiter-Saturn-Neptune. Transfer trajectories that provide a good compromise between the delta-V and the time of flight to Neptune are presented. In particular, the effects of the pericenter height for the gravity assist with Jupiter are studied in detail, since the final results have a strong dependence on this variable.
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The subject of the article is the characterization of the commercialization of the results of scientific activity. The starting point is to point out the Polish specificity of the legal regulation of the conduct of scientific activity and its coherence with the market environment. A special place in this regard is occupied by research institutes. The author presents the legal possibilities of commercialization of the results of scientific activity conducted by research institutes focusing on the so-called indirect commercialization, which he discusses in detail. In addition to procedural issues, the article discusses in detail the prerequisites for commercialization, including in particular the legally defined objectives of its implementation, the regulation of which indicates the specificity of Polish solutions.
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The aim of this paper is to analyze the performance of a radially-accelerated spacecraft in a capture mission scenario, in which a space vehicle transfers from a parabolic approaching trajectory of assigned semilatus rectum to a target circular orbit around a generic celestial body. The radial propulsive acceleration provided by the spacecraft propulsion system can be modulated within a suitable given range, and the radial thrust can be either inward- or outward-directed. The transfer mission performance is analyzed in an optimal framework, by minimizing the total flight time with an indirect approach. In this context, the paper proposes a semi-analytical method to reduce the computation time required to solve the optimal control problem. Using a proper description of the spacecraft dynamics in a dimensionless form, the paper reports a set of graphs and tables that allow the designer to obtain a rapid approximation of the optimal mission performance with an accuracy consistent with that of a preliminary trajectory design. Finally, the proposed approach is used to describe the minimum time capture trajectories in a mission scenario towards Ceres.
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In the study, structural optimization and prediction of bioinspired cell core are investigated numerically. The particle swarm optimization (PSO) is used to optimize the maximum transverse shear modulus for the selected bioinspired models by considering various factors such as bioinspired model, side length, and edge radius. The fitness function is formulated using ANSYS–MATLAB code. The prediction of the transverse shear modulus of various bioinspired cell cores is estimated by artificial neural network (ANN) by considering ranges of parameters such as bioinspired model, side length, and edge radius. It shows that the optimization problem with the maximization of transverse shear modulus yields the optimal bioinspired cell core. And, the prediction returned very satisfactory results.KeywordsANNPSOBioinspired coreTransverse shear modulusFEAOptimization
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Kluever’s analytical method for obtaining an optimal interplanetary trajectory using a solar-electric propulsion (SEP) system has been analysed, and various trajectory parameters, namely ∆V, transfer angle, coast angle and flight duration, have been computed for given initial and target orbit radii, initial power and spacecraft mass, specific impulse and efficiency of the thruster. Detailed analysis showed that there are grey regions where the analytical method has failed to provide the expected result.
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This paper discusses the current challenges of exploration of outer planets and proposes a nuclear thermal propulsion (NTP) system for future deep space exploration missions. The mission design problem with respect to the NTP system is presented where it is proposed that NTP-powered missions need to integrate the requirements and constraints of mission objective, spacecraft design, NTP system design, and launch vehicle limits into a self-consistent model. The paper presents a conceptual NTP-powered rendezvous mission to Neptune that uses a single high-performance–class commercial launch vehicle to deliver over 2 mT of useful payload in a direct transfer trajectory with total trip time being under 16 years.
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The Parker Solar Probe is a spacecraft designed to study the Sun’s corona from inside. It is providing unprecedented detailed information on the density and composition of the Sun’s atmosphere as well as the electromagnetic fields, plasma and solar wind. On the other hand, this probe is to achieve record speeds in the International Celestial Reference Frame (ICRF) never obtained before in any previous mission. It is expected that in the last perihelion of 2025 it would move at 0.064 % of the speed of light with respect to the barycenter of the Solar System. By this time it will approach only 9.86 solar radii to the center of the Sun. These orbital conditions make the Parker’s Solar Probe also an interesting experiment concerning the validity of General Relativity (GR). The combination of a high velocity and a relatively intense gravitational field increases the values of the post-Newtonian terms governing the orbital corrections by GR. In this paper, we consider an orbital model for the Parker Probe trajectory, including the important effect of radiation pressure, to calculate the relativistic corrections. From this model, we compare the magnitude of the corrections in order to evaluate the possibility of obtaining a test of GR from spacecraft missions orbiting close to the Sun.
Article
This work performs a computational investigation of the energy variations given by a powered Swing-By maneuver realized in an elliptical system. It extends previous works by giving the freedom to choose the location and the direction of the thrust vector, aspects that were not considered before in the literature. Those variations are obtained numerically as a function of the parameters related to the thrust (magnitude, direction and location of the application) and the orbital parameters of the primaries (eccentricity and true anomaly). The maneuver is realized around the smaller primary, and the energy variations are measured with respect to the main body of the system. The initial orbit of the space vehicle is defined by its periapsis distance, angle and approach velocity with respect to the smaller primary. The study is applied to a system composed of two primaries that are in elliptic orbits around the center of mass of the system. The eccentricity is varied as a free parameter, to measure its effects. The results show that the best maneuvers apply the thrust at a point inside the sphere of influence of the secondary body, but not in the periapsis of the orbit. The best direction of the thrust is not aligned with the motion of the space vehicle. The techniques studied here are applied in situations where it is desired to increase the energy of the space vehicle. Empirical equations are obtained for the energy variations, based on the simulations made in the present paper. The numerical approach makes the results more accurate and not limited to particular regions of the eccentricity.
Chapter
Leben verändert abiotische Bedingungen und hinterlässt mitunter massive Spuren in der Umwelt – sei es durch Bakterien vor Milliarden von Jahren oder durch uns Menschen heute. Die Suche nach solchen Ökosignaturen auf fernen Welten hat bereits begonnen. Doch welche Indikatoren für Leben sind besonders aufschlussreich und welche Welten sollen zuerst untersucht werden?
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Exploring the solar system is becoming more and more challenging and the associated space missions are becoming similarly more demanding concerning Δv, targeted at distant bodies. Recent examples for such missions are New Horizons, which visited the dwarf planet Pluto and Rosetta’s rendezvous with the comet 67P/Churyumov-Gerasimenko. These missions would not have been possible without the application of gravity assists, a technique already used for Pioneer 10 and 11 and the Voyager missions. It is based on transferring energy between a planet or other flyby partner and a spacecraft, which results in trajectory changes without associated propellant consumption. Low-thrust propulsion, which is usually operating continuously for significant amounts of time during a mission, is very efficient and thus often acts as mission enabler. The effort - expressed in used propellant mass fraction – to achieve a certain mission goal is usually smaller for low-thrust propulsion than for a similar mission applying chemical propulsion. This is due to the large specific impulse (typically >3000s) associated with low-thrust propulsion. To further enhance our ability to explore the solar system it is therefore desirable to combine these two techniques. Currently, a number of methods exists to optimize low-thrust trajectories and these have been applied to gravity-assist scenarios as well. However, up to now a method for optimization of the actual sequence of gravity- assist partners is not publically available. Instead, the respective mission analyst has provided the sequence, based on assumptions, estimates and experience. The major goal of this dissertation is to close this gap and investigate if it is possible to reduce the amount of expert information needed and for optimization and thus increase the degree to which the search space is searched in completeness. Reducing the amount of involved experience and trajectory resp. sequence information, improves the chance of finding unforseen and worthwhile new mission sequences. This dissertation provides an analysis of how to incorporate the gravityassist sequence into the optimization process and thus allow a complete, thorough and effective search of useful mission scenarios. First, it is analyzed how gravity-assist sequences are obtained for impulsive missions and whether the same technique can be similarly applied to low-thrust scenarios. A typical approach for gravityassist planning of impulsive mission scenarios is the application of Tisserand’s Criterion. It is an energy relation, derived for observations of comets in the 19th century within the context of the circular restricted three-body system. This criterion can be represented visually in the form of socalled Tisserand graphs, which are used to map possible gravity-assist sequences. Furthermore, two sources of errors are analyzed: First, the error is analysed, which is caused by applying this relation to the actual solar system and thus diverting from the circular restricted three-body system. Second, the error is analysed, which is caused by adding thrust into the equations of motion. It is shown that the thrust force is negligible in the balance of forces for realistic mission designs. However, the thrust’s effect on the specific orbit energy cannot be neglected. Next, a correction term to apply Tisserand’s Criterion in a low-thrust situation is derived. This term however, does not allow an a priori evaluation of the mission sequence and therefore the modified Tisserand’s Criterion cannot be used to map out possible paths of gravity assists similarly as the unmodified Tisserad’s Criteron for impulsive missions. A method, based on a heuristic search, a shape-based trajectory model and the inclusion of possible gravity-assist partners as variable, is set up. The heuristic search circumvents the usage of Tisserand’s Criterion. As a next step to establish the method, the respective variable structure is analyzed. Some of the relevant trajectory variables are shown to be interdepent. For instance, the flight times of the individual trajectory legs between all encountered bodies have to add up to thetotal mission flight time. Consequently, two types of variables are defined: global and local. The first are independent and thus can be used by an evolutionary algorithm to evolve the mission candidates into better (based on solution fitness) solutions during the search. The latter are interdependent. A number of example calculations are conducted to assess the success and usefulness of applying this search method. It is shown that for a single gravity assist in an Earth to Jupiter mission the obtained results are reliable concerning the gravity-assist partner and date and successfully improve the non-gravity assist benchmark by more than 20%. Performance for multi-gravity-assist missions is worse, but still solution improvement and a dominance of the global variables can be observed. Further calculations introduce constraints based on the variable regions of maximum Δv change and show that the solution quality and reliability can thus be improved. Furthermore, the limitations of reproducing existing trajectories are shown and discussed. Finally, the drawbacks of the applied shape-based trajectory model are expressed in a discussion concerning its relation to Tisserand graph diagrams. It is recommended to use a different trajectory model to address these drawbacks in future work.
Chapter
Leben verändert abiotische Bedingungen und hinterlässt mitunter massive Spuren in der Umwelt – sei es durch Bakterien vor Milliarden von Jahren oder durch uns Menschen heute. Die Suche nach solchen Ökosignaturen auf fernen Welten hat bereits begonnen.
Article
The present work quantifies the fuel consumption of a space vehicle in bi-impulsive interplanetary trajectories with an intermediary swing-by maneuver with the Moon. In this way, an interplanetary patched-conic approximation with a lunar swing-by maneuver is formulated with an important characteristic: the swing-by maneuver is designed before the determination of the trajectory by specifying its geometry. The transfer problem is then solved by a multi-point boundary value problem (MPBVP) with two constraints. The intermediary constraint is related to the geometry of the swing-by maneuver with the Moon, and the terminal constraint is related to the altitude of the arrival at the low orbit around the target planet. The proposed algorithm is built in such way that the MPBVP is split into two-point boundary value problems (TPBVPs): the first one is solved to ensure the satisfying of the intermediary constraint, and the second TPBVP is solved next to satisfy the final constraint. Both TPBVPs are solved by means of Newton–Raphson algorithm. The proposed algorithm is then utilized to determine the Earth–Mars and Earth–Venus trajectories with several geometric configurations. The geometric configuration with the smallest fuel consumption is obtained for both missions and compared to an interplanetary patched-conic approximation without swing-by maneuver with Moon. The results show advantages in performing swing-by maneuver with the Moon for interplanetary missions by saving fuel consumption without much increase of the time of flight.
Chapter
On 31 January 1958 America’s first satellite, Explorer 1, was sent into an elliptical orbit ranging out to an altitude of 2,000 kilometres. The Geiger-Müller counter that it carried revealed that electrically charged particles circulate in the Earth’s magnetic field. The instrument’s principal investigator was J.A. Van Allen of the University of Iowa, and this radiation became known as the Van Allen belt. In 1962, as Mariner 2 departed the Earth’s vicinity to make a fly-by of Venus, it found that interplanetary space is pervaded by particles that flow from the Sun as a ‘solar wind’. It was then realised that the radiation within the Earth’s ‘magnetosphere’ originated from this wind, and that auroral displays occurred when dense streams of particles forced their way into the open ‘cusps’ above the magnetic poles. In the 1960s NASA’s Ames Research Center, which is located south of San Francisco, sent a series of extremely successful Pioneers into solar orbit, some slightly inside the Earth’s orbit and some just outside it, carrying suites of ‘particles and fields’ instruments to report the state of the solar wind. One discovery was that the strength of the solar wind draws the Earth’s magnetosphere downstream to a considerable distance in a ‘magnetotail’.
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The Swing-By maneuver is a technique used in many space mission to modify the trajectory of a spacecraft. The most usual goal is to increase the energy of the spacecraft, but it is also possible to reduce this energy. An important application is to break a spacecraft coming to the Earth using a Swing-By with the moon, which is the example used in the present paper. Other possibilities also exist, such as reducing the velocity of a spacecraft going to the planets Mercury or Venus. The goal is to help a possible capture by the planet, or at least to provide a passage with smaller velocities to allow better observations during the passage. Therefore, the goal of the present paper is to study the energy loss that a spacecraft may have during a powered Swing-By maneuver, which is a maneuver that combines a close approach by a celestial body with the application of an impulsive maneuver. The behavior of the energy variation is analyzed as a function of the parameters related to the pure gravity maneuver: periapsis radius, angle of approach and approach velocity; and the parameters related to the impulsive maneuver: the location of application of the impulse and its direction and magnitude. The maneuver is performed in a system composed by two bodies, such as the Earth–moon system, around the secondary body, and the energy is measured with respect to the primary body of the system. This problem is solved by developing a mathematical algorithm that guides larger efforts in terms of computer simulations. The results show maps of conditions made from the numerical simulations for different points of application and direction of the impulse, where the maneuver is advantageous and how much more energy can be removed from the spacecraft.
Chapter
Since the dawn of the Space Age, hundreds of humans have entered this strange new realm in modern-day equivalents of the Yankee Clipper. Twenty-four (three of them twice) have orbited our Moon or landed upon it and viewed the Earth as a precious blue-green orb suspended in the inky blackness of the void. Our robot emissaries have tested the soils of the Moon, Mars and Venus, and have flown by all Solar System planets except frozen Pluto. The robotic exploration of local asteroids and comets and the satellites of Solar System planets continues, and four small craft — the intrepid Pioneer 10/11 and Voyager 1/2 — have become humanity’s first Galactic emissaries.
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Taking the exploring Mars via Venus gravity-assist as the background, a hybrid design method of gravity-assist trajectories for interplanetary missions is proposed to the problems of conventional design method of gravity-assist trajectory. First, based on analysis of characteristics of gravity-assist celestial bodies, we provide the possible parameter matching regions for gravity-assist trajectory by using the contour map of hyperbolic excess velocity. Then, while patching the segments of gravity-assist trajectories, we present the "Soft matching" strategy instead of the classical matching strategy. Finally, the hybrid optimal algorithm is used to optimize the design parameters of gravity-assist trajectories. This method could resolve effectively the problem that conventional method omits gravity-assist opportunities satisfied with constraints. Taking the exploring Mars via Venus gravity-assist in 2017-2018 years as an example, we not only provide the design results that agree with that of Okutsu, but also find a new trajectory profile in the same parameter region. In addition, we also analyze the transfer opportunities for exploring Mars with Venus gravity-assist in the period of 2010-2018, and provide the better design parameter regions. These researches will present the significant reference for the future Mars mission.
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