Impulsive Maneuver

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Othon C. Winter - One of the best experts on this subject based on the ideXlab platform.

  • Planar powered Swing-By Maneuvers to brake a spacecraft
    Computational and Applied Mathematics, 2018
    Co-Authors: Alessandra F. S. Ferreira, Antônio F. B. A. Prado, Othon C. Winter
    Abstract:

    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.

  • Analytical study of the powered Swing-By Maneuver for elliptical systems and analysis of its efficiency
    Astrophysics and Space Science, 2018
    Co-Authors: Alessandra F. S. Ferreira, Othon C. Winter, Antônio F. B. A. Prado, Denilson P. S. Santos
    Abstract:

    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 δ V $\delta V$ and the angle that defines the direction of the impulse with respect to the velocity of the spacecraft ( α $\alpha$ ). 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.

  • A numerical mapping of energy gains in a powered Swing-By Maneuver
    Nonlinear Dynamics, 2017
    Co-Authors: Alessandra F. S. Ferreira, Antônio F. B. A. Prado, Othon C. Winter
    Abstract:

    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.

Ryan P. Russell - One of the best experts on this subject based on the ideXlab platform.

  • Tisserand-Leveraging Transfers
    Journal of Guidance Control and Dynamics, 2014
    Co-Authors: Stefano Campagnola, Arnaud Boutonnet, Johannes Schoenmaekers, Daniel J. Grebow, Anastassios E. Petropoulos, Ryan P. Russell
    Abstract:

    Tisserand-leveraging transfers (TILTs) are introduced as a new method for computing low-Δv orbit transfers with the help of third-body perturbations. The TILTs can mitigate the costs and risk of planetary missions by reducing the orbit insertion Maneuver requirements while maintaining short flight times. TILTs connect two flybys at the minor body with an Impulsive Maneuver at an apse. Using the circular, restricted three-body problem, TILTs extend the concept of v-infinity leveraging beyond the patched-conics domain. In this paper, a new method is presented to compute TILTs and to patch them together to design low-energy transfers. The presented solutions have transfer times similar to the high-energy solutions, yet the Δv cost is significantly reduced. For this reason, TILTs are used in the reference endgame of ESA’s new mission option to Ganymede, JUICE, which is also presented here. JUICE’s low-energy endgame halves the cost of similar high-energy endgames, which makes TILTs a mission-enabling technolo...

  • Tisserand-leveraging transfers
    2012
    Co-Authors: Stefano Campagnola, Arnaud Boutonnet, Johannes Schoenmaekers, Daniel J. Grebow, Anastassios E. Petropoulos, Ryan P. Russell
    Abstract:

    Tisserand-leveraging transfers (TILTs) are introduced as a new method for computing low ∆v orbit transfers with the help of third-body perturbations. The TILTs can mitigate the costs and risk of planetary missions by reducing the orbit insertion Maneuver requirements while maintaining short flight times. TILTs connect two flybys at the minor body with an Impulsive Maneuver at an apse. Using the circular, restricted, three-body problem, TILTs extend the concept of v-infinity leveraging beyond the patched-conics domain. In this paper a new method is presented to compute TILTs and to patch them together to design low-energy transfers. The presented solutions have transfer times similar to the high-energy solutions, yet the ∆v cost is significantly reduced (up to 60%), thus enabling new orbiter missions to planetary satellites. For this reason, TILTs are used in the reference endgame of ESA’s new mission option to Ganymede, JUICE, which is also presented here. The "lunar resonances " of SMART1 are also explained in terms of low-thrust TILTs, suggesting future application of TILTs and low-thrust TILTs to design mission to the Moon and to other small body destinations. Finally, a new model called “conic-patched, multi-body model ” is introduced to allow a fast and accurate integration of the multi-body dynamics, and has applications beyond TILT

  • A fast tour design method using non-tangent v-infinity leveraging transfer
    Celestial Mechanics and Dynamical Astronomy, 2010
    Co-Authors: Stefano Campagnola, Nathan J. Strange, Ryan P. Russell
    Abstract:

    The announced missions to the Saturn and Jupiter systems renewed the space community interest in simple design methods for gravity assist tours at planetary moons. A key element in such trajectories are the V-Infinity Leveraging Transfers (VILT) which link simple Impulsive Maneuvers with two consecutive gravity assists at the same moon. VILTs typically include a tangent Impulsive Maneuver close to an apse location, yielding to a desired change in the excess velocity relative to the moon. In this paper we study the VILT solution space and derive a linear approximation which greatly simplifies the computation of the transfers, and is amenable to broad global searches. Using this approximation, Tisserand graphs, and heuristic optimization procedure we introduce a fast design method for multiple-VILT tours. We use this method to design a trajectory from a highly eccentric orbit around Saturn to a 200-km science orbit at Enceladus. The trajectory is then recomputed removing the linear approximation, showing a Δ v change of

  • A Fast Tour Design Method Using Non-Tangent V-Infinity Leveraging Transfers,” Celestial Mechanics and Dynamical Astronomy, 2010, to appear, DOI 10.1007/s10569-010-9295-1, on-line publication July 2010. 19 of 20 presented at the George H. Born Symposi
    2010
    Co-Authors: Stefano Campagnola, Nathan J. Strange, Ryan P. Russell
    Abstract:

    The announced missions to the Saturn and Jupiter systems renewed the space community interest in simple design methods for gravity assist tours at planetary moons. A key element in such trajectories are the V-Infinity Leveraging Transfers (VILT) which link simple im-pulsive Maneuvers with two consecutive gravity assists at the same moon. VILTs typically include a tangent Impulsive Maneuver close to an apse location, yielding to a desired change in the excess velocity relative to the moon. In this paper we study the VILT solution space and derive a linear approximation which greatly simplifies the computation of the transfers, and is amenable to broad global searches. Using this approximation, Tisserand graphs, and heuristic optimization procedure we introduce a fast design method for multiple-VILT tours. We use this method to design a trajectory from a highly eccentric orbit around Saturn to a 200 km science orbit at Enceladus. The trajectory is then recomputed removing the linear approximation, showing a ∆v change of less than 4%. The trajectory is 2.7 years long and comprises 52 gravity assists at Titan, Rhea, Dione, Tethys, and Enceladus, and several de-terministic Maneuvers. Total ∆v is only 445 m/s, including the Enceladus orbit insertion, almost 10 times better then the 3.9 km/s of the Enceladus orbit insertion from the Titan-Enceladus Hohmann transfer. The new method and demonstrated results enable a new class of missions that tour and ultimately orbit small mass moons. Such missions were previously considered infeasible due to flight time and ∆v constraints

Alessandra F. S. Ferreira - One of the best experts on this subject based on the ideXlab platform.

  • Planar powered Swing-By Maneuvers to brake a spacecraft
    Computational and Applied Mathematics, 2018
    Co-Authors: Alessandra F. S. Ferreira, Antônio F. B. A. Prado, Othon C. Winter
    Abstract:

    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.

  • Analytical study of the powered Swing-By Maneuver for elliptical systems and analysis of its efficiency
    Astrophysics and Space Science, 2018
    Co-Authors: Alessandra F. S. Ferreira, Othon C. Winter, Antônio F. B. A. Prado, Denilson P. S. Santos
    Abstract:

    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 δ V $\delta V$ and the angle that defines the direction of the impulse with respect to the velocity of the spacecraft ( α $\alpha$ ). 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.

  • A numerical mapping of energy gains in a powered Swing-By Maneuver
    Nonlinear Dynamics, 2017
    Co-Authors: Alessandra F. S. Ferreira, Antônio F. B. A. Prado, Othon C. Winter
    Abstract:

    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.

Antônio F. B. A. Prado - One of the best experts on this subject based on the ideXlab platform.

  • Planar powered Swing-By Maneuvers to brake a spacecraft
    Computational and Applied Mathematics, 2018
    Co-Authors: Alessandra F. S. Ferreira, Antônio F. B. A. Prado, Othon C. Winter
    Abstract:

    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.

  • Analytical study of the powered Swing-By Maneuver for elliptical systems and analysis of its efficiency
    Astrophysics and Space Science, 2018
    Co-Authors: Alessandra F. S. Ferreira, Othon C. Winter, Antônio F. B. A. Prado, Denilson P. S. Santos
    Abstract:

    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 δ V $\delta V$ and the angle that defines the direction of the impulse with respect to the velocity of the spacecraft ( α $\alpha$ ). 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.

  • Analysis of Impulsive Maneuvers to keep orbits around the asteroid 2001SN_263
    Astrophysics and Space Science, 2017
    Co-Authors: Willer G. Santos, Antônio F. B. A. Prado, Geraldo M. C. Oliveira, Leonardo B. T. Santos
    Abstract:

    The strongly perturbed environment of a small body, such as an asteroid, can complicate the prediction of orbits used for close proximity operations. Inaccurate predictions may make the spacecraft collide with the asteroid or escape to the deep space. The main forces acting in the dynamics come from the solar radiation pressure and from the body’s weak gravity field. This paper investigates the feasibility of using bi-Impulsive Maneuvers to avoid the aforementioned non-desired phenomena (collisions and escapes) by connecting orbits around the triple system asteroid 2001SN_263, which is the target of a proposed Brazilian space mission. In terms of a mathematical formulation, a recently presented rotating dipole model is considered with oblateness in both primaries. In addition, a “two-point boundary value problem” is solved to find a proper transfer trajectory. The results presented here give support to identifying the best strategy to find orbits for close proximity operations, in terms of long orbital lifetimes and low delta- V $V$ consumptions. Numerical results have also demonstrated the significant influence of the spacecraft orbital elements (semi-major axis and eccentricity), angular position of the Sun and spacecraft area-to-mass ratio, in the performance of the bi-Impulsive Maneuver.

  • A numerical mapping of energy gains in a powered Swing-By Maneuver
    Nonlinear Dynamics, 2017
    Co-Authors: Alessandra F. S. Ferreira, Antônio F. B. A. Prado, Othon C. Winter
    Abstract:

    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.

Stefano Campagnola - One of the best experts on this subject based on the ideXlab platform.

  • Tisserand-Leveraging Transfers
    Journal of Guidance Control and Dynamics, 2014
    Co-Authors: Stefano Campagnola, Arnaud Boutonnet, Johannes Schoenmaekers, Daniel J. Grebow, Anastassios E. Petropoulos, Ryan P. Russell
    Abstract:

    Tisserand-leveraging transfers (TILTs) are introduced as a new method for computing low-Δv orbit transfers with the help of third-body perturbations. The TILTs can mitigate the costs and risk of planetary missions by reducing the orbit insertion Maneuver requirements while maintaining short flight times. TILTs connect two flybys at the minor body with an Impulsive Maneuver at an apse. Using the circular, restricted three-body problem, TILTs extend the concept of v-infinity leveraging beyond the patched-conics domain. In this paper, a new method is presented to compute TILTs and to patch them together to design low-energy transfers. The presented solutions have transfer times similar to the high-energy solutions, yet the Δv cost is significantly reduced. For this reason, TILTs are used in the reference endgame of ESA’s new mission option to Ganymede, JUICE, which is also presented here. JUICE’s low-energy endgame halves the cost of similar high-energy endgames, which makes TILTs a mission-enabling technolo...

  • Tisserand-leveraging transfers
    2012
    Co-Authors: Stefano Campagnola, Arnaud Boutonnet, Johannes Schoenmaekers, Daniel J. Grebow, Anastassios E. Petropoulos, Ryan P. Russell
    Abstract:

    Tisserand-leveraging transfers (TILTs) are introduced as a new method for computing low ∆v orbit transfers with the help of third-body perturbations. The TILTs can mitigate the costs and risk of planetary missions by reducing the orbit insertion Maneuver requirements while maintaining short flight times. TILTs connect two flybys at the minor body with an Impulsive Maneuver at an apse. Using the circular, restricted, three-body problem, TILTs extend the concept of v-infinity leveraging beyond the patched-conics domain. In this paper a new method is presented to compute TILTs and to patch them together to design low-energy transfers. The presented solutions have transfer times similar to the high-energy solutions, yet the ∆v cost is significantly reduced (up to 60%), thus enabling new orbiter missions to planetary satellites. For this reason, TILTs are used in the reference endgame of ESA’s new mission option to Ganymede, JUICE, which is also presented here. The "lunar resonances " of SMART1 are also explained in terms of low-thrust TILTs, suggesting future application of TILTs and low-thrust TILTs to design mission to the Moon and to other small body destinations. Finally, a new model called “conic-patched, multi-body model ” is introduced to allow a fast and accurate integration of the multi-body dynamics, and has applications beyond TILT

  • A fast tour design method using non-tangent v-infinity leveraging transfer
    Celestial Mechanics and Dynamical Astronomy, 2010
    Co-Authors: Stefano Campagnola, Nathan J. Strange, Ryan P. Russell
    Abstract:

    The announced missions to the Saturn and Jupiter systems renewed the space community interest in simple design methods for gravity assist tours at planetary moons. A key element in such trajectories are the V-Infinity Leveraging Transfers (VILT) which link simple Impulsive Maneuvers with two consecutive gravity assists at the same moon. VILTs typically include a tangent Impulsive Maneuver close to an apse location, yielding to a desired change in the excess velocity relative to the moon. In this paper we study the VILT solution space and derive a linear approximation which greatly simplifies the computation of the transfers, and is amenable to broad global searches. Using this approximation, Tisserand graphs, and heuristic optimization procedure we introduce a fast design method for multiple-VILT tours. We use this method to design a trajectory from a highly eccentric orbit around Saturn to a 200-km science orbit at Enceladus. The trajectory is then recomputed removing the linear approximation, showing a Δ v change of

  • A Fast Tour Design Method Using Non-Tangent V-Infinity Leveraging Transfers,” Celestial Mechanics and Dynamical Astronomy, 2010, to appear, DOI 10.1007/s10569-010-9295-1, on-line publication July 2010. 19 of 20 presented at the George H. Born Symposi
    2010
    Co-Authors: Stefano Campagnola, Nathan J. Strange, Ryan P. Russell
    Abstract:

    The announced missions to the Saturn and Jupiter systems renewed the space community interest in simple design methods for gravity assist tours at planetary moons. A key element in such trajectories are the V-Infinity Leveraging Transfers (VILT) which link simple im-pulsive Maneuvers with two consecutive gravity assists at the same moon. VILTs typically include a tangent Impulsive Maneuver close to an apse location, yielding to a desired change in the excess velocity relative to the moon. In this paper we study the VILT solution space and derive a linear approximation which greatly simplifies the computation of the transfers, and is amenable to broad global searches. Using this approximation, Tisserand graphs, and heuristic optimization procedure we introduce a fast design method for multiple-VILT tours. We use this method to design a trajectory from a highly eccentric orbit around Saturn to a 200 km science orbit at Enceladus. The trajectory is then recomputed removing the linear approximation, showing a ∆v change of less than 4%. The trajectory is 2.7 years long and comprises 52 gravity assists at Titan, Rhea, Dione, Tethys, and Enceladus, and several de-terministic Maneuvers. Total ∆v is only 445 m/s, including the Enceladus orbit insertion, almost 10 times better then the 3.9 km/s of the Enceladus orbit insertion from the Titan-Enceladus Hohmann transfer. The new method and demonstrated results enable a new class of missions that tour and ultimately orbit small mass moons. Such missions were previously considered infeasible due to flight time and ∆v constraints