Optimization of sprint interplanetary trajectories with nuclear bimodal thermal propulsion

Interplanetary missions require fast and fuel-efficient transfers. Combining small times transfers of high-thrust and efficiency of low-thrust propulsion can provide a good compromise. Saving an amount of fuel from the initial high-thrust burn and using it to correct the trajectory could lead to an economy of fuel. We investigated the optimal way to take advantages of both high and low-thrust propulsion benefits in order to maximize the payload mass of the mission. Using a simple model of ideal engine of limited power and the transporting trajectory method, we determined the analytical expression of final payload mass. The solution of the optimization problem gave us the optimal repartition of fuel between high and low-thrust maneuvers for a given thrust of thermal propulsion and electrical power of low-thrust propulsion system. As the mass of the low-thrust propulsion system depends on the electrical power, we took it into account to determine the optimal electrical power for a sprint trajectory in a given time. As a result, we could obtain the interval of transfer time for which the combination of high and low thrust becomes optimal.

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Numerical and Analytical Study of Optimal Low-Thrust Limited-Power Transfers between Close Circular Coplanar Orbits

Mathematical Problems in Engineering ◽

10.1155/2007/59372 ◽

2007 ◽

Vol 2007 ◽

pp. 1-23 ◽

Cited By ~ 4

Author(s):

Sandro da Silva Fernandes ◽

Wander Almodovar Golfetto

Keyword(s):

Boundary Value Problem ◽

Optimization Problem ◽

Analytical Study ◽

Numerical Study ◽

Boundary Value ◽

Performance Criterion ◽

Point Boundary ◽

Low Thrust ◽

Transformation Theory ◽

Limited Power

A numerical and analytical study of optimal low-thrust limited-power trajectories for simple transfer (no rendezvous) between close circular coplanar orbits in an inverse-square force field is presented. The numerical study is carried out by means of an indirect approach of the optimization problem in which the two-point boundary value problem, obtained from the set of necessary conditions describing the optimal solutions, is solved through a neighboring extremal algorithm based on the solution of the linearized two-point boundary value problem through Riccati transformation. The analytical study is provided by a linear theory which is expressed in terms of nonsingular elements and is determined through the canonical transformation theory. The fuel consumption is taken as the performance criterion and the analysis is carried out considering various radius ratios and transfer durations. The results are compared to the ones provided by a numerical method based on gradient techniques.

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A Numerical Study of Low-Thrust Limited Power Trajectories between Coplanar Circular Orbits in an Inverse-Square Force Field

Mathematical Problems in Engineering ◽

10.1155/2012/168632 ◽

2012 ◽

Vol 2012 ◽

pp. 1-24 ◽

Cited By ~ 3

Author(s):

Sandro da Silva Fernandes ◽

Carlos Roberto Silveira Filho ◽

Wander Almodovar Golfetto

Keyword(s):

Force Field ◽

Gradient Method ◽

Trajectory Optimization ◽

Optimization Problem ◽

Numerical Study ◽

Direct Method ◽

Variation Theory ◽

Second Variation ◽

Low Thrust ◽

Limited Power

A numerical study of optimal low-thrust limited power trajectories for simple transfer (no rendezvous) between circular coplanar orbits in an inverse-square force field is performed by two different classes of algorithms in optimization of trajectories. This study is carried out by means of a direct method based on gradient techniques and by an indirect method based on the second variation theory. The direct approach of the trajectory optimization problem combines the main positive characteristics of two well-known direct methods in optimization of trajectories: the steepest-descent (first-order gradient) method and a direct second variation (second-order gradient) method. On the other hand, the indirect approach of the trajectory optimization problem involves two different algorithms of the well-known neighboring extremals method. Several radius ratios and transfer durations are considered, and the fuel consumption is taken as the performance criterion. For small-amplitude transfers, the results are compared to the ones provided by a linear analytical theory.

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Rendez vous with Saturn's rings

International Astronomical Union Colloquium ◽

10.1017/s0252921100101885 ◽

1984 ◽

Vol 75 ◽

pp. 743-759 ◽

Cited By ~ 2

Author(s):

Kerry T. Nock

Keyword(s):

Solar Energy ◽

Electric Propulsion ◽

Power Source ◽

Propulsion System ◽

Low Thrust ◽

Ring Plane ◽

The Earth ◽

Total Impulse ◽

Saturn's Rings

ABSTRACTA mission to rendezvous with the rings of Saturn is studied with regard to science rationale and instrumentation and engineering feasibility and design. Future detailedin situexploration of the rings of Saturn will require spacecraft systems with enormous propulsive capability. NASA is currently studying the critical technologies for just such a system, called Nuclear Electric Propulsion (NEP). Electric propulsion is the only technology which can effectively provide the required total impulse for this demanding mission. Furthermore, the power source must be nuclear because the solar energy reaching Saturn is only 1% of that at the Earth. An important aspect of this mission is the ability of the low thrust propulsion system to continuously boost the spacecraft above the ring plane as it spirals in toward Saturn, thus enabling scientific measurements of ring particles from only a few kilometers.

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