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Related Concept Videos

Orthogonal Trajectories01:26

Orthogonal Trajectories

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Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
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According to Raoult’s law, the partial vapor pressure of a solvent in a solution is equal or identical to the vapor pressure of the pure solvent multiplied by its mole fraction in the solution. However, Raoult's Law is only valid for ideal solutions. For a solution to be ideal, the solvent-solute interaction must be just as strong as a solvent-solvent or solute-solute interaction. This suggests that both the solute and the solvent would use the same amount of energy to escape to the...
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Many common substances around us exist as a solution, such as ocean water, air, and gasoline. All solutions are mixtures of substances that are composed of varying amounts of two or more types of atoms or molecules. A mixture with a non-uniform composition is a heterogeneous mixture, whereas a mixture with a uniform composition is a homogeneous mixture. The components that make the homogeneous mixture are evenly spread out and thoroughly mixed. 
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There is no one solvent that can dissolve every type of solute. Some substances that readily dissolve in a certain solvent might be insoluble in a different solvent. A simple way to predict which substances dissolve in which solvent is the phrase "like dissolves like". This means that polar substances, such as salt and sugar, dissolve in a polar substance like water. In contrast, non-polar substances are more soluble in non-polar solvents such as carbon tetrachloride.
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There are two criteria that favor, but do not guarantee, the spontaneous formation of a solution:
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Standard solutions refer to solutions with a precisely known concentration or composition. A primary standard is a highly pure, high molar mass, stable substance that is entirely soluble in water, the most commonly used solvent in analytical chemistry. The primary standard solution can be used to standardize secondary standards, which are substances with known concentrations but are less pure and stable. Standard solutions are essential for achieving accurate and reliable results in analytical...
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An Automated Solution of the Low-Thrust Interplanetary Trajectory Problem.

Jacob A Englander1, Bruce A Conway2

  • 1Aerospace Engineer, Navigation and Mission Design Branch, NASA Goddard Space Flight Center, Greenbelt, MD, 20771, USA, Member AIAA.

Journal of Guidance, Control, and Dynamics : a Publication of the American Institute of Aeronautics and Astronautics Devoted to the Technology of Dynamics and Control
|March 9, 2018
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Summary
This summary is machine-generated.

Designing low-thrust interplanetary missions is complex. This study introduces an automated hybrid optimal control method to efficiently find optimal trajectories, saving significant analyst time.

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Area of Science:

  • Aerospace Engineering
  • Astrodynamics
  • Mission Design

Background:

  • Preliminary design of low-thrust interplanetary missions involves complex discrete parameter selection and trajectory optimization.
  • Evaluating numerous potential trajectories requires extensive human analyst hours, making the process inefficient.

Purpose of the Study:

  • To develop an automated approach for preliminary low-thrust interplanetary mission design.
  • To address the computational expense and complexity associated with traditional mission design methods.

Main Methods:

  • The mission design problem is formulated as a hybrid optimal control problem.
  • The proposed method automates the selection of discrete parameters (e.g., flybys, destinations) and control variables for trajectory optimization.

Main Results:

  • Demonstrated the effectiveness of the hybrid optimal control approach on hypothetical missions.
  • Successfully applied the method to missions targeting Mercury, the main asteroid belt, and Pluto.

Conclusions:

  • The automated hybrid optimal control method offers a desirable solution for complex low-thrust interplanetary mission design.
  • This approach significantly reduces the human effort and time required for preliminary mission analysis.