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### How to best think of the State Transition Matrix, and how to use it to find periodic Halo orbits?

I'll state my mathematical question about the state propagation and state transition matrices first, then show you a simple problem for which I would like to use these concepts to generate a densely ...
742 views

### Are large halo orbits around L₁'s and L₂'s preferred over small orbits for reasons other than geometry?

There have been many examples of the placement of satellites in orbits around Lagrange points, most have been sun-earth and earth-moon $L_1$ and $L_2$ due to their proximity to earth. In each case ...
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### What is the difference between halo orbits and Lissajous orbits?

The Wikipedia articles for halo orbit and Lissajous orbit leave me wondering how these two orbits are different from an orbital mechanical point of view. Could they be discussed together here, so I ...
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### Could the Lunar Lagrange Points work for space telescopes?

Every orbit in space has its pros and cons. Low Earth Orbit has accessibility but frequent eclipses whereas a Solar Lagrange Point is clear and stable but distant. In the case of the Lunar Lagrange ...
207 views

### Is a solar free-return trajectory possible?

I'm coining a new phrase: "Dyson circuit". Is it possible, with current solar orbital capabilities (see Parker Solar Probe), to drive artificial satellites in a free-return trajectory around the Sun? ...
303 views

### Two-body problem VS Three-body problem Applications

The two-body problem deals with two bodies under certain assumptions while the restricted three-body problem deals with three bodies where one has a negligible mass (i.e. spacecraft or comet) I was ...
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### How to prepare for an interview for a Pure Mathematics position at ISRO's Space Application Center?

I have completed a Master's in Pure Mathematics. I have read topics like Abstract Algebra, Linear Algebra, Functional Analysis, Topology, Cryptography, Course in C++, etc. Recently I found an ...
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### How to get Ltool by Martin et.al?

I am just starting work on dynamics of CRTBP. Over several papers I see that "Ltool" is used for trajectory design, But I am unable to find over internet. Can somebody help me to identfy how to ...
167 views

### Can L3 have halo orbits?

I've recently said you see one co-linear libration point, you seen 'em all. That's what I always say and while halo and other orbits associated with Sun-Earth L1 and L2 work similarly, L3 is 2 AU ...
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### Is it obvious or easily-proven that L4 and L5 must be in the parental orbital plane?

Looking at the question and answer and diagrams from Are Lagrangian points associated only with the smaller body? got me wondering. L4 and L5 each form an equilateral triangle with the two main ...
176 views

### Distant retrograde Orbit in CR3BP Question

How can i calculate the initial vy0 component for a distant retrograde orbit in Sun-Earth CR3BP around Earth?
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### L2 point in multi-moon system

For an SF novel, if there were two large moons orbiting a planet, let's say one moon the size of Earth's moon and the 2nd moon about 20% larger, and the planet roughly the size of the Earth, would the ...
139 views

### Roughly how many kinds of closed or periodic orbits are there in the circular restricted three-body problem?

Question: Roughly how many kinds of closed or periodic orbits are there in the circular restricted three-body problem? Has anyone made an attempt to enumerate and classify/categorize them? Notes: If ...
Following up on a previous question about the classification of periodic orbits, how can they be constructed, especially the planar Lyapunov family, around libration points $L_1$ and $L_2$? And how ...