Questions tagged [three-body]

Questions regarding the relative motion of three masses.

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0answers
31 views

Hill approximation of the CRTBP (Circular Restricted Three-Body Problem) derivation

Dear fellow space enthusiasts, Let us first consider the classical CRTBP equations of motion by defining the position vector of the spacecraft \begin{equation} \boldsymbol{r}=[x,y,z]^{T}, \end{...
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Why does it cost more to get to L4/5 than C3=0?

I was looking at Delta-V budgets and noticed that it costs 4.1 km/s to get from LEO to L4/5, but just 3.2 km/s for LEO to geocentric C3 = 0 (escape velocity). I find that counter-intuitive. Why does ...
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1answer
94 views

Nickname and citation for famous, historic three-body spacecraft trajectory design “manual”; something like “DoKaRoMo”?

There is a heavily-cited work about the use of three-body orbits with four authors, I think some at NASA at the time. I know that I've cited this abbreviation in my own posts a few times, but I can't ...
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Station-keeping delta-v per year for an Earth-Moon vanilla halo orbit?

This answer reminds us that an Earth-Moon L1 or L2 vanilla1 halo orbit remaining always visible to some patch on the Moon's surface requires station-keeping. Queqiao uses such an orbit having ...
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1answer
107 views

Why shouldn't we illustrate spacecraft trajectories on top of static pseudo-potential surfaces?

Three-body spacecraft orbits1 are regularly discussed here and from time to time someone will include a pseudo-potential plot from Wikipedia in their explanation. The discussion often goes south when ...
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Thrown-together $200 million mission to asteroid 2020 SO; check out or nudge to longer-lasting mini-moon orbit

This tweet says in part: Earth's potential new minimoon, 2020 SO may be the Surveyor 2 Centaur rocket body, launched in September 1966. Integrating backwards shows 2020 SO2 to also be orbiting Earth ...
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How many times will the Photon fire its Curie in order to “reach the right spot” to deploy CAPSTONE towards the Moon?

The Verge's How small launcher Rocket Lab plans to pull off its first mission to the Moon next year says (though this has since been addressed†): Photon is going to need it all in order to get NASA’s ...
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How is it possible to connect trajectories at a Poincare section using the “bisection” method?

When constructing a heteroclinic connection (a connection between two different periodic orbits at two different libration points), the stable and unstable manifolds of two different libration points ...
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110 views

What does the term “libration point gateway” mean?

In the Circular Restricted Three Body Problem, natural paths exist between periodic orbits or the libration points that have negligible cost. These are commonly known as free transfers between ...
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Is the Jacobi constant stationary along a periodic orbit?

In the book called "Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems", link here, the author states that if the dynamical system has an integral of motion which is not ...
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162 views

What is the physical interpretation of the eigenvalues of the monodromy matrix and how are they associated with the invariant manifolds?

To define the monodromy matrix, assume that the period for one cycle of a halo orbit is denoted as $T$, the initial time as $t_0$, and the state-transition matrix is defined as $\phi$. Then, the ...
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178 views

Are there some three-body orbits that can't be escaped? Can we know without propagating forever?

update: Searching for "choreographies" I found this Physics SE question which is related but different because it asks only if periodic solutions can be proven to be periodic numerically and my ...
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Who called the Lagrangian points as “Libration” points and and why was the terminology “Libration” used?

I am curious about the naming and why were the equilibrium solutions of the CR3BP called as Libration points? Who called them that and what is the history behind it?
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How can you construct the periodic orbits around libration points L1 and L2 in the circular restricted three-body problem and prove their existence?

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 ...
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Why do we prefer using the rotating reference frame rather than the Inertial frame in the three-body problem?

As the title says, I wanted to ask why do we prefer using the rotating reference frame rather than the Inertial frame in the three-body problem to place the primaries? And how is it better for ...
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164 views

How does a butterfly orbit move in 3D? Way to generate or visualize?

The paper Earth-Moon Near Rectilinear Halo and Butterfly Orbits for Lunar Surface Exploration (AAS 18-406) says Periodic Orbits in the Earth-Moon System The current investigation focuses on three ...
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Does Kerbal Space Program have a software migration path to Lagrange points, halo orbits, and other 3-body goodies?

At about 05:37 in Scott Manley video Kerbal Space Program 2 - What We Know About The Sequel So I’m cautiously optimistic and I really obviously want this to be ...
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198 views

Do horseshoe orbits have anything to do with Lagrange points? Do words fail us here?

I said (2010 SO16 is associated with Lagrange point L3 but wanders so far behind and ahead of it that the orbit is called "horseshoe"... and the comment was made: Not really. L3 is unstable. ...
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How well can the orbits of Jupiter Trojans to be visited by Lucy be predicted?

The orbits of the large planets are very well known and their position may be precisely predicted for the planning of complex swing by maneuvers of interplanetary space probes. There are exact ...
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139 views

Do Lissajous orbits have stable/unstable manifolds?

The question Did DSCOVR travel “along the stable manifold of it's future SE L1 Halo orbit” to get there? is specific to DSCOVR's trajectory from Earth to its primarily heliocentric orbit near Sun-...
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How to find Near Rectilinear Halo Orbits (NHROs)?

Looking all the good questions and answers in this site referent to CR3BP dynamics, periodic orbits, state transition matrices, etc. I wonder: what algorithm or steps do I have to follow to find the ...
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Software (besides Ltool) to simulate CR3BP (three body) problems?

Are there any other softwares for CR3BP besides Ltool? As I've learnt here Ltool is not generally available to the public. I would like to simulate three body orbits within the standard circular ...
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175 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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Going from LEO to lunar using only low-thrust ion propulsion - can it be done?

@SF.'s question What are the parameters of the new Iodine electrical rocket engine developed by RSC Energia? links to the short RT article 'Ten times cheaper': Russian space company testing iodine ...
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149 views

Efficient trajectories from earth orbit to EML-1

What are the lowest delta-v trajectories a spacecraft could take from Earth to EML-1? (Earth Moon Lagrange point 1). provided the payload is massive. ( the amount of time it takes is not an issue)
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Did DSCOVR travel “along the stable manifold of it's future SE L1 Halo orbit” to get there?

I just wrote (and have since removed) the following paragraph in this answer: As can be heard in this video SpaceX's launch of the DSCOVR spacecraft to Sun-Earth L1 went there almost directly. The ...
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“Pythagorean Three Body Problem” - need some points from an accurate solution for comparison

note: if you up-vote (or even if you don't), don't forget to scroll down and see the excellent answer as well - it's beautiful! The Pythagorean Three Body Problem also know as Burrau's problem is a ...
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1answer
2k views

Are some Halo Orbits actually Stable?

UPDATE: I found another reference! While I always enjoy a good video starring Jimmy and Linda Carter, this one has Dennis Wingo describing ISEE-3's original Halo orbit. He describes Sun-Earth $L_1$ as ...
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561 views

Balancing a mirror

A possible way of heating up Mars is to use mirrors to direct more sunlight towards the planet. I am not asking about the feasibility or cost of such a gigantic project, but I have a question ...
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503 views

A constant parameter in a three body system?

In a two body system, there are a lot of orbital parameters not changing over time, like eccentricity or the orbital plane. A constant parameter can be a combination of two or more, like even though ...
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Low Energy Transfer within Earth-Moon system

Practical aspects of a total low energy transfer to the Moon have been seen in missions like GENESIS, which uses Weak stability Boundary legs of Earth and Sun to reach ESL-2. This four body model ...