Questions tagged [three-body]

Questions regarding the relative motion of three masses.

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Can a gravity assist be designed without using simulation?

Suppose a three body scenario with an artificial satellite, a planet (much massive than the satellite), and a sun (much massive than the planet). There is no other significant force on these three ...
paki eng's user avatar
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Why is the Sun influence a mere perturbation to the Moon NRHO (the orbit the Gateway should be put in the context of project Artemis)?

An article of the relevant literature Heliocentric Escape and Lunar Impact from Near Rectilinear Halo Orbits asserts: "As the spacecraft departs the immediate vicinity of the NRHO, the effects of ...
Franklin's user avatar
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Can Tisserand's parameter be modified to correct for perturbing eccentricity?

Tisserand's parameter is an "almost" conserved quantity in the CR3BP, even after flybys (useful for identifying asteroids). $$T_P = \dfrac{a_p}{a}+2\sqrt{\dfrac{a}{a_p}(1-e^2)}\cos(i)$$ It ...
SE - stop firing the good guys's user avatar
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At what point did Artemis 1's Orion execute the orbital inclination change for its return transit?

Orion is returning to Earth with a marked orbital inclination compared to its Lunar Distant Retrograde Orbit (DRO). Orbital inclination changes require a great deal of delta-v, and Orion is on a tight ...
Woody's user avatar
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What is the substantial difference between transit orbits and manifold trajectories in the frame of circular restricted three body problem?

In my MSc thesis I faced the problem of unstable hyperbolic invariant manifold trajectories (UHIMs) emanating from planar Lyapunov orbits around two collinear Lagrange points L1 and L2 of the Sun-...
g_don's user avatar
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If Earth had a second moon, where would it be positioned? [closed]

Could Earth theoretically have another moon, beside the existing one, that would have a stable orbit? If it is possible, could Newtonian physics describe where it would be (i.e its position relative ...
Hale's user avatar
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What are "transcritical, pitchfork, period-doubling, torus, and subharmonic bifurcations" in the context of three-body orbits? (e.g. butterflies)

MattB's excellent and well-sourced answer to Where do the butterflies land on this bifurcation plot? (Earth-Moon three-body butterfly orbits) begins: I'm fairly certain that the butterfly family is ...
uhoh's user avatar
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Where do the butterflies land on this bifurcation plot? (Earth-Moon three-body butterfly orbits)

Below is a $\mu = 0.01215$ bifurcation plot from E. J. Doedel, E.J. et al's Elemental periodic orbits associated with the libration points in the circular restricted 3-body problem International ...
uhoh's user avatar
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How does JPL define the exact position of Lagrange points in the real solar system where (I thought that) they can't be defined?

My answer to Does the distance to L2 vary? is The correct answer is "No, they are only mathematically defined when the orbit is circular". but @DavidHammen's answer explains that they can ...
uhoh's user avatar
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Where is Artemis on this Earth-Moon three-body bifurcation plot? Where's the near-rectilinear halo orbit for example?

Below is a $\mu = 0.01215$ bifurcation plot from E. J. Doedel, E.J. et al's Elemental periodic orbits associated with the libration points in the circular restricted 3-body problem International ...
uhoh's user avatar
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Why did we think that the object was gonna hit the Moon March 4th 2022? Who's been tracking and predicting it so closely?

The Guardian's 'Out-of-control' Chinese rocket falling to Earth... Oops, I mean Out-of-control SpaceX rocket on collision course with moon says that Bill Gray's Project Pluto/DSCOVR says that the 2015 ...
uhoh's user avatar
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Is JWST Halo orbit prograde or retrograde and why?

There is confusion in my mind over the direction of JWST’s halo orbit, depending in the source of graphics. Observing from the Earth, does JWST orbit clockwise or counterclockwise around the antisolar ...
Woody's user avatar
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JWST Halo Orbits for Dummies: can halo orbits be usefully approximated by Simple Harmonic Motion?

Halo Orbits for Dummies: can halo orbits be usefully approximated by Simple Harmonic Motion? I am an undergraduate in the Kerbal Academy of Astrodynamics. Patched conics have given me an intuitive ...
Woody's user avatar
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After CAPSTONE inserted to "highly efficient ballistic lunar transfer trajectory" by Lunar Photon; to what separate orbit for its safe disposal? How?

NASA Ames's feature CAPSTONE’s CubeSat Prepares for Lunar Flight says CAPSTONE will use a hydrazine-fueled propulsion system during most of its three- to four- month journey to the Moon. This line of ...
uhoh's user avatar
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Is there a fairly detailed outline of CAPSTONE's "highly efficient ballistic lunar transfer trajectory" from LEO to lunar near-rectilinear halo orbit?

NASA Ames's feature CAPSTONE’s CubeSat Prepares for Lunar Flight says CAPSTONE will use a hydrazine-fueled propulsion system during most of its three- to four- month journey to the Moon. This line of ...
uhoh's user avatar
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Did New Horizons look for "sailboats" in the Pluto-Charon system's sailboat region? Did it pass through it or avoid it?

In this answer to If we could send an orbiter to the Pluto-Charon system, could we put it in a stable orbit? I wrote: Totally by accident I've just happened to run across the 2014 open access paper A ...
uhoh's user avatar
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Earth-Sun decayed L1 to L4 transfer

Assume CR3BP (Circular Restricted 3-Body Problem) where a satellite occupies the Earth-Sun L1 point. The satellite dies, stops station-keeping, experiences a small perturbation (minimal effect on ...
Curtis Klein's user avatar
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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{...
space_monkey's user avatar
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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 ...
Schwern's user avatar
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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 ...
uhoh's user avatar
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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 ...
uhoh's user avatar
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8 votes
3 answers
614 views

Why shouldn't we illustrate spacecraft trajectories on top of static zero velocity 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 ...
uhoh's user avatar
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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 ...
uhoh's user avatar
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4 votes
1 answer
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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 ...
uhoh's user avatar
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1 vote
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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 ...
John's user avatar
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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 ...
John's user avatar
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2 votes
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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 ...
John's user avatar
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8 votes
1 answer
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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 ...
John's user avatar
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4 votes
2 answers
537 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 ...
uhoh's user avatar
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2 votes
2 answers
437 views

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?
John's user avatar
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2 votes
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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 ...
John's user avatar
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5 votes
1 answer
309 views

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 ...
John's user avatar
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8 votes
1 answer
569 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 ...
uhoh's user avatar
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7 votes
3 answers
3k views

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 ...
uhoh's user avatar
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2 votes
2 answers
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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. ...
uhoh's user avatar
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4 votes
1 answer
159 views

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 ...
Uwe's user avatar
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4 votes
1 answer
426 views

Do ("non-halo") Lissajous orbits have stable/unstable manifolds?

The question Did DSCOVR travel “along the stable manifold of its future SE L1 Halo orbit” to get there? is specific to DSCOVR's trajectory from Earth to its primarily heliocentric orbit near Sun-Earth ...
uhoh's user avatar
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2 votes
0 answers
551 views

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 ...
Julio's user avatar
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3 votes
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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 ...
Karthi Ramachandran's user avatar
1 vote
1 answer
273 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?
NtinosG's user avatar
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21 votes
2 answers
3k views

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 ...
uhoh's user avatar
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1 vote
1 answer
253 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)
Sam G.'s user avatar
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Did DSCOVR travel "along the stable manifold of its future SE L1 Halo orbit" to get there?

I just wrote (and have since removed) the following paragraph in this answer to How many times do you have to circle the Earth to break orbit?: As can be heard in this video SpaceX's launch of the ...
uhoh's user avatar
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6 votes
1 answer
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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 ...
uhoh's user avatar
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17 votes
4 answers
4k views

Are some Halo Orbits actually Stable? (stable orbits about unstable Lagrange points)

update: some more sources; the broken site spacecraftforall.com/a-new-orbit used to have an interactive simulation, here's an old screen shot: Hat tip to @NgPh for finding this Space College page ...
uhoh's user avatar
  • 149k
11 votes
4 answers
860 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 ...
SE - stop firing the good guys's user avatar
4 votes
2 answers
670 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 ...
SE - stop firing the good guys's user avatar
12 votes
1 answer
1k views

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 ...
Kuldeep Barad's user avatar