30

The piece that you are asking about not only can be done, but it has been done. SMART-1 was launched in to GTO in 2003 and entered orbit around the Moon in 2004, using only an Ion engine to do so. It gradually reduced its orbit around the Moon, eventually colliding in to it. The trick is to use the Lagrange points to give one more time to do a proper orbit.


6

The rotating reference frame is usually preferable over an inertial reference frame when analyzing three-body motion. Two main reasons for this: The motion is determined by the two primary bodies, so it makes sense to use these to define the reference system The typical three-body dynamics for which you would use such a reference system, such as Libration ...


5

You have missed another option for mirror placement, orbit them around the Mars. In much the same way as Larry Niven's, Ringworld is built. Your circle of mirrors are in a polar orbit of Mars. The mirrors always face the sun and direct the light to the surface of Mars. You might need to do something with the moons of Mars to prevent issues between the ...


4

There are really two questions here: Do there exist $n$-body systems with long-term stability? Can a third body (massive or not) be shown, a-priori, to be bounded or to escape—without resorting to numerical simulation? 1. Stability of $n$-body systems It is widely known that $n$-body systems are "chaotic" when $n>2$. However, this must be unpacked ...


4

There are a couple of potential solutions to this problem. One would be to place the mirrors at a distance just a little closer to Mars than the L2 point and let the radiation pressure counter the weak Mars net gravity field. One doesn't have to be right in line either, but a "halo" orbit circling the Mars/Sun line would allow you to balance forces while ...


4

@ChrisR's comment I'm not sure I understand why using a Lagrange point would help. Couldn't one simply raise the orbit slowly until it passes the sphere of influence of the Earth (which is a virtual boundary not a real one of course), and then slow down such that the vehicle is in a highly elliptical orbit around the Moon, and then circularize it? Going ...


3

To answer the revised question, "does KSP have a software migration path that will allow for n-body physics options" Yes, it has its "mod" framework, which has been used to provide these features for several years.


3

Normally I don't answer my own questions, and certainly not right-away, but since there are forces trying to close the question in part because the answer will not be about space exploration, I'd like to get at least one answer in, and at the same time demonstrate that they are wrong. Will Kerbal Space Program 2 have Lagrange points, halo orbits, and other ...


3

"Libration" comes from latin "librare" and means "to keep balance". And this is because in a three-body problem objects keep balance in this points. I do not know who named it "Libration Points" first, I would assume LaGrange or Euler. I would even assume: they have been first called "libration points" and later "LaGrange Points". Nethertheless: both means ...


3

I just ran it, and mine look pretty much like those in the paper. See some coordinates at the bottom. Here are some {x,y} coordinates at the times in the left column: 0. {1.,3.} {-2.,-1.} {1.,-1.} 5. {2.46917,-1.22782} {-2.2782,-0.20545} {0.34106,0.901049} 10. {0.77848,0.141392} {-2.02509,0....


3

To double the insolation on Mars would require a mirror or array of mirrors with an area, projected onto a plan perpendicular to the Sun-Mars line, equal to that of Mars itself divided by the efficiency of the system. In principle, there appear to be three places where such a reflector could be: the first or second Lagrange point or a Sun synchronous polar ...


3

That would be the Jacobi integral ($C_\text{J}$, or $C_\text{H}$ in Hill's problem): In celestial mechanics, Jacobi's integral (also The Jacobi Integral or The Jacobi Constant; named after Carl Gustav Jacob Jacobi) is the only known conserved quantity for the circular restricted three-body problem. Unlike in the two-body problem, the energy and ...


3

Wow, three years and still no answers!. I will give it a try. What I am going to answer applies just for transfers between periodic orbits at the Lagrangian points (the OP asked so many things but I think that is the fundamental one) Let's put that we want to transfer from Earth-Moon L1 to L2 using the CR3BP dynamics Define the periodic orbits around L1 ...


2

There is another parameter known as Tisserand's parameter which stays constant for a given body in 3 body probelm. This is more useful in identifying any given asteroid or comet. Given by $T = \dfrac{a_e}{a}+2\sqrt{\dfrac{a}{a_e}(1-e^2)}cos(i)$ where e subscript represents parameters of perturbing body and no subscript for small body. It stays constant ...


2

In fact it could be arbitrarily low. But wait before you rejoice. The Moon has an elliptic trajectory. This elliptic motion perturbs any orbit of a satellite in LEO. If you first assume your satellite is in the same plane as the Moon and describe the system as a time dependent Hamiltonian system with two degrees of freedom, a process called Arnold diffusion ...


2

Yes it is constant along the trajectory as the Jacobi energy is computed using the initial state vector. From Wikipedia's Jacobi integral: In celestial mechanics, Jacobi's integral (also known as the Jacobi integral or Jacobi constant) is the only known conserved quantity for the circular restricted three-body problem. Unlike in the two-body problem, the ...


2

Eigenvalues and Eigenvectors Before specifically addressing the monodromy matrix, it's important to make sure you have a physical understanding of what eigenvalues and eigenvectors represent in general. I highly recommend 3blue1brown's youtube video on this topic: I will distill the important points below. Consider the two-...


1

Assume three point masses, Newtonian gravity and no losses. If we can also assume no perturbations of any other kind, and perfect placement of the bodies in the initial conditions, then a 3-body Klemperer rosette -- three bodies of equal mass, in an equilateral triangle, with any rotationally symmetrical initial velocities comfortably below barycentric ...


1

This is a supplemental answer to @CallMeTom's answer. Wikipedia's Lagrangian point; History says: The three collinear Lagrange points (L1, L2, L3) were discovered by Leonhard Euler a few years before Joseph-Louis Lagrange discovered the remaining two3,4 3"KoLoMaRo" (Wang Sang Koon, Martin W. Lo, Jerrold E. Marsden and Shane D. Ross) Dynamical ...


1

@Diane’s answer to the question Ordering of the Lagrange points describes how different so-orbital situations are connected with one another. The curves drawn there represent "zero-velocity" curves in the co-rotating frame. These are not the true orbits; but they serve as bounds to the actual orbits. They may also approximate orbits that remain close to ...


1

One way is to choose an Earth apoapsis distance, then simply try many of them, where many = thousands or even millions, and see which ones result in something that is close enough to periodic to meet your currently unstated criterion for what would be considered a sufficiently "distant retrograde orbit around Earth". I believe (someone please correct me ...


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