orbital | High level orbital mechanics package | Animation library

I am trying to solve a low thrust optimal control problem for Earth orbits, i.e. going from one orbit to another. The formulation of the problem includes six states (r_1, r_2, r_3, v_1, v_2, v_3) and 3 controls (u_1, u_2, u_3) with a simplified point model of gravity. When I specify the full initial state and half of the final state, the solver converges and yields a good solution. When I try the full final state, the problem is over constrained.

My thought on how to remedy this is to allow the trajectory to depart the initial orbit at any point along the orbital curve and join the final orbit an any point along the final orbital curve, giving it more degrees of freedom. Is there a way to constrain the initial and final values of all 6 states to a cspline curve? This is what I have tried so far:

Following this excellent tutorial on making a procedural solar system, and so far it's coming along nicely. My only problem with it is that the orbit speeds aren't as accurate as I'd like. I want the orbital periods to follow Kepler's Third Law. Only problem is that I don't know how to get it to work like that.

Here is the code related to the orbits. How do I get it to work how I want it to?

Short version

As suggested in comments, I am leaving a summarized, short version of the problem I found here. The original complete explanation can be found below.

In summary, I am currently using the deSolve package and am interested in implementing events in response to root functions. I understand that I can use such events to introduce sudden changes in the state variables of the model, but I would like to also modify parameter values of the model in response to such root functions.

Is this possible?

Long version

I have implemented an orbital numerical propagator (a function to calculate the position of a space satellite given an initial position and velocity state) in R. The problem is formulated as a set of 6 ODEs (X, Y and Z components for position and velocity). My implemented models calculate the acceleration at any given time, and then I use the deSolve package to perform integration and calculate the trajectory.

A key parameter that must be decided when performing such calculation is the center of the frame of reference, which is usually placed at the center of mass of the celestial object that exerts the most significant gravitational influence on the satellite. This is because, even though in principle it is possible to perform integration and calculate the trajectory using any arbitrary frame of reference, in practice we only obtain reasonable results when the center of coordinates is placed on the celestial object that exerts the main gravitational influence (i.e., Earth for Earth-orbiting satellites, Moon for Moon-orbiting satellites, and so on), as discussed in this SE question.

Initially, my implementation used a constant center of coordinates, either provided by the user or automatically determined from the sphere of influence of the different main celestial objects.

However, this is not appropriate for modeling interplanetary space missions, since the celestial object that exerts the main gravitational influence changes during the trajectory. A good example is the Apollo missions, where satellites started in an Earth orbit, and then moved to a Moon orbit.

I have managed to detect when such changes of the central celestial object happen, and return it as part of the results of the integrator. However, in order to actually perform the correct modeling, the central body being used during integration needs to be changed when these changes are detected. This process of "changing the central body" involves two tasks (note that it is just a shift of the center of coordinates, with no rotations involved):

1. Subtracting the coordinates of the celestial body to be used as the new center of coordinates from the coordinates of the satellite (by doing so, the coordinates of the satellite are now referred to the new celestial body).
2. Modifying the value of the argument specifying the central celestial body that is passed to the function calculating acceleration, which is one of the elements of the list of parameters provided to the function defining the ODE model.

I believe Task 1 can be easily solved by using a root-activated event. In order to do so, I define a variable in an environment specifically created for this purpose that stores the value of the automatically calculated celestial body that exerts the main gravitational influence in each iteration of the integrator. At a new iteration, a new value is calculated, and is compared with the previous value. If it is the same, nothing happens. But if it is different, a root function would return 0, triggering an event function. The event function would then return the position minus the coordinates of the new central celestial body.

However, I am unsure about how to perform Task 2, since this would involve changing one of the initial parameters provided to the ODE model. Any ideas on this would be greatly appreciated! (either a continuation of my approach, or a completely different one).

I am leaving a simplified version of the involved code.

My main function is called hpop, and is the user-level function to which the initial state vector and other parameters are passed. It looks like this:

I’ve got very basic knowledge of JS. Following three.js docs Loading 3D models I have succesfully rendered 3D object and centered it:

I'm learning three.js, and I'm implementing it in my angular 11 project, I made a very simple demo using a SphereBufferGeometry, and I deployed it to github pages, when I'm browsing it on an android phone, it's working normally, but when I open it on an iphone (safari), all the UI disappear and all I see is a grey background

this is my component ts file:

Hey and thanks for your help in advanced.

I've watched a few youtube videos on how to add Solar System and orbiting Gravity in Unity and ended up using the this for help for the solar system gravity part.

https://www.youtube.com/watch?v=Ouu3D_VHx9o&t=114s&ab_channel=Brackeys

But right after i decided to trying to make my planet orbit the sun i used this Wikipage for the math equation

• https://en.wikipedia.org/wiki/Orbital_speed

But for some reason either my planets flies away of the sun start flying towards the planet. I've been looking around for 2 days and can't seem to make it work and tried diffrent type of possiblies.

Here is my code

i am new to webgl and i am currently learning shaders. i am currently trying to make pointers with plane buffer geometry but currently , shader wont compile .

this the error i face when trying to compile

i am new to webgl and i am currently learning shaders. i am currently trying to wrap a texture around a sphere to give an earth globe image but faced issues when trying to do so, with the fragments and vertex glsl.

this is the error i am currently facing, and it occurs when i try to load the texture

I am creating a Space simultation in Unity using Newtons Law of gravitation and Centripetal force calculations to re-create the motion of the planets. Recently i have tried to implement realistic masses such as 3.285e+23 and i have converted them to managable numbers using a massScale 1e-24f. but since implementing these new masses and converting them, the smaller planet of the three has started deleting itself shortly after runtime without any error being thrown. I will also add that i dont have any sort of Destroy Line in my code either.