Why a big moving attractor object gives a slingshot to other object with using gravity formula rathe-CodePudding

I have a big spherical Gameobject which moves forward in 3D with constant velocity. I have other spherical objects that other big object needs to attract to itself. I am using Newton's law of universal gravitation formula to attract other objects, but as expected, other objects are doing a slingshot movement much like the space shuttles doing when needed with other planets' orbits to accelerate.

I actually want a magnetic effect that without taking the masses into account, all other objects will be catched by the big object. How can I do that? Do I need a different formula? Or do I need to change the movement behavior of the objects altogether?

CodePudding user response：

If I got it right you expect to have something like this: https://www.youtube.com/watch?v=33EpYi3uTnQ

You can do a spherical raycast or have an sphere collider as trigger to detected the objects that are inside of your magnetic field.
Once you know those objects you can calculate the distance from each of them to the magnetic ball.
You can make an inverse interpolation to know how much strength/"magnetism" is getting into that object.
Then you can apply some force on the attracted object towards the magnetic ball's center.

Something like this algorithm:

var objectsInsideField = ListOfObjects;
foreach (o in objectsInsideField) {
    var distance = (o.position - center.position).magnitude;
    var strength = distance / fieldRadius; // fieldRadius == spherical radius
    o.AddForce(dir: o.position - center.position, strength: strength)
}

Of course, you need to do some adjustments and probably add some multipliers to make the force to be meaning.

The final result should be: for each sequential frame, if the object is inside the magnetic field it moves towards the center a bit. The next frame it should be even close to the center so the strength is even bigger.. and so and so.

CodePudding user response：

First of all, since the big objects is moving with constant velocity, a coordinate frame with axes parallel to the axes of the original coordinate system will be moving uniformly with constant velocity, so this new moving coordinate system is also inertial and you can write all your equations of motion in it, calculate everything with respect to it, and at the end you add the uniform movement to the results. The benefit is that the big object is stationary in this coordinate system, so simpler physics applies.

The slingshot effect occurs most likely because your objects are treated as mass-points, rather than bigger 3D entities (like spheres), for which the centers of mass never get too close enough. Hence maybe some sort of collision detection may eliminate this problem, especially if you decrease significantly or kill completely the elastic collision resolution.

All of what I am saying is a bit speculative as I have no access to details.