I don't know if this question get her place in physics.stackoverflow forum. I prefer post here, with code etc.

So, I want simulate 2D movements (no rotation) of an asteroid in space affected by a planet's gravity, the problem is how integrate that ? Any better integration for performance ?

Here is the code in C:

struct vec2 { float x; float y; }; struct body { double mass; //kg struct vec2 prev_pos; //for semi-implicit euler method struct vec2 pos; //position struct vec2 v; //velocity }; void move_asteroid(float dt) { //semi-implicit euler integration #1 -moving the object asteroid.pos.x += asteroid.v.x * dt; asteroid.pos.y += asteroid.v.y * dt; //START float x = planet.pos.x - asteroid.pos.x; float y = planet.pos.y - asteroid.pos.y; float d = x * x + y * y; //distance^2 between asteroid and center of planet //acceleration float ah = G * ((planet.mass * asteroid.mass) / d); //gravity //get components of gravity float rad = atan2(y, x); float ax = ah * cos(rad); float ay = ah * sin(rad); //semi-implicit euler integration #2 -update velocity asteroid.v.x += ax * dt; asteroid.v.y += ay * dt; } 

this is for 'fun' and sadly my knowledge is quite not good, I try to find with my vocabulary (not native english), if you have directions, ideas for better implementation (like study RK4 for correctness etc), it's welcome