XNA: adding a force to a vector

Question

i do have 2 points on a 2d plane. one has already an vector that does determine in which direction it will move.

now i want to add a vector to this existing vector. so he accelerates in the direction of the other point.

to be a bit more clear, it is about 2 asteroids flying in space (only 2d) and gravitation should move them a bit closer to each other.

what i did build till now is this:

c = body.position - body2.position;
dist = c.Length();

acc = (body.masse * body2.masse) / (dist * dist);

xDist = body2.position.X - body.position.X;
yDist = body2.position.Y - body.position.Y;

direction = MathHelper.ToDegrees((float)(Math.Atan2((double)yDist, (double)xDist)));

body.velocity.Y = body.velocity.Y + (float)(Math.Sin(direction) * acc);
body.velocity.X = body.velocity.X + (float)(Math.Cos(direction) * acc);

in the moment the direction calculated is completly off. surely i am making just a stupid mistake, but i have no idea.

Answer 1

Not completely sure what you try to do. Why can't you just use Vector2.Add(v1, v2)?

Answer 2

You need to pass your direction angle in in radians to Math.sin and Math.Cos (rather then in degree as you do in your smaple code).

see also: http://msdn.microsoft.com/en-us/library/system.math.sin.aspx

The angle, a, must be in radians. Multiply by Math.PI/180 to convert degrees to radians.

Answer 3

My mechanics and linear algebra are a bit rusty but I think you should be able to do it without resorting to trigonometry. These formulae probably need tweaking, I'm not sure if I got u and -u mixed up.

Here it is in pseudo code

T is whatever time period you're iterating over
G is the gravitational constant

body1 starts with  a velocity of v1
body2 starts with  a velocity of v2

c = body.position - body2.position

c1 is a vector
use the vector c to get a vector of length 1 in the direction of the force

u = c1 / c.Length()

body1 should have an acceleration vector of a1 =  G * body2mass/c.Length()^2 * (-u)

body2 should have an acceleration vector of a2 = G * body1mass/c.Length()^2 * (u)

body1 has a new velocity vector of v1 + a1/T

body2 has a new velocity vector of v1 + a2/T

rinse and repeat