Gravity and deltas

[2NywAqkS]

I've got a nice program I'm working on which simulates gravitational orbits however I'm having a lot of problems surrounding the use of time deltas. Where should they go, because where ever I put the * delta, adjusting it completely changes the orbit path(e.g. Flies of into space).

My Code:

double dx = -x;
double dy = -y;
double direction = atan2(dy, dx);
double distanceSquared = (dx*dx + dy*dy) / 10;

double force = 0.004 * ((mass * solarSystem->mass)/(distanceSquared));
double acceleration = force / mass;

double xacceleration = acceleration * cos(direction);
double yacceleration = acceleration * sin(direction);

xVel += xacceleration;
yVel += yacceleration;

x += xVel * delta * 0.01;
y += yVel * delta * 0.01;

[ne555]

double distanceSquared = (dx*dx + dy*dy) / 10; ¿why 10?
x += xVel * delta * 0.01; ¿why 0.01?

> Where should they go
Where there is time involved.

Also, you are considering that acceleration and velocity are constant in a chronon, that will introduce error.

[2NywAqkS]

¿why 10?

to give the effect that it is closer.

¿why 0.01?

to slow down time in my program.

As for your last point, I have thought of that but I can't think of a solution. Is it the chronon problem that is cause the inconsistencies in relation to fps? or do I need to multiply more things by delta?

[Stewbond]

When I do these types of problems, I like to add dT as an argument. Then my callback timer will determine the value of dT when calling this function.

Now, in terms of where I´d put dT in this case: Certainly lines 12 and 13 need it. In those lines you are summing the acceleration. I think you mean to integrate it. remember:
a = dv/dt; so dv = a*dt

Likewise:
v = dx/dt; so dx = v*dt

That means that you certainly need it in lines 15 and 16 as well (which you already have).

Regarding the 0.01, don´t factor it in here. It isn´t part of the integration. Consider it only when calculating the dT so that no matter when you use delta, it will be correct. It certainly is not a problem to do this, especially since simulating the earth around the sun would otherwise take a year to compute, but you have to ensure that the same constant is applied everywhere and the only safe way to do that is at the source.