Intercept of sunrise on an Airplane - objective-c

Question

I want to calculate predicted Time of closest approach between an aircraft and Sunrise or Sunset keeping in mind:
Airplane Flying South-westbound as sunrise approaches
Red line is the GreatCircle Track on airplane.
Blue circle is the Airplane.
moment of intersection with sunrise and the Airplane
1- sun Declination (latitude) and crossing Longitude is known , plus the radius of sunrise which is approx 5450 Nautical miles, so sunrise can be shown as a circle with known centre and radius.
2- I used 2D Vector code which did not work since Great circle Path can not be applies to XY plane.
2- The Airplane is flying on Great circle Track which is curved and Latitude change is not Linear, how can I use Airplane Speed as Velocity Vector if latitude change is not constant ?
/// Va - Velocity of circle A.
Va = new Vector2(450, 0);
I used c# code
/// Calculate the time of closest approach of two moving circles. Also determine if the circles collide.
///
/// Input:
/// Pa - Position of circle A.
/// Pb - Position of circle B.
/// Va - Velocity of circle A.
/// Vb - Velocity of circle B.
/// Ra - Radius of circle A.
/// Rb - Radius of circle B.
// Set up the initial position, velocity, and size of the circles.
Pa = new Vector2(150, 250);
Pb = new Vector2(600, 400);
Va = new Vector2(450, 0);
Vb = new Vector2(-100, -250);
Ra = 60;
Rb = 30;
/// Returns:
/// collision - Returns True if a collision occured, else False.
/// The method returns the time to impact if collision=true, else it returns the time of closest approach.
public float TimeOfClosestApproach(Vector2 Pa, Vector2 Pb, Vector2 Va, Vector2 Vb, float Ra, float Rb, out bool collision)
{
Vector2 Pab = Pa - Pb;
Vector2 Vab = Va - Vb;
float a = Vector2.Dot(Vab, Vab);
float b = 2 * Vector2.Dot(Pab, Vab);
float c = Vector2.Dot(Pab, Pab) - (Ra + Rb) * (Ra + Rb);
// The quadratic discriminant.
float discriminant = b * b - 4 * a * c;
// Case 1:
// If the discriminant is negative, then there are no real roots, so there is no collision. The time of
// closest approach is then given by the average of the imaginary roots, which is: t = -b / 2a
float t;
if (discriminant < 0)
{
t = -b / (2 * a);
collision = false;
}
else
{
// Case 2 and 3:
// If the discriminant is zero, then there is exactly one real root, meaning that the circles just grazed each other. If the
// discriminant is positive, then there are two real roots, meaning that the circles penetrate each other. In that case, the
// smallest of the two roots is the initial time of impact. We handle these two cases identically.
float t0 = (-b + (float)Math.Sqrt(discriminant)) / (2 * a);
float t1 = (-b - (float)Math.Sqrt(discriminant)) / (2 * a);
t = Math.Min(t0, t1);
// We also have to check if the time to impact is negative. If it is negative, then that means that the collision
// occured in the past. Since we're only concerned about future events, we say that no collision occurs if t < 0.
if (t < 0)
collision = false;
else
collision = true;
}
// Finally, if the time is negative, then set it to zero, because, again, we want this function to respond only to future events.
if (t < 0)
t = 0;
return t;
}
I accept any answer in any language:
JAVA , JS, Objective-C , Swift , C#.
All I am looking for is the Algorithm. and how to Represent the Airplane Speed as Velocity Vector2D or Vector3D.