TryGetSecant.cs

public bool TryGetSecant(Vector3 position, Vector3 velocity, Vector3 acceleration, float arcDistance, out Vector3 secant) {
	if (acceleration == Vector3.zero) {
		secant = velocity;
		return false;
	}

	var axis = Vector3.Cross(velocity, acceleration);
	if (axis == Vector3.zero) {
		secant = velocity;
		return false;
	}

	var radius = Mathf.Pow(velocity.magnitude, 3.0F) / axis.magnitude;

	var inwards = Vector3.Cross(axis, velocity).normalized;
	var radiusVector = -inwards * radius;
	var center = position + -radiusVector;

	var angle = arcDistance / radius;
	var rotation = Quaternion.AngleAxis(angle * Mathf.Rad2Deg, axis);
	var endpoint = center + rotation * radiusVector;
	secant = position - endpoint;

	return !(secant == Vector3.zero);
}