code: def arc_distance(theta_1, phi_1,
                         theta_2, phi_2):
      
      temp = np.sin((theta_2-theta_1)/2)**2+np.cos(theta_1)*np.cos(theta_2)*np.sin((phi_2-phi_1)/2)**2
      distance_matrix = 2 * (np.arctan2(np.sqrt(temp),np.sqrt(1-temp)))
      return distance_matrix
docs: Calculates the pairwise arc distance between all points in vector a and b.