The methods of celestial navigation to fix the ship position in line with the stars are only applied in the twilight time interval when both the celestial bodies and the horizon apppear simultaneously. This means that these methods cannot be used during the night even if the stars are visible. This paper proposes a novel approach which uses the azimuth of the celestial body in order to establish the great circle equation relating the observed body to the ship position when the celestial bodies appear. In addition, the proposed method does not demand the horizon and sextant equipment as with the previous methods. The key advantage which differentiates this method from previous ones is its ability to determine the ship position during the night when the horizon is invisible. Firstly, the vector calculus is applied to find the mathematical equation for the ship position through analyzing the relationship between the ship position and the great-circle azimuth of the observed body. Secondly, the equation system for the ship position is expanded into a standard system in which the input for the proposed mathematical system are the great-circle azimuth and the coordinates of the observed body. Finally, the numerical technique is also proposed to solve the nonlinear system for the ship position. To verify the validation of this proposed method, a numerical experiment is carried out and the results show that it can be applied well in practice.

Abstract
1. Introduction
2. The celestial sphere on Cartesian coordinatesystem
3. The observing azimuth of celestial bodies
4. The azimuth method for fixing the shipposition in celestial navigation
5. The algorithm of proposed method andnumerical experiment for validation
6. Conclusion
References

• Van-Suong NGUYEN(Faculty of Navigation, Vietnam Maritime University) Corresponding Author
• Nam-Kyun IM(Department of Navigation Science, Mokpo National Maritime University)
• Quang-Dan DAO(Faculty of Navigation, Vietnam Maritime University)