Skip to main content Accessibility help

Vector Solution for the Intersection of Two Circles of Equal Altitude

  • Andrés Ruiz González (a1)

A direct method for obtaining the two possible positions derived from two sights using vector analysis instead of spherical trigonometry is presented. The geometry of the circle of equal altitude and of the two body fixes is analyzed, and the vector equation for simultaneous sights is constructed. The running fix problem is also treated.

Corresponding author
Hide All
1. Bowditch, Nathaniel, (1995). The American Practical Navigator. Pub. N°9, DMA.
2. Admiralty Manual of Navigation, Volume 1, BR 45 (1), General, Coastal Navigation and Pilotage. (1987–2006), TSO London. ISBN: 978-0-11-772880-6
3. Admiralty Manual of Navigation, Volume2, BR 45 (2), AstroNavigation. (2004) TSO London. ISBN: 1-870077-65-2
4. Watkins, R. and Janiczek, . (1978–79) P. M., Sight Reduction with Matrices, NAVIGATION, Journal of The Institute of Navigation, Vol. 25, No. 4, 447–48.
5. Severance, W. Robert. (1989). Overdetermined celestial fix by iteration. IoN Vol. 36, No. 4.
6. Metcalf, T. R. (1991). Advancing Celestial Circles of Position, NAVIGATION, Vol. 38, No. 3, 285288.
7. Kaplan, G. H. (1996). The Motion of the Observer in Celestial Navigation, Navigator's Newsletter, Issue 51, 1014.
8. Navigational Algorithms - Vectorial equation of the circle of equal altitude. (2006). Andrés Ruiz González,
9. Max, Kurtz. (1991) Handbook of Applied Mathematics for Engineers and Scientist. McGraw-Hill. ISBN 07-035685-8
10. Gery, W. Stanley. (1997). The Direct Fix Of Latitude And Longitude From Two Observed Altitudes. NAVIGATION Vol. 44, No. 1.
11. Van Allen, A. James. (1981). An Analytical Solution Of The Two Star Sight Problem Of Celestial Navigation. NAVIGATION Vol. 28, No. 1.
12. Torben, Kjer. (1981). Unambiguous two body fix methods derived from crystallographic principles. NAVIGATION Vol. 28, No. 1.
13. Kotlaric, S. (1981). K-12 Method By Calculator: A Single Program For All Celestial Fixes, Directly Or By Position Lines NAVIGATION Vol. 28, No. 1, 1981
14. Bennett, G. G. (1979). General Conventions And Solutions-Their Use In Celestial Navigation. NAVIGATION Vol. 26, No. 4.
15. Daub, C. T. (1979). A Completely Programmable Method Of Celestial Navigation. NAVIGATION Vol. 26, No. 1,
16. Ogilvie, R. E. (1977) A New Method Of Celestial Navigation. NAVIGATION Vol. 24, No. 1
17. A'Hearn, M. F., and Rossano, G. S.. (1977) Two Body Fixes By Calculator. NAVIGATION Vol. 24, No. 1
18. Flynn, R. W.. (1972). Computer Sight Reduction Based On Intersection Of Equal Altitude Circles. NAVIGATION Vol. 19, No. 1
19. Kotlaric, Stjepo. (1971). New Short Method Tables (K11) For Direct Finding Of A Two Star Fix Without Use Of Altitude Difference Method. NAVIGATION Vol. 18, No. 4
20. Earle, Michael, A. (2000). A Vector Solution for Navigation on a Great Ellipse. Journal of Navigation, 53, 473481.
21. Chih-Li, Chen, Tien-Pen, Hsu and Jiang-Ren, Chang. (2004). A Novel Approach to Great Circle Sailings: The Great Circle Equation. Journal of Navigation, 57, 311320.
22. Earle, Michael, A. (2005). Vector Solutions for Great Circle Navigation. Journal of Navigation, 58, 451457.
23. Wei-Kuo, Tseng and Hsuan-Shih, Lee. (2007). The Vector Function for Distance Travelled in Great Circle Navigation. Journal of Navigation, 60, 158164.
24. Wight, C. (1976). Direct Methods Of Latitude And Longitude Determination By Mini-Computer. NAVIGATION Vol. 23, No. 2
25. Fox, C. (1975) Finding Latitude And Longitude By Calculators. NAVIGATION Vol. 22, No. 4
26. Dozier Charles, T. (1949). A Simultaneous Two-Star Fix. NAVIGATION Vol. 2, No. 4, 1949
27. Little, Joseph, W. (1967). An Engineering Approach To The Mathematics Of Celestial Navigation. NAVIGATION Vol. 14, No. 3
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Navigation
  • ISSN: 0373-4633
  • EISSN: 1469-7785
  • URL: /core/journals/journal-of-navigation
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed