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Depression of a Foreground Reference Line

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Technical Report

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US Naval Observatory Washington United States

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In the Appendix on the following pages is a simple geometric development that provides a result that might be of use for celestial navigation. It assumes an observer at some height above the sea surfaceheight radius of the Earth looking toward the horizon. The development provides a formula for the depression angle the angle below a horizontal plane at zenith distance 90 of some reference line or point that lies on the sea surface, short of the horizon. The waterline of a ship or a distant shoreline would be examples. It assumes that the observers height h and the line-of-sight distance l to the reference line or point are known. The distance l does not have to be known very precisely. Such a line could be used in place of the true horizon for celestial navigation in the case where the true horizon was not visible if, for example, it was obscured by low-lying haze or fog or blocked by a land mass. However, to use this kind of foreground reference line for celestial navigation, its depression angle must be known, and used in place of the depression of the horizon. Obviously the depression of such a line will be greater than that of the true horizon. This development provides a formula for the depression angle.

Subject Categories:

  • Navigation and Guidance
  • Theoretical Mathematics

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