Distance From Eye to Horizon of a Sphere

This program computes the line-of-sight distance to the horizon of a sphere at any distance from (height of) the eye as reckoned from the surface or center of the sphere.   The radius and distance can be in any convenient linear units.   The initial default values are the mean lunar radius and distance of the eye above the surface, both in kilometers.

Radius
Distance
Distance To Eye Reckoned From
Center         Surface
Line-Of-Sight Distance to Horizon (H) = 58.9508269662
Surface Distance to Horizon (S) = 58.9282118485

Distance to (height of) eye is reckoned from surface.






Where the Distance to the Eye Is Reckoned From the Surface of the Sphere:


Given the radius (R) of the sphere and the distance (d) (height of) of the eye above the surface of the sphere, the general equation for the line-of-sight distance (H) to the sphere horizon viewed from that point is:


The horizon distance (S), corresponding to (H), but measured along the curved surface of the sphere, corresponding to the sailing distance is:



Where: R > 0 and d > 0 and angles are in degrees



Where the Distance to the Eye Is Reckoned From the Center of the Sphere:


Given the radius (R) of the sphere and the distance (D) of the eye from the center of the sphere, the general equation for the line-of-sight distance (H) to the sphere horizon viewed from that point is:


The horizon distance (S), corresponding to (H), but measured along the curved surface of the sphere, corresponding to the sailing distance is:



Where: D > R and R > 0 and angles are in degrees



© Jay Tanner - PHP Science Labs 2017 - v1.13