linguistic:voice_change, quality:correction, linguistic:paraphrasing
Arc distance

Another relationship involves the great-circle distance s along the arc over the curved surface of the Earth to the horizon; this is more directly comparable to the geographical distance on a map.

It can be formulated in terms of γ in radians,

then

Solving for s gives

The distance s can also be expressed in terms of the line-of-sight distance d; from the second figure at the right,

substituting for γ and rearranging gives

The distances d and s are nearly the same when the height of the object is negligible compared to the radius (that is, h ≪ R).