<Dl> <Dd> Δ σ = arccos ⁡ (sin ⁡ φ 1 ⋅ sin ⁡ φ 2 + cos ⁡ φ 1 ⋅ cos ⁡ φ 2 ⋅ cos ⁡ (Δ λ)). (\ displaystyle \ Delta \ sigma = \ arccos (\ bigl () \ sin \ phi _ (1) \ cdot \ sin \ phi _ (2) + \ cos \ phi _ (1) \ cdot \ cos \ phi _ (2) \ cdot \ cos (\ Delta \ lambda) (\ bigr)).) </Dd> </Dl> <Dd> Δ σ = arccos ⁡ (sin ⁡ φ 1 ⋅ sin ⁡ φ 2 + cos ⁡ φ 1 ⋅ cos ⁡ φ 2 ⋅ cos ⁡ (Δ λ)). (\ displaystyle \ Delta \ sigma = \ arccos (\ bigl () \ sin \ phi _ (1) \ cdot \ sin \ phi _ (2) + \ cos \ phi _ (1) \ cdot \ cos \ phi _ (2) \ cdot \ cos (\ Delta \ lambda) (\ bigr)).) </Dd> <P> The distance d, i.e. the arc length, for a sphere of radius r and Δ σ (\ displaystyle \ Delta \ sigma) given in radians </P> <Dl> <Dd> d = r Δ σ . (\ displaystyle d = r \, \ Delta \ sigma .) </Dd> </Dl>

Shortest path between two points on a surface