# Heat map of portion of the sky visible for a given observatory on Earth?

Reading Calculating area of visible sky I started wondering which portion of the sky one could observe how long given the 3D coordinates of an observatory, and two points in time.

In other words, I would love to have a formula $$f(\lambda,\varphi,h,t_1,t_2, \delta, \alpha)$$ for an observatory at $$(\lambda, \varphi, h)$$ with longitude $$\lambda$$, latitude $$\varphi$$, height $$h$$ above the geoid which shows how many hours between time $$t_1$$ and $$t_2$$ which point $$(\alpha, \delta)$$ of the sky is visible. Here, $$\alpha$$ is the right ascension and $$\delta$$ the declination. I am sure this calculation has been done before, and I am simply missing the search terms.

For convencience, let us assume the reference frame to be the usual WGS84. Let's further assume, that our observatory is on a hill on an otherwise flat landscape, so that we that we do not have to worry about skyline or mountains concealing our view to the sky.