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How would one calculate the rotation/tilt of the earth to simulate the Night Sky in a self-written tool or app. I am trying to built an app for my telescope to show me on my phone what I am looking at. I can already simulate the exact positions of stars at the 1.1.2000 at 00:00:00 but I dont know how the "earth" should be rotated so I can simulate the sky from my current position and accurate time.
There are App and tools like stellarium that can achive this but I just cant get the angles right: 
If anyone could point me in the right direction and tell me what I need to change/calculate it would help me a lot.
If you do not require arcminute precision, you can approximate Greenwich sidereal time as the Earth rotation angle $ heta(t)$. IERS Technical Note 32 §5.4.4 gives $$ egin{align} heta(t) &= 2 pi (0.77905~72732~640 + 1.00273~78119~11354~48~ t) &approx 280.46^circ + 360.985612^circ~ t end{align} $$ where $t$ is a real number of days since JD 2451545.0 (2000-01-01 12:00 TT ≈ 11:59 UTC).
For an observer at north latitude $phi$ and east longitude $lambda$, things should line up like this:
Local sidereal time $ = mathrm{LST} approx heta(t) + lambda$
Zenith (RA, Dec) $ = (alpha, delta) = (mathrm{LST},~ phi)$
North horizon $(alpha, delta) = egin{cases} (mathrm{LST + 12h},~ 90^circ - phi) & mathrm{if}~phi >= 0 (mathrm{LST},~ 90^circ + phi) & mathrm{if}~phi < 0 end{cases}$
East horizon $(alpha, delta) = (mathrm{LST + 6h},~ 0^circ)$
The transformation between equatorial and horizontal coordinates can be composed of two rotations, similar but not necessarily identical to those in Wikipedia: Celestial coordinate system. For example, you could:
- Start with the north horizon vector pointing at the north celestial pole, and the zenith vector pointing at (0h, 0°).
- Rotate the ground counterclockwise as seen from the north horizon vector by LST.
- Rotate the ground clockwise as seen from the east horizon vector by $phi$.
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Sorry, but I need another one. What else could that suggest?
I am finite, I apologize, but it does not come close to me. Are there other variants?
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