Need Simple equation for Rise, Transit, and Set time I've been looking, unsuccessfully, for hours for a simple set of equations:

Input: 
RA and Dec of an object
Observers Lat and Lng
Current Time

Output: 
Rise Time 
Transit Time
Set Time
(and, hopefully) max elevation at transit 
(and, hopefully) current alt and az of object

It seems like this should be a simple relationship, but I haven't been able to find it.
If an equation simply gives the current alt/az for an object, I guess I could solve for az and then find the maximum for a given time range. 

Questions: 
1. Anybody know of such equations? Or, even better, some sample code. 
2. If not, can anybody point me in the right direction?

Thanks
I'm not sure it qualifies as "simple", but, using 
http://idlastro.gsfc.nasa.gov/ftp/pro/astro/hadec2altaz.pro (and some 
additional calculations/simplifications): 

$ 
   \begin{array}{|c|c|c|c|} 
\hline 
    \text{Event} &amp; \text{Time} &amp; \phi  &amp; Z \\ 
\hline 
    \text{Any} &amp; \text{t} &amp; \tan ^{-1}(\cos (\lambda ) \sin (\delta )-\cos 
      (\delta ) \cos (\alpha -t) \sin (\lambda ),\cos (\delta ) \sin (\alpha 
      -t)) &amp; \tan ^{-1}\left(\sqrt{(\cos (\lambda ) \sin (\delta )-\cos (\delta 
      ) \cos (\alpha -t) \sin (\lambda ))^2+\cos ^2(\delta ) \sin ^2(\alpha 
      -t)},\cos (\delta ) \cos (\lambda ) \cos (\alpha -t)+\sin (\delta ) \sin 
      (\lambda )\right) \\ 
\hline 
    \text{Rise} &amp; \alpha -\cos ^{-1}(-\tan (\delta ) \tan (\lambda )) &amp; \tan 
      ^{-1}\left(\sec (\lambda ) \sin (\delta ),\cos (\delta ) \sqrt{1-\tan 
      ^2(\delta ) \tan ^2(\lambda )}\right) &amp; 0 \\ 
\hline 
    \text{Transit} &amp; \alpha  &amp;  
\begin{cases} 
                   \delta &gt;\lambda  &amp; 0 \\ 
                   \delta =\lambda  &amp; \text{Zenith} \\ 
                   \delta &lt;\lambda  &amp; \pi  
                  \end{cases} 
    &amp; \frac{\pi }{2}-\left| \delta -\lambda  \right| \\ 
\hline 
    \text{Set} &amp; \alpha +\cos ^{-1}(-\tan (\delta ) \tan (\lambda )) &amp; \tan 
      ^{-1}\left(\sec (\lambda ) \sin (\delta ),-\cos (\delta ) \sqrt{1-\tan 
      ^2(\delta ) \tan ^2(\lambda )}\right) &amp; 0 \\ 
\hline 
    \text{Lowest Point} &amp; \alpha +\pi  &amp;  
\begin{cases} 
                   \delta &gt;-\lambda  &amp; 0 \\ 
                   \delta =-\lambda  &amp; \text{Nadir} \\ 
                   \delta &lt;-\lambda  &amp; \pi  
                  \end{cases} 
    &amp; \left| \delta +\lambda  \right|-\frac{\pi }{2} \\ 
\hline 
   \end{array} 
$

where: 


$\phi$ is the azimuth of the object 
$Z$ is the altitude of the object above the horizon 
$\alpha$ is the right ascension of the object 
$\delta$ is the declination of the object 
$\lambda$ is the latitude of the observer 
$t$ is the current local sidereal time 


Note the two-argument form of arctangent is required so that the 
results are in the correct quadrant: 
https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Two-argument_variant_of_arctangent 

Additional caveats: 


If $\left| \delta -\lambda \right|&gt;\frac{\pi }{2}$, the object is 
always below the horizon, and the equations for rising time and 
setting time will not work. 
If $\left| \delta +\lambda \right|&gt;\frac{\pi }{2}$, the object is 
always above the horizon (circumpolar), and the equations for rising 
and setting time will also not work. 
The measurements above are in radians. You can convert $\pi \to 
  180 {}^{\circ}$ for degrees.
Because we use the local sidereal time, the longitude doesn't 
appear in any of the formulas above. However, we do need it to find 
the local sidereal time, as below. 
To find the local sideral time $t$ in radians, we use 
http://aa.usno.navy.mil/faq/docs/GAST.php and make some substitions 
to get: 


$t = 4.894961212735792 + 6.30038809898489 d + \psi$ 

where $\psi$ is your longitude in radians, and $d$ is the number of 
days (including fractional days) since "2000-01-01 12:00:00 UTC". Traditionally, we use $\phi$ for longitude, but I'm already using it in the formulas above for azimuth.

If you combine the formula for local sidereal time and 
azimuth/altitude and assume excessive precision, you get my answer to 
https://astronomy.stackexchange.com/a/8415/21 

Additional computations for these results at: 
https://github.com/barrycarter/bcapps/blob/master/STACK/bc-rst.m 

I was going to add some graphs to show how the altitude is NOT a sine wave and how the azimuth is NOT a straight line (although you might expect them to be), but they turned out not to be terribly instructive/helpful.

You might also be able to get simpler formulas if you set $t$ to be the "hour angle" (which is $\alpha-t$ in the current setup).