You can have the camera automatically follow the sun, moon or galactic centre by tapping one of the indicator arrows while in Flying mode:
For example, if we tap the sun indicator (orange), the camera is immediately adjusted to look directly at the sun (of course, never do this in real life, even through your camera's viewfinder). If you adjust the time of day, you'll see that the camera follows the sun - even after it sets.
One side benefit of tracking the sun like this is that you can immediately read off the azimuth and altitude from the info bar at the top of the map area. In the example above, the center of the sun's disc lies at 62.4° from true north and 2.9° above the horizon.
To cancel tracking, simply tap the sun indicator once again (or tap one of the other tracking indicators). Alternatively, if you override the camera orientation, tracking will be cancelled. (In Flying mode this is done using two fingers to pan around - only one finger is needed is Enhanced mode.)
If you want to switch to Enhanced mode, you can (press the "Enhance" button at the right of the map area): tracking will be maintained until you cancel it by overriding the camera orientation. You can zoom the camera in/out while in enhanced mode and still maintain tracking.
All of the above applies equally to the moon and galactic center. Happy tracking!