Most of these calculations will be done for current location and time. But user should be able to easily change location and/or time.
Trivial / common calculations
Sun/moon rise/set, twilight hours (astronomical, nautical, civil), their location, distance, position in the sky (as seen by eye, also astronomical values such as right accession and declination), shadow length
Current moon phases, illumination
Current terrestrial illumination (lux, i.e. how much light does come from sun, moon and skyglow)
Moon calendar (such as showing the phases of moon for next X amount of days
Their relative positions to each other (the image you see on the website)
World map with sun lit and dark areas (including twilight) layered on.
Apollo landing sites
Short mission overview, astronauts, mission objectives, photos, etc.
Earth and sun as seen from those locations at the moment. This could be animated, i.e. sun and earth positions will be superimposed on live camera, as if you were on the moon.
More advanced calculations with notifications.
Optional, sun set, sun rise reminders with customizable advance warning time (useful for boaters, hikers)
Planets and how they are positioned around sun.
Optional notifications when planets rise and set.
Next super moon, blood moon, blue moon
Solstices, equinoxes, etc.
Sun / moon apogee (furthest away from earth), perigee (closest to earth)
Current images of sun to show sun spots etc.
Upcoming lunar and solar eclipses and when/how (full, partial) they will be seen from current location
Transits (such as Mercury or Venus passing in front of sun)
Paid features. Trial and infrequent usage will be free, but these will require some sort of subscription
Interactive positioning of sun on live camera image. This is great when you are buying a house because it will easily show if the building next door will block the sun or if your bedroom will be drenched with early morning sun, etc.
Aurora predictions and notifications if there is visible aurora from my location
Is tonight a good night to observe skies? This app will tell you depending on
latest weather forecast (the less clouds the better, also warmer temperature and drier air helps, too),
Nighttime light pollution for my current location (downtown Seattle is terrible for sky watching, but outskirts of Wenatchee is great.)
position of sun and moon (when will night happen, and will it be a moonless dark night, which is critical for deep sky objects),
are there any interesting objects (users can choose their favorite objects, or we can choose from our catalog e.g. Saturn is always a delight to look at etc.)
Similarly to above, we will help you find a nearby place if you want to observe the night skies, but your current location is not suitable. We will check nearby weather, light pollution, and available state parts etc. and recommend you an alternative observation place within an amount of driving distance (hours or miles)
Helping you set your solar arrays at the most optimal angle. Sun’s position in the sky changes throughout the day and year. Also weather patterns change around the year, too. Finally, some solar panels are needed for only part of the year, e.g. they are installed for Christmas trees or for summer houses. With this app, you can easily calculate the most optimal angle for your solar panels according to your needs and circumstance of your location. I imagine that the app guides the user, also helps them verify with built-in gyroscope that correct angle is set.