The app itself does not collect or use any personal information. Apple is very strict about this and if an app uses something like your location access to contacts, when the app is first run Apple will present the user with a panel asking for that permission.
SkySafari does ask for the user's location. This is needed to automatically display the sky correctly for your location. You can deny this and enter the location manually. Denying location also means the compass feature will be less accurate and in some cases may not work at all. Apple's compass framework requires the location in order to convert magnetic north to true north.
All Android, we require is permission to write to storage and permission for location. Some versions on Android lump some of these permissions together so is you ask for permission to write to storage, it presents this to the user as access of "Multimedia data".
We also make use of the App Analytics service called Flurry (https://developer.yahoo.com/
Please let me know if you need further clarification.