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.
We also make use of the App Analytics service called Flurry (https://developer.yahoo.com/analytics/). This collects anonymous usage information based upon a random key that is generated and is specific to each device. There is no way to tie this back to a user.
Please let me know if you need further clarification.