Astrophotographers often use the "500 Rule" as a way to estimate the maximum shutter speed that can be used to capture the night sky before star trailing becomes noticeable. Here is a simple calculator, in night vision friendly red (or daytime color mode), to find recommended maximum shutter speeds based on your lens focal length and digital camera sensors crop ratio.
The 500 Rule is just a starting point for night sky astrophotography. You can try selecting a more conservative rule in the app (400, 300, etc.) for better focused shots. As always, experiment and find out what works best with your setup!
Developer Note: This is my first App Store release. Please let me know how this app works for you, how it doesnt, or what you would like to see in further updates. Thanks!