Ask HN: Is it legal to provide a phone tracking service?

Let's assume that I made up a small algorithm that takes a phone number as input and spits out the current location (country and maybe city) and availability information (on or off).

Now let's assume I wrap it into a nice service that checks for location changes constantly and alerts the customer whenever one of the monitored phone numbers has changed its location.

Assuming that I'm feeding public data into my service, is it legal?

Please keep in mind this is not a question of ethics.