If you find that the web app always opens at the 'wrong' location, e.g. the default location (Timbuktu) or a place you visited in the app months ago, chances are you have saved a bookmark for the app that includes a specific location (and probably date and time also).
To have the web app open at the location you last visited, you should save the bookmark as http://app.photoephemeris.com, ensuring that there are no additional parameters saved in the link. By default, the app will append various parameters such as the pin location, map center and date and time, so you likely will need to edit the bookmark.
Here's how to do that using Safari - if you're using a different browser, the exact steps for adding and editing a bookmark may be different, but the principle is the same.
Save a bookmark
When you save a bookmark for the TPE Web App as shown below, the bookmark will be for the specific location, date and time that you're viewing when you create it:
On editing the bookmark, you can see the additional parameters that must be removed in order to have the app open at the most recently used location and the current date/time;
Edit the bookmark as shown to delete the extra parameters:
You should be left with a clean bookmark as shown:
When you access this bookmark, the app will open at the last visited location and at the current time and date.