It's possible that cookies or local storage are disabled in your browser. This article shows suitable Settings for Google Chrome which will allow the web app to load and display correctly.
These screenshots are from Chrome Version 61.0.3163.100 (Official Build) (64-bit) running on macOS Sierra.
1) Go to Settings:
2) Scroll down the page:
3) Choose Content Settings:
4) Choose Cookies:
5) Check that your settings match those shown here:
If you prefer more restrictive settings, you can choose to Block third-party cookies, but Allow [*.]photoephemeris.com, as shown:
We do not recommend enabling "Keep local data only until you quit your browser" - enabling this setting will cause the web app not to retain your saved locations, last selected date, location, map zoom level, and other settings between sessions.