Is there any program that can show real time earth globe and can show us day and night likewise on earth?
Better if we can see timings of different cities on rotating globe.
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I would check out Marble, it supports "Day/Night View" - Sun shadowing based on day time. It is not only available on Windows, but also Mac, Linux, and some mobile devices.
Marble is a Virtual Globe and World Atlas that you can use to learn more about Earth: You can pan and zoom around and you can look up places and roads. A mouse click on a place label will provide the respective Wikipedia article.