Pray for the life of Nebuchadnezzar … and for the life of Belshazzar …: This does not mean that the lives of Nebuchadnezzar and Belshazzar were in danger. It is simply a way of wishing long life to them. Good News Translation “pray for King Nebuchadnezzar … and … Belshazzar, that they may live as long as the heavens last” captures the idea.

The only Belshazzar known to history was not the son of Nebuchadnezzar, but of Nabonidus, who was the last of the Babylonian kings. Nabonidus came to power a few years after the death of Nebuchadnezzar. Dan 5.2 also has Belshazzar as son of Nebuchadnezzar.

For Babylon see the comments on verse 9. Here it refers to the country of Babylonia (so Good News Translation).

That their days on earth may be like the days of heaven is given a slightly different interpretation in the New American Bible (New American Bible), which says “that their lifetimes may equal the duration of the heavens above the earth” (compare a similar expression in Deut 11.21). This is an equally possible literal understanding of the Greek text, but the meaning of either rendering is expressed in Good News Translation with “that they may live as long as the heavens last.” Heaven or “heavens” here refers to the universe, and in some languages this clause can be expressed as “that they may live as long as the sun, moon, and stars last.” It may sound strange that the exiles are calling on their fellow Jews in Jerusalem to pray for the welfare of their captors, but it is only what Jeremiah himself called for in his letter to the exiles (Jer 29.7).

Quoted with permission from Bullard, Roger A. and Hatton, Howard A. A Handbook on The Shorter Books of the Deuterocanon. (UBS Helps for Translators). New York: UBS, 2006. For this and other handbooks for translators see here.