What is the required distance between two vessels in the fog?

The short answer is there is no set number of distance for vessels operating in "restricted visibility" , rather there is a set of guidelines set forth in the International and Inland Rules of the Road governing your speed, look outs and conduct when operating in the fog. Rule 19 will specifically address this question in detail. Please check out the link provided below for more detailed info. Check out Rules 2,4,5,6,7,8, 19 & 35.