Imagine a mostly homogenous culture with one unified language has a period of diaspora into the galaxy, under circumstances that make ongoing communication impossible. Assuming a space-faring civilization has access to audio/video recording at the very least, how much deviation in language could be reasonably expected if those travelers were to encounter one another 100 years in the future? 500? 1000? What other factors are at play that I'm not thinking of?
The rate of divergence would be influenced by so many nonlinear factors, but you can probably take a reasonable guess based on history. How much should we expect the language to develop in one of the groups, before we even consider the divergence of the other? The use of audio/video recording might slow that process, but think about the rate of language change that we've experienced since the invention of recording technology. For example, the mid-Atlantic accent was common in upper class and particularly in broadcast media during the middle of the 20th century, and it definitely sounds odd and dated today. So even with recordings to add stability, we know there will be some changes. On longer time scales, the languages may have changed quite a bit just within the individual groups. Have you ever tried to read Beowulf in Old English? (I don't have enough reputation to post more than two links, but it's freely available online.) It's pretty indecipherable, and that's with 1000 years of development within only one language. With that much change, the two different groups would pretty much be speaking different but related languages, perhaps like French and Portuguese.
In addition to changes in accent and speech patterns, vernacular would certainly develop in response to technological advancement. Since the rate of technological change is generally considered to be nonlinear with respect to time, advanced civilizations will need to come up with a whole lot of new words even over a few decades. As such, technological development is probably the most important factor in determining the divergence as well. Consider how much a language would have to adapt to suit the differences in the two time periods, and then assume that the languages of the two groups would have evolved in arbitrary directions.
How similar are the environments for the two isolated groups? Will they have advanced in the same areas of science and engineering? Have they prospered to a similar extent? What size are the groups? Do they have the same goals? The time scale certainly matters. In 100 years, they'll certainly still be able to communicate. They might be able to get their message across after 500 years. By 1000 years, they may not even recognize any words, and may have to rely on historians who both studied the same ancient languages, as if we encountered a civilization with a totally unknown language, but which had a portion of people who had studied Latin in high school.
For a lower bound, consider the divergence between American English and British English following the colonization of North America. These two regions weren't in total isolation, but there's still a considerable contrast. There have been some linguistic studies on language evolution, which might give you some more things to think about. See "Is the rate of linguistic change constant?"
I am not sure anyone and predict what a language will be like in a thousand years. But a hundred or couple hundred, that's not so hard--we have plenty of historical examples.
If these people our moving to a new plant then they will encounter new things and situations that we don't have words for in our language. This will lead to new words being made and add to our dictionary. In addition it would also lead to new expression and slang words
path of least resistance
It has been noted throughout history that language follows the rule of least resistance. In this cause this mean that over time words that we use a lot we will change to make them easier to say. One example of in our language would be saying "thanks" in place of "thank you" or "bro" in place of "brother". As time went by these changes would catch on at first only in informal language but as generations pass by (and people stop listening to the outdated recordings from the home planet) it becomes acceptable for formal speech.