There is scannable object on Nessus near the crashed ship where we first meet Failsafe in the first mission there. Scanning the object leads Ghost to reveal that "It's been 127 of our years since Nessus last traveled through our system". 7066 Nessus being a real life location has a known orbital period of 121.4 years. Its orbit however is unstable and is thus prone to decay. If we know the rate of decay we should be able to calculate how long it would take for 7066 Nessus to gain an orbital period of 127 years, and thus how many years in the future that Destiny takes place. Assuming of course that in Destiny they still use Solar years, ie. one complete Earth orbit around the Sun. However I can't seem to find any information in regards to the decay of its orbit, or at least none that I can understand.
[spoiler]Yes because of inaccurate calendars and our own orbit slightly changing over time years would actually become longer, which over a long enough amount of time would could cause significant skews to our calculations. But I don't care enough to do that much math.[/spoiler]