When Does the TV Show "Legends of Tomorrow" Season One (2016) Take Place?
"Legends of Tomorrow" season one is a comedy science fiction television series showran by Phil Klemmer with Chris Fedak [adapting "Showcase" #20 (1959) by Dave Wood, "Time Masters" #1-#8 (1989-1990) by Bob Wayne with Lewis Shiner as well as the Hawkman story in "Flash Comics" #1 (1939) by Gardner Fox] that first released January 21st, 2016. So when is "Legends of Tomorrow" season 1 set?
It takes place on an alternate timeline of the fictional DC Films Universe in the year:
We know this because in season 1 episodes 1 "Pilot, Part 1" and 2 "Pilot, Part 2", soon after the prologue, Rip Hunter is asking Gideon, his time-traveling ship's on-board artificial intelligence to "Set a course. United States. Star City. January, 2016." and in season 1 episode 4 "White Knights", Rip says to his team, ..."your former lives in January 2016." The first episode's early portion then includes a superimposed title card announcing visiting "TIBET 2016", "PITTSBURGH 2016", "ST. ROCH 2016", and "CENTRAL CITY 2016". So we know it's January of 2016 AD at the start of the season.

The End of Time
We know this because in season 1 episodes 1 "Pilot, Part 1" and 2 "Pilot, Part 2", soon after the prologue, Rip Hunter is asking Gideon, his time-traveling ship's on-board artificial intelligence to "Set a course. United States. Star City. January, 2016." and in season 1 episode 4 "White Knights", Rip says to his team, ..."your former lives in January 2016." The first episode's early portion then includes a superimposed title card announcing visiting "TIBET 2016", "PITTSBURGH 2016", "ST. ROCH 2016", and "CENTRAL CITY 2016". So we know it's January of 2016 AD at the start of the season.
Additionally, many important scenes take place in the Time Masters Council, which is in "The Vanishing Point" where Chronos tells us, "time doesn't exist there the way it does on Earth." These scenes are often labeled with the title card "TIME MASTERS COUNCIL". Season 1 episode 7 "Marooned" contains flashbacks to Rip's past in "The Vanishing Point", and season 1 episode 12 "Last Refuge" begins in this setting for a first of two prologues. The Vanishing Point is clearly analogous to other fictional portrayals of The End of Time. The season's final series of episodes take place in this setting.
Additionally, there's a 2166 AD prologue and the very first shot of the very first scene of season 1 episode includes a title card reading "LONDON 2166". Season 1 episode 13 "Leviathan" brings the "Legends" back to the year 2166 AD and ?.
Before "Part 1" is even halfway over, the characters arrive on their first adventure in time. Professor? Ray Palmer says, "This is unbelievable. 1975." and very soon a calendar can be seen in the background with "1975 ACADEMIC YEAR" at the top. The episode's conclusion and the beginning of "Part 2" is in "NORWAY 1975". Rip Hunter even specifies it is "October 19th, 1975" so it's certainly October of 1975 AD.
Season 1 episode 3 "Blood Ties" begins with a short prologue that opens immediately with an "ANCIENT EGYPT 1700 BC" title card and there's a flashback later that picks up where this prologue leaves off. Though most of the episode continues the 1970s setting with "LEIPZIG 1975" and "CENTRAL CITY 1975" at least these two parts take place in 1700 BC.
Season 1 episode 4 "White Knights" the characters visit the twentieth century again and it's clear because the US Department of Defense fax Gideon finds in archives leading the team to this moment includes the date "January 26, 1986". Plus, Rip almost immediately says to the crew, "The year is 1986." and there's a multitude of references across episodes 3, 4, and 5 to the then-ongoing Cold War between the United States of America and the Soviet Union, which lasted from 1947 AD to 1991 AD. Furthermore, a title card at the very first shot of the episode reads "WASHINGTON, D.C. 1986" so it's sometime after January and certainly within the 1986 AD calendar year.
Season 1 episode 6 "Star City 2046" debuts the setting of the 2046 AD futuristic setting of the city featured in some episodes of "Arrow". Posters are visible in the background telling citizens to "VOTE McCallister" ... "FOR PRESIDENT IN 2040" so it must be after November of 2040 AD. The time is more clearly identified when Rip says, "This... this is 2046." quite early after their arrival and by a superimposed title card reading "STAR CITY 2046" soon afterward.
Season 1 episode 8 "Night of the Hawk" and season 1 episode 9 "Left Behind" bring the group to the 1950s and it's nailed down when the A.I Gilbert declares at the end of the previous episode, he has determined they should go to "Harmony Falls, Oregon in March of 1958" next. When Jefferson "Jax" Jackson says, "I thought girls from 1958 moved a little bit slower!" halfway through episode 8 we get a fun confirmation that they took Gilbert's advice. Plus, the very first shot of episode 8 includes the title card: "HARMONY FALLS 1958". So it's certainly March of 1958 AD.
Season 1 episode 9 "Left Behind" even moves forward from there. Ray Palmer and Kendra Saunders/Hawkgirl posed as a married couple and he says, "Happy second anniversary." making 2 full years since the beginning of episode 8 meaning it's March of 1960 AD. A superimposed title card also reads "TWO YEARS LATER" and the ship's onboard A.I Gideon says to Rip, "then again, this is 1960."
1958 + 2 = 1960.
Season 1 episode 10 "Progeny" Rip's motley crew arrives in 2147 AD. Just at the very end of episode 9 "Left Behind", Rip demands, "Gideon, plot a course for Kasnia Conglomerate, the year 2147." Furthermore, early in episode 10, a title card labels it: "KASNIA CONGLOMERATE 2147".
This episode also features three flashbacks the first of which begins with a shot of a standing calendar with "1920 OCTOBER 1920" at the top. The second one includes close-ups of documents dated for "the 21st day of January in the year 1920" but is implied to take place after the first. So it's certainly October of 1920 AD at this point.
Season 1 episode 11 "The Magnificent Eight", features yet another "time-jump" that is immediately labeled by a superimposed time and place setting title card that says, "SALVATION 1871" and then specified by Rip to be: "The town of Salvation, the Dakota Territory, 1871." The Dakota Territory is a legal distinction that only existed from March 2nd, 1861 AD to November 2nd, 1889 AD in the real world. It is therefore 1871 AD.
The same episode also includes another very quick flashback to 1700 BC. And a final moment in 1990 AD labeled "CENTRAL CITY 1990" with another time and place setting title card. There's a secondary prologue for season 1 episode 12 "Last Refuge" in this setting accompanied by an identical title card.
Episode number 12 "Last Refuge" also moves on with a segment of time-travel to 2007 AD. The helpful A.I. Gideon clearly, says, ..."I calculate a ninety-six percent likelihood that she is headed to Starling City, circa 2007.", referring to an opponent the heroes need to stop. The very next shot has a "STARLING CITY 2007" title card.
Before this episode ends, we are also taken to 2014 AD.
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