The entire law about what happens on January 20th, 2017 is what the Constitution says
Before he enter on the Execution of his Office, he shall take the following Oath or Affirmation:—”I do solemnly swear (or affirm) that I will faithfully execute the Office of President of the United States, and will to the best of my Ability, preserve, protect and defend the Constitution of the United States.”
Just an aside that the Constitution is not gender neutral
The swearing in of the President is entirely by tradition, not law. There is no requirement that the taking of the Oath occur in any specific place, nor be administered by any specific person. In the event of some outlandish scheme like Trump being detained, his plane being blocked from going to DC, the Capital police shutting down D.C., Donald Trump could take the Oath of Office in Palm Beach administered by his son in law.
Lyndon Johnson took the Oath of Office while Air Force One was sitting on Love Field in Dallas, Texas. The Oath was administered by a local Federal judge