The BBC news podcast Science in Action episode New Planet Hunting Mission covers the upcoming TESS mission between
01:00 and 07:15 with Sara Seager, TESS deputy director of science, Massachusetts Institute of Technology, Cambridge, Massachusetts.
03:30 Dr. Seager mentions that the launch window only lasts 40 seconds, with (at least one) subsequent launch window occurring the following day.
The repeating of the launch window after about 1 day suggests (to me at least) that the narrowness of the window is strongly associated with the rotation of the Earth. TESS' orbit is always bound to Earth, but requires careful synchronization with the Moon's orbit having a 2:1 resonance as discussed in this answer as well as the video and other linkes therein.
In 40 seconds, Cape Canaveral rotates about 0.17 degrees around Earth's axis, moving only about 16 kilometers in a Geocentric frame.
Is the launch on the very edge of what the Falcon 9 is capable of energetically, or is it too challenging computationally or navigationally to insert into the complex series of maneuvers outside this 40 second, 16 km, 0.17 degree window that repeats the following day?
Or could this be in part a bit of SpaceX bravado or excess as might be indirectly inferred from the question, answers, and comments associated with Why would a mission to Sun-Earth L1 have an instantaneous launch window?. That doesn't seem likely as the window has a specific, finite duration of 40 seconds, rather than the 1 second, effectively instantaneous window discussed there.
More on the potential daily repeats of the window is suggested by the Spaceflight 101 article TESS Orbit Design:
Because of the large number of constraints and high variance in starting conditions found in the relative geometry of the initial orbit and the Moon, trajectory designers developed an automated trajectory design algorithm that takes into account the spacecraft parameters, error statistics, force models and the various constraints like eclipses, upper boundaries for perigee, apogee and period, etc. The automated process delivers an optimized solution for each feasible launch date which is then put through a Quality Assurance process to verify that all requirements are satisfied – creating five discrete launch windows per month, each between one and four days in duration.
This paragraph does not directly address the 40 second window, but instead suggests the window might repeat for as many as four consecutive days some times, if I understand correctly.
Handy links for explanations and discussions of the $C_3$ parameter (re "Is the launch on the very edge of what the Falcon 9 is capable of energetically, or..."):
- What is the "launch energy" or C₃ measured in km² / s²
- How can I calculate the Characteristic Energy to Sun-Earth L1?:
- How to interpret and use characteristic energy C3 in this case?
- Generating plot of LV's performance as a function of the C3 parameter
- Relationship of 'C3' to Delta-V for interplanetary missions
- C3 calculation in interplanetary missions