"Sorry, doctor, I'm going to have to come in on a different day--I have another appointment that would be really hard to move, in terms of the kinetic energy requirements."
The characters are talking about upcoming total solar eclipses. Partial solar eclipses are fairly frequent (2–5 per year), but total eclipses are less frequent (about every 18 months), and most of them will not be in convenient locations for a particular set of people. Cueball seems to be talking about total eclipses visible in much of North America: April 8, 2024 and August 12, 2045. (There was also an annular eclipse on October 14, 2023.) Making plans for eclipses is awkward given the uncertainty present for anything else far in the future, such as whether the attendees will have children by then, and whether the technology they are using to keep track of their appointments (Google Calendar in this case) will even still exist over 22 years in the future.
Black Hat claims he can't make it, as he vaguely and obscurely claims he already knows he has "a thing" on August 12, 2045. People do not usually have events scheduled for precise dates that far in the future in their personal calendars and, combined with the fact that Black Hat remembers this date without checking (but also without specifying what he'll be doing then), implies that this could be another of his grand and sinister plans... or he just doesn't want to go. This might also be a reference to an old Soviet joke.
The title text is someone asking to reschedule a medical appointment to see the eclipse. The eclipse is hard to move because that would require hastening or delaying it by moving the Earth, Moon or Sun, any of which would require vast amounts of energy.
This was published a year before the next such eclipse in America; so, if you're someone who plans things a year in advance, this serves as a reminder to put it on your calendar.