Comments by "EebstertheGreat" (@EebstertheGreat) on "The SAT Question Everyone Got Wrong" video.

  1. Another complication with timekeeping that he didn't have time to get into is the equation of time. The Earth's orbit is not circular but elliptical with the Sun at one focus. So the angular velocity of the Earth is not constant. That means that the length of a solar day actually varies over the course of a year. The longest solar day can be up to 30 seconds longer than the mean solar day, and the shortest can be up to 20 seconds shorter. In order to have days of equal length, we instead average these out and use the mean solar day. If you mark the spot the sun is at 12:00 civil time every day throughout the year (ignoring daylight saving), you will see that it's not always in the same spot, but rather traces out a sort of figure 8 shape called an analemma. (The exact shape depends on latitude.) But even that would be too simple. The Earth's orbit is not constant over time but changes in multiple ways, notably including the precession of the equinoxes. This means that the year as measured relative to the seasons (the tropical year) differs from the year as measured relative to the stars (the sidereal year). This also affects the length of the day, albeit barely. The "sidereal day" as defined by astronomers is technically not measured relative to the stars but relative to the seasons. The true rotation period in an inertial frame of reference is 8.372 858 milliseconds shorter than the sidereal day. And in fact, all of the precise values are in some sense averages, because there are many tiny disturbances in the rotation of the Earth's crust, both due to movement in the core and due to tidal effects and even melting ice. Since some of these changes are secular, even these average values slowly change over time. At some point, you realize that most of these are more parameters in a model than measurements of any particular thing.
    1