This is the last full week of instruction before Thanksgiving.
First, a short rant. It’s unfortunate that students are racking up harmful absences. There is an institutional attendance policy, but we’re really not permitted to enforce it as written and yet it doesn’t change. This puts faculty in the dangerous position of having to decide when to enforce it and when to”compassionately” ignore it and break institutional policy. That’s a position I don’t want to be in. Either way, faculty are blamed (blamed for not being kind to the student by dropping them or blamed for ignoring institutional policy and being kind to the student) and “held accountable” so there’s no way to win. Administrators can willfully ignore published policy when they wish, but faculty can’t. The object is to keep as many students enrolled as possible and any attempt at pushing back against that is treated as ill behavior toward students. I just don’t see how an institution can work like this, but it’s my daily situation. Rant over.
This week we begin the fourth chapter, that on time. We don’t address what time is, becuase no one knows, but we do address the measurement of time because astronomers probably invented that. For our purposes, time is that which is demarcated by periodically occuring natural phenomena. HUH? In other words, we mark the passage of time (not time itself) by observing periodic natural phemonema. Sunrise. Noon. Sunset. Midnight. A stick’s noon shadow. A stick’s sunset shadow. Moonrise. Moonset. These are all observable periodic phenomena and we can model them all with our celestial spheres.
Our goal is to understand the analemma and how to use it to predict the dates of earliest sunrise, earliest sunset, latest sunrise, and latest sunset. They don’t occur on the most logical dates, and we want to understand why.
Measuring time requires the concept of hour angle, defined operationally as follows:
- Pick a celestial object (star, Sun, etc.).
- With a fingertip, trace out an arc from the north celestial pole to the object, continuing past the object (if it’s north of the celestial equator) to the celestial equator (if the object is south of the celestial equator you’ll hit the celestial equator before you hit the object) and stop. Your fingertip should always be on the celestial equator at this moment.
- Slide your fingertip along the celestial equator toward the celestial meridian (choose the shorter route, not the longer one), counting the number of time bumps you pass along the way. Stop when your finger gets to the celestial meridian.
- The number of time bumps you pass plus the fraction of the way from the last time bump you passed to the celestial meridian, expressed in hours, is the object’s hour angle.
The object’s hour angle tells you how much time elapses between rising and crossing the celestial meridian. It also tells you how much time elapses between crossing the celestial meridian and setting. By convention, objects on the eastern side of the celestial meridian have negative hour angles and objects on the western side have positive hour angles so you need to think in terms of absolute values to get these durations. Oh, and this means that double the hour angle’s absolute value tells you how much time the object is above the horizon.
At this point, we can investigate the duration of daylight (interval from sunrise to sunset) at the equator and at Hickory and begin to get an idea of seasonal variations and thus establish an operational definition of seasons.
The biggest benefit of this approach with the celestial sphere kits is that is completely eliminates the pitfall of thinking seasons are caused by a varying Earth-Sun distance. In this model, the Earth-Sun distance simply cannot vary and if students pay attention, they will notice this.
Next, we define a prime mover. A prime mover is just a name I made up for an object we’re going to track for the purposes of measuring the passage of time. Specifically, we’re going to observe the object and measure its hour angle. That hour angle can then be used to define a timescale unique to that prime mover. We will use Sun as our prime mover. At any given moment, the “time kept by our prime mover” is just Sun’s hour angle plus twelve hours. The twelve hours is needed as an offset to put the zero point at midnight, not at noon as it would otherwise be (hour angle is zero if the prime mover is on the celestial meridian).
There are actually TWO Suns! One is the Sun we’re used to, the true or apparent Sun, and the other one is an mathematical creation called the mean Sun. Each one can be used to establish its separate time scale.
We can now extend this and predict the times of sunrise and sunset for different locations.
Feedback welcome as always.