# Tidal Timing

Quote of the Day

The final test of a leader is that he leaves behind him in other men the conviction and the will to carry on.

— Walter Lippmann. I completely agree with this statement – your legacy as a manager is the team and processes that you formed while you were in charge.

## Introduction

Figure 1: Illustration of the Cause of Tides (Source).

After a discussion on the annual time shift of the winter solstice, our lunch time topic changed to the topic of tides. During this discussion, I mentioned that tides have a period of about 12 hours and 25 minutes (Figure 1). I will show you how to compute this period in this post.

The key to understanding this odd period is to note that the Moon creates the tides by pulling on the ocean, which  means the tides follow the motion of the Moon. Because of how gravity and inertia work, there is also a second tidal bulge on the side of the Earth opposite of the Moon. Thus, we experience two tides for each time the Moon passes over our heads.

To compute the period of the tides, we begin by computing the period of the tidal bulge that moves underneath the Moon. Since the Earth is rotating on its axis and the moon is revolving around the Earth, the period of the Moon's orbit as seen from an observer on the Earth is longer than 24 hours because the Earth must "catch up" with the Moon for it to be seen in its same position as the time of the last tide.

I will be working approximately here – it turns out that tides are also a function of the position of the Sun, which I will be ignoring. We can compute the period of the tides using the approach shown in Figure 2. My rough calculations show the tidal period is about 12 hours and 26 minutes.

Figure 2: Calculation of the Period of Tides.

There are numerous subtleties associated with computing the exact period of the tides. For more details, see this web page and the Wikipedia.

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