14.2: The Tides Follow the Moon
- Page ID
- 31694
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Because Earth rotates on its axis, the locations beneath (and opposite to) the Moon (and Sun) rotate with the Earth. Every 24 hours, the Earth rotates on its axis, but a point on Earth’s surface directly beneath the Moon will take 24 hours and 50 minutes to rotate directly beneath the Moon the following day. That’s because the Moon orbits the Earth, and advances in its orbit by 50 minutes each day.
If the Earth was not orbiting the Sun, the Moon would complete one orbit around the Earth in 27 days, what’s called a sidereal month. But the Earth does move and by the time the Moon makes a complete circle around the Earth, the Earth has moved forward in its orbit, too. For the Moon to reach the same point with respect to the Sun and Earth (i.e., to move into the same configuration as 27 days earlier), an additional 2.5 days are required. So, the complete cycle of the tides requires 29.5 days, what’s known as the synodic month, the time it takes for the Moon to transit around the Earth and return to its starting point relative to the Earth and Sun.
The phases of the Moon mark different waypoints in the Moon’s orbit during the synodic month. When the side of the Moon facing Earth is fully illuminated by the Sun, the Moon is said to be full; it’s a full Moon. When the Moon is not visible at all, the Moon is said to be new; it’s a new Moon. The point halfway between new and full is called the first quarter. The right half of the Moon is illuminated during the first quarter (in the Southern Hemisphere, it’s the left half). Following the full Moon, at the halfway point between the full Moon and the new Moon, the left half of the Moon is illuminated at the third quarter. From the new Moon to the full Moon, the Moon grows brighter each night; the Moon is waxing. When the Moon grows dimmer, as it does during the transition from full to new Moon, the Moon is waning.
Though not necessary for an understanding of tides, we can divide the Moon’s orbit even further, and it’s fun to do so because the Moon is the most visible object in the night sky. The sliver of Moon between the new Moon and first quarter, and between the third quarter and new Moon, is called a crescent Moon. We distinguish the two crescent moons as a waxing crescent—from new to first quarter—and a waning crescent—from third quarter to new. Similarly, the three-quarters-full Moon is called a gibbous Moon. From first quarter to full, it’s a waxing gibbous, and from full to third quarter, it’s a waning gibbous. Feel free to use these terms next time you are out beneath the Moon with someone special. They are sure to be impressed.