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Gravitation and Tides, Lecture notes of Geometry

Geometry

during a synodic month, La Jolla experiences two spring tides and two neap tides. http://tidesandcurrents.noaa.gov neap tide spring tide.

Typology: Lecture notes

2022/2023

Uploaded on 02/28/2023

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SIO15: Lecture 2 Supplement: Tides
attraction of bodies due to their mass
Gravitation and Tides
• Moon pulls on Earth with force, Fg
• Earth pulls on Moon with opposite force, -Fg
• as Moon orbits, Earth’s surface is deformed -> tidal bulge
• Moon orbits at 27.3 days (sidereal month)
!! Example is shown for equator.
Fig. 2.15
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attraction of bodies due to their mass

Gravitation and Tides

• Moon pulls on Earth with force, Fg

• Earth pulls on Moon with opposite force, -Fg

• as Moon orbits, Earth’s surface is deformed -> tidal bulge

• Moon orbits at 27.3 days (sidereal month)

!! Example is shown for equator.

Fig. 2.

Gravitation and Tides

  • Earth’s surface feels the pull of the Moon on the near side more than on the far side.
  • On the near side, Earth bulges because forces add.
  • On the far side, Earth bulges because centrifugal force is greater than attraction of Moon.
  • At the same time, each point on Earth circles the center of mass of the Moon-Earth system (barycenter, B) once for each lunar orbit. Circular motion causes fictitious (apparent, inertial) centrifugal force, Fc, which is the same for each point.
  • Forces add up like vectors and deform Earth’s surface. Fig. 2.

SIO15: Lecture 2 Supplement: Tides

Change of Tides at a Specific Location

Most places on Earth experience

two high tides and two low tides

per day ( semi-diurnal tides ).

A few places experience only one

high and one low tide per day

( diurnal tides ).

http://ocean.peterbrueggeman.com/piertide.html

For example, the tides on

October 5, 2007 at the SIO pier

looked like the diagram to the

right:

The tides throughout the day

look like this:

0 24 Fig. 2.

Change of Tides at a Specific Location

geographic location of semi-diurnal, diurnal tides and mixed tides

(depends on many factors, e.g. water body dimensions, coastlines,

geometry of continental shelf)

Fig. 2.

The Moon, Sun and Tides

the Sun also pulls on Earth though the lunar (Moon) tides are stronger

Spring tide: when Sun, Earth and Moon are aligned (syzygy), then Sun and Moon pull together. The different between high and low tide is then largest. This happens during Full Moon - when the Moon is on the other side of Earth - and during New Moon - when the Moon is on the same side of Earth as the Sun is. The period between Full Moons is about 29.5 days (synodic month). Fig. 2.

The Moon, Sun and Tides

Neap tide: when Sun, Earth and Moon make a right angle where Earth is in the corner. Then Sun’s and Moon’s effects partially cancel each other. The difference between high and low tide is then smallest. This happens during Quarter Moons twice a month.

Waxing Moon Waning Moon

Moon’s orbit is actually slightly elliptical. If Moon is at its perigee (point on orbit closest to Earth) then spring tides are higher. Spring tides are particularly high twice a year (Jun/Jul and Dec/Jan). In Dec/Jan, the Moon is near perigee AND Earth is near perihelion. In Jun/Jul, the Earth is near aphelion. The Dec/Jan spring tide is often called the King tide (biggest spring tide of the year). Fig. 2.