We're dividing today's class into two separate topics.
One is about the tides and the other about the Tropics.
--end of award-worthy poetry---
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Helpful terms for today:
Perigee: the point of least distance between Earth and the moon
Perihelion: the point of least distance between the Earth and Sun.
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TIDES
And, yes, we understand that tide talk is the astronomical equivalent of visiting a Medieval dentist who harbors irrational grudges. Nevertheless, despite the torment, we proceed. Earth generally experiences two high tides and two low tides a day, The tides result from a differential gravitational force. To understand this idea we now turn to Newton:
"The magnitude of the gravitational force exerted between two massive objects is proportional to the masses of both and inversely proportional to the square of their separation distance."
If you double the distance between two objects, the force is reduced to a quarter; triple the distance, the force is one ninth of the original value. Now, if all massive objects were point masses, as described in elementary physics texts, then the matter would be simple: the forces would be equal along each mass and the math would treat us sweetly. Of course, the physical world doesn't have point masses. Instead all massive objects occupy a specific volume, whether they're volleyballs or planets. Differential gravity arises from this inconvenient breadth.
Regard Earth and the Moon. Both bodies exert a force on one another. However, the magnitude of the force varies within each body because different regions experience a different gravitational force. The portion of Earth closest to the Moon feels a greater tug than the planet's center because gravity falls off with the square of the distance, which is 6,371 km (3,959 miles).
Regard Earth and the Sun. Yet, again, both bodies exert a force on each other. And, likewise, the gravitational force the Sun exerts on Earth varies along its volume. The part of Earth closest to the Sun (noon) experiences less gravity than the part farthest away (midnight.) However, the Sun is much farther away from us than the Moon. The Sun's mean distance is 93 million miles; the Moon's is 240,000 miles, so the 'tidal force' the Sun causes will be less than the Moon (44% as great, actually.) This is because the force difference between the near and far sides of Earth relative to the Sun is not as profound as the difference the Moon induces.
Both the Sun and Moon contribute to the high tides, although, as mentioned previously, the latter is more influential than the former. Each day, as Earth rotates beneath the Moon, the planet 'bulges' along the Earth-moon line. This bulge region has a high tide. Yet, so, too does the point on Earth that is diametrically opposite of the first bulge. Here, our intuition fails us. Though it might be easier to understand why the area just under the Moon has a high tide because of the differential gravity, one is at a loss to know why the most distant region also experiences one.
Think of this: the pull of the Moon, and to a lesser extent, the Sun, exerts a "bulging effect" on Earth, similar, in principle, to the effect of squeezing the planet into an oblong shape. When we regard this issue physically, we can think of Earth's center as being stationary, with the two opposite points along the Moon-Earth line pulled away. The water is drawn toward both these bulges, while the two areas perpendicular to it experience low tides. The water amount is constant, so an excess in one region must create a deficiency in another.
Spring and neap tides Both the moon and the Sun exert tidal forces on Earth. The Sun's tidal force influence is 44% that of the moon's. When the moon and Sun are aligned,as they are during a full or new moon, the tides will be at their highest. We refer to these higher tides as "spring tides." When the moon is at the quarter phase, the Sun and moon will be working in opposite directions and the tides will be lower. We call these lower tides "neap tides." When the moon is new or full around the same time it is near or at perigee, we'll have perigean spring tides,which will be higher than other spring tides. They are known as "King Tides." Finally, when Earth is at or near perihelion around the same time as the full or new moon it at or near perigee,we'll experience a perihelic perigean spring tide. We call these "Poseidon's Tides."
To add a little more complexity, we remind the reader (yes, we know you haven't forgotten) that the angle between the Sun, Moon and Earth is always changing. During New Moon, the Moon is between the Sun and Earth, so both Moon and Sun are pulling in the same direction and their gravitational influence is combined. At full moon, Earth is between the Moon and Sun. They're pulling in different directions, of course, but they're both operating along the bulges. The tides occurring around the new and full moon are known as "spring tides." The lowest high tides happen during the first and last quarter (quadrature), when the Moon and Sun are operating perpendicularly and therefore diminishing the tidal effect.
Here is where we watch the gears turning: Every so often, the Moon will reach perigee around the time it is either at full moon or new moon. This coincidence is called 'astronomical high tide,' a term also applied merely to the tides corresponding to the full and new moon. (Although the term 'spring tide' is more apt.) Perigee doesn't generally correspond to the full or new moon because the period between successive perigees, called an 'anomalistic month,' is about 27.5 days, whereas the phase cycle, called a 'synodic month,' is 29.5 days. However, when they correspond, the tides will be quite high. We call these "King Tides."
We're almost done.
Now, every so often, Earth will be at or near perihelion when the moon is new or full when at or near perigee.
Having Earth close to the Sun while the moon is close to Earth at new or full moon produces the highest tides, known appropriately as 'Poseidon's Tides."
Differential gravity is never distance sensitive so that these close approaches of Sun, Earth and moon can produce a dramatic effect.
We quickly review the four main tide types
SPRING TIDE: The high tide that occurs when the moon is new or full. These tides are higher than any other tides during the lunar cycle.
NEAP TIDE: The high tide that occurs when the moon is at first or last quarter, These high tides are lower than any other tides during the lunar cycle.
KING TIDE: The high tide that occurs when the moon is at or near perigee when the moon is new or full.
POSEIDON'S TIDE: The high tide that occurs when the moon is at or near perigee when full or new at the time when Earth is at or near perihelion.
TROPICS
Lamentable fact: The Sun doesn't pass directly overhead everywhere on Earth.
Recall from a previous lesson that the ecliptic, the Sun's annual path through the sky, passes north and then south of the celestial equator. It reaches its northernmost point on the June solstice, when it is 23.5 degrees north of the celestial equator. It attains its southernmost point on the December solstice, when it is 23.5 degrees south of the celestial equator.
The Sun's position relative to the Celestial Equator determines the latitude where the Sun can reach the zenith, the point directly overhead.
On the March and September equinox the Sun is on the Celestial Equator and will pass directly overhead at Earth's equator. More accurately, an equatorial observer will see the Sun pass directly overhead when the Sun crosses the meridian.
Today (April 8), the Sun is about 7.5 degrees north of the Celestial Equator. One will therefore find the Sun over head at the latitude 7.5 degrees North.
On the June solstice, the Sun will be 23.5 degrees north of the Celestial Equator. The Sun will pass through the zenith at the latitude 23.5 degrees North on this date. This line defines the "Tropic of Cancer."
On the December solstice, the Sun will be 23.5 degrees south of the Celestial Equator. The Sun will pass through the zenith at the latitude 23.5 degrees South on this date. This line defines the "Tropic of Capricorn."
Only in the tropics will one ever see the Sun overhead. And, yes you are correct. Earth's 23.5 degree tilt is responsible for the 23.5 degree north and 23.5 degree south latitude boundaries. if Earth were tilted by 43 degrees, we here in Portland, ME, would be living in the tropics! Oh,well.
One added note. Only in two regions would one ever be able to see the midnight Sun effect, when the Sun is above the horizon for twenty four hours for at least part of the year. In the Northern Hemisphere, the midnight Sun effect is visible at or north of the Arctic Circle. In the Southern Hemisphere, the midnight Sun effect is visible at or south of the Antarctic Circle.
The Arctic Circle's latitude is 66.5 degrees north
The Antarctic Circle's latitude is 66.5 degrees south
To understand why these boundaries are located at this latitude, just subtract 23.5 from 90 degrees: 90 - 23.5 = 66.5
The midnight Sun effect is only visible at the Arctic Circle around the June Solstice.
The midnight Sun effect is visible at the North Pole for a little more than six months. The closer one is to the north pole, the longer the period of the midnight Sun effect.
Today, April 8th, the Sun passes directly overhead at 7.5 degrees north. Observers at the latitude 82.5 degrees north will now start to see the Midnight Sun effect. (90 - 7.5).
Tomorrow we'll move back off Earth to observe the planets.
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