18 Jan 2005AST 2010: Chapter 31 Earth, Moon, and Sky.

18 Jan 2005 AST 2010: Chapter 3 1

Earth, Moon, and Sky

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Locating Places on EarthIn order to be able to locate places, we need to establish a reference frame or system of coordinatesChances you are already familiar with the notions of North, South, East, and West which help orient oneself while traveling through the country


North, South, East, West

The Earth's axis of rotation defines the North and South Poles

East is the direction towards which the Earth rotatesWest is the opposite of EastThe four directions, north, south, east, and west, are well defined at almost all locations on Earth despite the fact our planet is round rather than flat

The only exceptions are exactly at the North and South poles where East and West are ambiguous

The Earth’s equator is a circle on its surface, halfway between the North and South Poles


Coordinates on a SphereOn a flat surface it is sufficient to have a rectangular grid and the cardinal directions (north, south, east,...) to orient oneself and specify the location of placesOn a sphere, such as our planet, one requires a slightly more complex system of coordinatesWe need some new definitions and notions that will help us orient ourselves and specify places on the surface of the Earth


Great CirclesA great circle is any circle on the surface of a sphere whose center is at the center of the sphereExamples: The Earth's equator is a great circle

on the Earth's surface One can also imagine great circles

that pass through the North and South Poles


Meridian and LongitudeA meridian is a great circle that passes through the North and South PolesAny place on Earth’s surface will have a meridian passing through it, and this specifies the east-west location, or longitude, of that placeBy international agreement, your longitude is defined as the number of degrees of arc along the equator between your meridian and the one passing through Greenwich, England

Thus, the longitude of Greenwich is zero degrees, or 0°

The meridian passing through Greenwich is called the prime meridian


LongitudesGreenwich, England, was selected as the 0°-longitude location, after many international negotiations, because it lies between continental Europe and the United States, and because it was the site for much of the development of a way to measure longitude at seaLongitudes are measured either to the east or to the west of the Greenwich meridian from 0° to 180°


LatitudesThe latitude of a point on Earth’s surface is the number of degrees of arc that point is away from the equator along the meridian passing through the pointLatitudes are measured either north or south of the equator from 0° to 90°


Example of Latitude and Longitude

The latitude and longitude of the U.S. Naval Observatory in Washington, D.C., are 38.921° N and 77.066° W, respectively

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Celestial Sphere RevisitedTo specify the positions of objects in the sky, it is useful to adopt the notion of celestial sphere It was introduced by ancient astronomers, who

thought that the Earth was surrounded by a solid dome, on which luminous objects were attached

The celestial sphere is an imaginary sphere surrounding the Earth and having its center at the center of the Earth

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DeclinationDeclination on the celestial sphere is measured the same way that latitude is measured on Earth's surface In other words, declination is

measured from the celestial equator toward the north (positive) or south (negative)

For example, the star Polaris, located near the north celestial pole, has a declination of almost +90°

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Right Ascension (1)Right ascension (RA) on the celestial sphere is measured the same way that longitude is measured on Earth's surfaceHowever, RA is different from longitude in that its starting point has been (arbitrarily) chosen to be the vernal equinox

The vernal equinox is the point on the celestial sphere where the ecliptic (the Sun’s path) crosses the celestial equator

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Right Ascension (2)Right ascension can be expressed either in units of angle (degrees) or in units of timeThis is because the celestial sphere appears to turn around the Earth once a day as the planet spins on its axisThus the 360° of RA that it takes to go once around the celestial sphere can just as well be set to 24 hours This implies that 15° of arc corresponds to 1 hour

of time The hour can be further subdivided into minutes

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Foucault’s Pendulum

ExperimentIn 1851, French physicist Jean Foucault suspended a 60-m pendulum weighing about 25 kg from the domed ceiling of the Pantheon in Paris and started the pendulum swinging evenlyIn the absence of Earth’s rotation, the pendulum would have oscillated back and forth in the same exact directionHowever, it became clear after few minutes of oscillations that the direction of oscillation was changing due to the rotation of the Earth, thereby providing the first direct observation of the Earth's rotation

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SeasonsYou are no doubt familiar with the fact that at mid latitudes such as the United states there are significant variations in the amount of heat we receive from the Sun in the course of a yearFor centuries now, the year has thus been divided in seasons to reflect the fact that some periods of the year are either warmer or colder

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What Causes Seasons?Contrary to what most people believe, the seasons are NOT caused by changing distance between the Earth and the SunThe distance of the Earth from the Sun varies by 3% only through the yearThis variation is NOT sufficient to explain the temperature variations experienced throughout the yearIt cannot explain the fact that temperature variations are stronger the closer one gets to the polesNote also it cannot account for the fact that seasons in the Southern hemisphere are reverse relative to those in the Northern hemisphere

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Actual Cause of Seasons

The seasons are caused by the 23° tilt of the Earth's axis relative to the plane in which it circles the Sun

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Seasons and Sunshine (1)By virtue of angular momentum conservation, the Earth's axis of rotation (tilted by 23° relative to the Earth's path around the Sun), always points in the same direction (relative to distant stars)This means that regions of the earth's globes at times lean towards (or away) from the SunAs the Earth orbit around the Sun, a given region "leaning toward/away from the Sun" varies and changes the illumination received from the Sun

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Seasons and Sunshine (2)Example: In June, the Northern hemisphere leans into the

Sun and is more directly illuminated In December, the situation is reversed and the

Northern hemisphere leans away from the Sun. The situation is reverse in the Southern

hemisphere In September, and March, the Earth leans

"sideways" relative to the Sun , and the two hemisphere receive more or less the same illumination

There are actually two effects to consider The angle of the illumination The duration of the illumination

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Angle of IlluminationSince the Earth's tilt has a fixed orientation (relative to the stars), the angle of illumination from the Sun changes throughout the year, and so the amount of light received on a given region of the Earth's surface changes in time As much of the Sun’s light is transformed into heat in Earth's oceans, lakes, ground, and atmosphere, the temperature varies accordingly with the angle of illumination

Summer Winter

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Duration of IlluminationYou have no doubt observed the duration of the day changes with the seasons

In the summer, days are longer, and the Sun gets to shine longer: more illumination is received, it becomes much warmer

The situation is reverse in the winter as the days are shorter and lesser amounts of illumination are received on the ground, the temperature gets colder

This variation of the duration of the day again is caused by the tilted axis

In June, the Sun spend more time above the Celestial equator, the illumination of the Northern hemisphere last longer, days are longer and warmer in the Northern hemisphere

Situation reversed in the Southern hemisphere which see little of the Sun in June, but gets most of it in December

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Keeping TimeThe measurement of time is based on the rotation of the EarthThroughout history, time has been determined by the positions of the Sun and stars in the skyOnly recently have mechanical and electronic clocks taken over this important function of regulating our livesThe most fundamental astronomical unit of time is the day, measured in terms of the rotation of the EarthThere is, however, more than one way to define the day

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Length of DaySolar day Usually, one defines the day as the

rotation period of the Earth, with respect to the Sun, this is the solar day

People of all countries set their clock to the solar day

Sidereal day Rotation period of the Earth relative, or

with respect, to the stars Used by astronomers to measure time

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Sun Earth

1 day

~1o

1o

1o = 24 hours/360 ~ 4 minutes

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Difference between Solar and Sidereal Days

A solar day is slightly longer than a sidereal day because the Earth moves a significant distance along its orbit around the Sun in a dayGiven that there are (roughly) 365 days in a year, the Earth moves roughly 1 (~360°/365) along its orbit This implies that each day the Earth has to rotate

by an extra degree to have the Sun back to the zenith to a chosen reference meridian

In other words, the Solar day is longer than the sidereal day by 1 degree

Given that there 360° in one 24 hours, 1 corresponds to 24/360 hours. That's 0.066 hour or, equivalently, 4 minutes

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ClocksOrdinary clocks are set to solar time This implies that stars appear to rise 4 minutes earlier each dayAstronomers prefer using sidereal time because in that system, a star rises at the same time every day

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Apparent Solar Time (1)Apparent solar time is determined from the actual position of the Sun in the skyEarliest measurements of time were accomplished with sun dials and thus provide a measure of the apparent solar timeToday we adopt the middle of the night as the starting point of the day, and measure time in hours elapsed since midnight

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Apparent Solar Time (2)During the first half of the day, the Sun has not reached the meridian Those hours are referred to as before

midday (ante meridiem, A.M.) Hours of the second half of the day, after

noon, are referred to as P.M. (post meridiem)

The apparent solar time seems simple enough...

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Apparent Solar Time (3)It is, however, not very convenient to use because the exact length of the day varies slightly during the year because the speed of the Earth changes along its orbit around the SunBecause of the Earth's tilted rotation axis, the apparent Solar time does not advance at a uniform rateApparent solar time has long been abandoned since the advent of exact clock that runs at a uniform rate

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Mean Solar Time (1)Mean solar time is based on the average value of the solar day over the course of the year A mean solar day contains exactly 24 hours and is what we use every day time keeping It is inconvenient for practical purposes because it is determined by the position of the Sun

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Mean Solar Time (2)Why it is inconvenient: Noon occurs when the Sun is located

overhead This implies that noon happens at

different times at different longitudes If mean solar time was strictly applied,

travelers would have to continue adjust their watch as they travel east or west

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Abandonment of Mean Solar Time

Mean solar time was used until roughly the end of the 19th century in the United StatesBasically all towns had to keep their own local timeThe need for a standardization became evident and pressing with the development of the railroads and telegraphA first standard was established in 1883

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Standard TimeThe nation was divided in four standard time zones in 1883Today, a fifth zone is added to include Alaska and HawaiiWithin each zone, all places keep the same standard timeThe standard time is adjusted to correspond to the time of a meridian lying roughly at the middle of the time zone

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Daylight Saving TimeDaylight saving time is simply the local time of a location plus one hour Adopted for spring and summer use in

most states in the US as well as in many other countries to prolong the sunlight into evening hours

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International Date Line (1)The problem!

The fact that as one travels eastward, the time advances poses a practical problemAs one travels around the world, one passes a new time zone approximately every 15°Basically as one travels east to the next time zone, one adds one hour to the time on one's watchThis implies that if one goes around the globe, one will end up adding 24 hours to one's watch

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International Date Line (2)The solution!

An international date line was established by international agreement along the 180o meridian of longitude The date line runs essentially across the middle

of the Pacific ocean By convention at the date line, the date of the

calendar is changed by one day While crossing from West to East, i.e. advancing

ones time, one compensates by decreasing the date

Crossing from East to West, you increase the date by one day

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International Date Line (3)Note that this implies that a given event will be referred by people living in different cities as a different date and time Japan’s attack on Pearl Harbor happened

on Sunday, December 7, 1941, according to people living in the US, whereas Japanese remember it as Monday, December 8, 1941

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The Challenge of the Calendar

Calendars are used to keep track of time over the course of

long time spans to plan, or anticipate the changes of the

seasons to honor special religious or personal

anniversaries

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Calendar UseFor a calendar to be useful, it must used by people who agree on a common units or natural time intervalsThe natural units of our calendar are the day

based on the period of rotation of the Earth on its axis the month

based on the period of revolution of the moon about the Earth

the yearbased on the period of revolution of the Earth about the Sun

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Calendar MaintenanceHistorically, difficulties arose in maintaining a sound calendar because the three reference intervals were not commensurate to one another The rotation period of the Earth is by

definition 1.0000 day The period of the moon (the time to

complete its cycles) called the lunar month is 29.5306 days

The period of revolution of the Earth around the Sun (the tropical year) is 365.2422 days

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Origins of Our CalendarOur western calendar derives from one established by the Greeks as early as during the 8th century B.C. The Greek calendar eventually evolved into the Julian calendar introduced by Julius CesarThe Julian calendar has 365.25 days fairly close to the actual value of 365.2422

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Julian CalendarThe Romans implemented this calendar by declaring the normal year to have 365 days, and one year every fourth year, a leap year, having 366 days, thus making the average year (after four years) exactly 365.25The Romans based their calendar basically on the SunHowever the months are in fact a vestige of attempts to fit in a calendar based on the phases of the Moon

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Problems with Julian Calendar

The Julian calendar was adopted by the Christian Church early on It still differed from the true year by about 11 minutes This was an amount that accumulated

over centuries to an appreciable error

By 1582, the 11 minutes per year had accumulated to the point that the first day of spring was occurring on March 11, instead of March 21

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Enters Gregorian Calendar…

If the trend had continued, the celebration of Easter would have eventually been held in the winter rather than the springPope Gregory XIII, a contemporary of Galileo, felt it necessary to institute a reform of the Julian calendar

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Gregorian Calendar Reform

Ten days to be dropped out of the calendar to bring the vernal equinox back to March 21

By proclamation, October 4, 1582, became October 15A change in the rule for leap year was introduced in order to make the average closer to the tropical year

Three of every four century years, all leap years under the Julian calendar, would be a common year henceforth

Only century years divisible by 400 would be leap years Thus 1700, 1800, and 1900, all divisible by 4 but not by

400, were NOT leap years in the Gregorian calendar On the other hand the years 1600, and 2000, both

divisible by 400, were leap years

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The MoonThe Moon is the second brightest object in Earth's sky after the Sun However, unlike the Sun, it does not shine under its own power, but merely glows with reflected sunlight

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Phases of the Moon (1)

The Moon viewed from the Earth's surface appears to have a cycle of phases through timeThe cycle begins with a dark out Moon, a phase called the new MoonFor 2 weeks Night after night, the Moon becomes progressively more and more illuminatedEventually, the Moon's disk becomes fully visible, a phase referred to as full MoonAs time progresses further, the Moon is then less and less illuminated until it comes back to the new Moon phaseThe cycle then repeats itself

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Phases of the Moon (2)

New Moon: The lighted side of the Moon faces away from the Earth. This means that the Sun, Earth, and Moon are almost in a straight line, with the Moon in between the Sun and the Earth. The Moon that we see looks very dark.First Quarter: The right half of the Moon appears lighted and the left side of the Moon appears dark. During the time between the New Moon and the First Quarter Moon, the part of the Moon that appears lighted gets larger and larger every day, and will continue to grow until the Full MoonFull Moon: The lighted side of the Moon faces the Earth. This means that the Earth, Sun, and Moon are nearly in a straight line, with the Earth in the middle. The Moon that we see is very bright from the sunlight reflecting off itLast Quarter: Sometimes called Third Quarter. The left half of the Moon appears lighted, and the right side of the Moon appears dark. During the time between the Full Moon and the Last Quarter Moon, the part of the Moon that appears lighted gets smaller and smaller every day. It will continue to shrink until the New Moon, when the cycle starts all over again

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Moon Sidereal PeriodThe Moon sidereal period is the period of revolution of the Moon around the Earth measured with respect to distant starsThe Moon sidereal period amounts to 27.3217 sidereal days

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Moon Rotation PeriodThe Moon rotates on its axis in exactly the same time it takes to revolve about the Earth As a consequence, although the Moon does

travel around the Earth, one ends up always seeing the same face of the Moon i.e. the one with the man in the Moon...

Note that the so-called dark side of the Moon (the back side, hidden face, i.e. the side one does not see from Earth's surface) does not actually bear its name properly The back side of the Moon is actually illuminated

through half of its orbit around the Earth

18 Jan 2005AST 2010: Chapter 31 Earth, Moon, and Sky.

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Transcript of 18 Jan 2005AST 2010: Chapter 31 Earth, Moon, and Sky.