6 Jul 2005AST 2010: Chapter 31 Earth, Moon, and Sky.

6 Jul 2005 AST 2010: Chapter 3 1

Earth, Moon, and SkyEarth, Moon, and Sky

AST 2010: Chapter 3 26 Jul 2005

Locating Places on EarthLocating Places on EarthIn order to be able to locate places, we need to establish a reference frame or system of coordinatesChances are 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, WestNorth, South, East, WestThe Earth's axis of rotation defines the North and South PolesEast 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 that it 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 the Earth’s surface, halfway between the North and South Poles


Coordinates on a SphereCoordinates 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 CirclesGreat 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 surfaceOne can also imagine great circles that pass through the North and South Poles


Meridian and LongitudeMeridian 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


LongitudesLongitudes

Greenwich, 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°


LatitudesLatitudes

The latitude of a point on the 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 Example of Latitude and LongitudeLongitude

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


Celestial Sphere RevisitedCelestial 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 imaginary sphere surrounding the Earth and having its center at the center of the Earth


DeclinationDeclinationDeclination on the celestial sphere is measured the same way that latitude is measured on the 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 about +90°


Right Ascension (1)Right Ascension (1)Right ascension (RA) on the celestial sphere is measured the same way that longitude is measured on the 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


Right Ascension (2)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° (=360°/24) of arc corresponds to 1 hour of time The hour can be further subdivided into minutes


Foucault’s Pendulum ExperimentFoucault’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 a 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


Seasonal QuestionSeasonal Question

Why is it hotter in Why is it hotter in summer and summer and

colder in winter colder in winter here?here?


SeasonsSeasonsYou 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 the yearFor centuries now, the year has thus been divided into seasons to reflect the fact that some periods of the year are either warmer or colderThe difference between seasons gets more pronounced the closer one gets to the polesThe seasons in the Southern Hemisphere are the opposite of those in the Northern Hemisphere


What Causes Seasons?What Causes Seasons?Contrary to what most people believe, the seasons are NOT caused by the changing distance between the Earth and the SunThe distance of the Earth from the Sun varies by only about 3% during the course of the year

Remember that the Earth’s orbit is nearly circular

This small variation is NOT sufficient to explain the significant variations in temperature experienced throughout the yearThe common belief is also contradicted by the fact that the Earth is actually closest to the Sun in January, when the Northern Hemisphere is in the middle of winter


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


Seasons and Sunshine (1)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, as the Earth travels around the Sun, a given surface of the Earth receives different amounts of sunlight


Seasons and Sunshine (2)Seasons and Sunshine (2)Example:

In June, the Northern Hemisphere leans into the Sun and is more directly illuminatedIn December, the situation is reversed and the Northern Hemisphere leans away from the SunThe situation is reversed in the Southern HemisphereIn September and March, the Earth leans "sideways" relative to the Sun , and the two hemispheres receive more or less the same illumination

There are actually two effects to considerThe angle of the illuminationThe duration of the illumination


Angle of IlluminationAngle 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


Duration of IlluminationDuration 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: as more illumination is received, the temperature becomes much warmerThe situation is reversed 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 HemisphereSituation reversed in the Southern Hemisphere which sees little of the Sun in June, but gets most of it in December


Keeping TimeKeeping 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


Length of DayLength of DayUsually, the day is defined 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

Astronomers also use a sidereal day, which is defined in terms of the rotation period of the Earth with respect to the starsA solar day is slightly longer than a sidereal day because the Earth moves along its path around the Sun in a day


Difference between Difference between Solar Day and Solar Day and Sidereal DaySidereal Day

Given that there are about 365 days in a year, the Earth moves roughly 1° (360°/365) of arc per day along its orbit

This implies that each day the Earth has to rotate by an extra degree to complete a solar day In other words, the solar day is longer than the sidereal day by 1°Given that there 360° in one 24 hours, 1° corresponds to 24/360 hours, or about 4 minutesThus, the solar day is about 4 minutes longer than the sidereal day


ClocksClocksOrdinary clocks are set to solar time

This implies that stars appear to rise 4 minutes earlier each day

Astronomers prefer using sidereal time because in that system a star rises at the same time every day


Apparent Solar Time (1)Apparent Solar Time (1)Apparent solar time is determined from the actual position of the Sun in the skyThe earliest measurements of time were accomplished with sundials and thus provided 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 During the first half of the day, the Sun has not reached the meridian

Those hours are referred to as before midday (ante meridiem, or A.M.)The 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 ...


Apparent Solar Time (2)Apparent Solar Time (2)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 SunAnother reason is that because of the Earth's tilted axis of rotation 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


Mean Solar TimeMean Solar TimeMean 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 in everyday time-keeping It is inconvenient for practical purposes because it is determined by the position of the Sun

Noon occurs when the Sun is located overheadThis implies that noon happens at different times at different longitudesIf mean solar time was strictly applied, travelers would have to continue adjusting their watches as they travel east or west


Abandonment of Mean Solar Abandonment of Mean Solar TimeTime

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


Standard TimeStandard TimeThe nation was divided into 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 zoneDaylight 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


International Date Line (1)International Date Line (1)The fact that as one travels eastward time advances poses a practical problem

As one travels east, one passes a new time zone approximately every 15° and thus has to add 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

An international date line was established by international agreement along the 180° meridian of longitude

The date line runs essentially across the middle of the Pacific OceanBy convention, at the date line the date of the calendar is changed by one day

Crossing the line from west to east, i.e. advancing ones time, one compensates by decreasing the dateCrossing from east to west, you increase the date by 1 day


International Date Line (2)International Date Line (2)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


The CalendarThe CalendarCalendars are used

to keep track of time over the course of long time spans to plan, or anticipate the changes of the seasonsto honor special religious or personal anniversaries

For a calendar to be useful, it must used by people who agree on 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 axisthe month, based on the period of revolution of the moon about the Earththe year, based on the period of revolution of the Earth about the Sun


Calendar MaintenanceCalendar 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 dayThe period of the moon (the time to complete its cycles), called the lunar month, is 29.5306 daysThe period of revolution of the Earth around the Sun (the tropical year) is 365.2422 days


Origins of Our CalendarOrigins 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


Julian Calendar & Gregorian Julian Calendar & Gregorian CalendarCalendarThe Romans implemented this calendar by

declaring the normal year to have 365 days, and one year every fourth year, a leap year, to have 366 days, thus making the average year (after four years) exactly 365.25Although the Julian calendar represented a great advance, it still differed from the true year by about 11 minutes

This was an amount that accumulated over the centuries to an appreciable error

To fix the problem, Pope Gregory XIII, a contemporary of Galileo, felt it necessary to institute a reform of the Julian calendar As a result, today most of the world has adopted the Gregorian calendar established in 1582


The MoonThe MoonThe Moon is the second brightest object in the Earth's sky after the Sun However, unlike the Sun, it does not shine under its own power, but merely glows with reflected sunlightViewed from the Earth, the Moon appears to have a cycle of phases during the course of a month

The cycle begins with the Moon starting dark — the new moon phase — and getting more and more illuminated by sunlight over the course of about two weeksAfter the Moon’s disk becomes fully bright — the full moon phase — it begins to fade, returning to dark about two weeks laterThe cycle then repeats itself

39AST 2010: Chapter 36 Jul 2005

Phases of the Moon [Phases of the Moon [AnimationAnimation]]


The Moon’s Sidereal and The Moon’s Sidereal and Rotation PeriodsRotation Periods

The Moon’s sidereal period, which is the period of its revolution around the Earth with respect to the stars, is 27.3217 daysThe 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, the Moon always keeps the same face turned toward the The so-called dark side of the Moon (its back side, the side we never see from Earth) does not actually bear its name properlyThe back side of the Moon is actually illuminated through half of its orbit around the Earth


Eclipses of the MoonEclipses of the MoonA lunar eclipse occurs when the Moon enters the shadow of the Earth

This figure is not to scale

6 Jul 2005AST 2010: Chapter 31 Earth, Moon, and Sky.

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Transcript of 6 Jul 2005AST 2010: Chapter 31 Earth, Moon, and Sky.