James T. ShipmanJerry D. WilsonCharles A. Higgins, Jr.

Place and Time

Chapter 15

Sec 15.1 Cartesian Coordinates

• A two-dimensional system is one in which two lines are drawn perpendicular with an origin assigned at the point of intersection.

• Horizontal line = x-axis• Vertical line = y-axis• The system we commonly use is the Cartesian

coordinate system, named after the French philosopher/mathematician René Descartes (1596-1650).

Section 15.1

Sec 15.1 Cartesian Coordinates

• x number gives the distance from the y-axis.• y number gives the distance from the x-axis.• Many cities are laid out in a Cartesian pattern

with streets running N-S & E-W.

We want to be able to determine locations on Earth and in space.

Section 15.1

(x,y) locates a point

Sec 15.2 Latitude and Longitude

• Location on Earth is established by means of a coordinate system – latitude & longitude

Section 15.2

Sec 15.2 Latitude and Longitude

• Latitude - the angular measurement in degrees north and south of the equator

• The latitude angle is measured from the center of the Earth relative to the equator.

• Lines of equal latitude are circles drawn on the surface and parallel to the equator.

Section 15.2

Sec 15.2 Latitude and Longitude

• Longitude is the angular measurement, in degrees, east or west of the reference meridian, the Prime Meridian (0o) at Greenwich, England.• A large optical telescope

was located there.

• Maximum value of 180o E or W

Section 15.2

Sec 15.2 Latitude and Longitude

Section 15.2

Sec 15.3 Time

• Time - the continuous forward flowing of events• The continuous measurement of time requires

the periodic movement of some object as a reference.

• The second has been adopted as the international unit of time.

• Vibration of the cesium-133 atom now provides the reference of a second – 9,192,631,770 cycles per second

Section 15.3

Sec 15.3 Time

• Apparent Solar Day – the elapsed time between two successive crossings of the same meridian (line of longitude) by the sun (~361o)

• Sidereal Day – the elapsed time between two successive crossings of the same meridian by a star other than the sun (360o)

Section 15.3

Sec 15.3 Time

• During one complete revolution (orbit) around the Sun, the Earth rotates (spins) 365.25 times but one complete revolution is only 360o.

• Therefore during each full rotation the Earth moves slightly less than 1o of angular distance.• 360o/365.25 days = ~0.985o/day

Section 15.3

Sec 15.3 Time

• The Earth is divided into 24 time zones, each containing approx. 15o of longitude or 1 hour. (Remember that the Earth rotates 15o/hour!)

Section 15.3

Sec 15.3 Time

• The first time zone begins at the prime meridian and extends approximately 7.5o both east and west.

• The centers of each time zone are multiples of 15o.

Section 15.3

Sec 15.3 Time

• Traveling west you will “gain” time.• As you cross into a new time zone, your watch

will be 1 hour ahead of the new time zone.• Example: Driving from Texas (at noon) into New

Mexico (now it is only 11 A.M.)• Driving east you “lose” an hour.• Therefore if you travel all the way around the

Earth going west, you will “gain” 24 hours.

Section 15.3

Sec 15.3 Time

• The International Date Line is located at the 180o meridian – exactly opposite the Prime Meridian.

• When one crosses the IDL traveling west, the date is advanced into the next day.

• When one crosses the IDL traveling east, one day is subtracted from the present date.

Section 15.3

Sec 15.4 Determining Latitude and Longitude

• During a year the Sun appears to change its overhead position from 23.5o N to 23.5o S.• 23.5o N is the farthest north and 23.5o S is the

farthest south that the vertical noon Sun reaches.

• Tropic of Cancer – the parallel at 23.5o N• Tropic of Capricorn – the parallel at 23.5o S• As the Earth revolves around the Sun, the noon

Sun is directly over different latitudes during the year because of the constant 23.5o tilt of the Earth to the Sun.

Section 15.4

Sec 15.4 Determining Latitude and Longitude

Section 15.4

Sec 15.4 Determining Latitude and Longitude

• At 12 noon, the Sun is on the observer’s meridian and appears at its maximum altitude about the southern horizon.• (for all observers north of the sun)

• Zenith – position directly overhead, therefore always 90o from the horizon

• Altitude – the angle measured from the horizon to the Sun at noon

• Zenith Angle – angle from the zenith to the Sun at noon (complementary angle of the altitude)

Section 15.4

Sec 15.5 The Seasons and the Calendar

• Seasons affect everyone.• Many of our holidays were originally celebrated

as a commemoration of a certain season of the year.• Easter – coming of spring• Thanksgiving – harvest• Christmas – Sun beginning its “journey” north

• Original dates more-or-less set by the movement of the Earth around the Sun.

Section 15.5

Sec 15.5 The Seasons and the Calendar

• As the Earth revolves around the Sun, its axis remains tilted 23.5o from the vertical.

• This constant tilt of the Earth with respect to the Sun causes the Earth’s seasons.

• As the Earth revolves around the Sun we also designate 4 particular days – Winter solstice, Vernal equinox, Summer solstice, and Autumnal equinox .

• Light/dark hours are always the same at the equator.

Section 15.5

Sec 15.5 The Seasons and the Calendar

Section 15.5

Sec 15.5 The Seasons and the Calendar

• Winter Solstice – 23.5oS = Tropic of Capricorn• Sun lower in N. Hemisphere, fewer hours of daylight,

& less intense sunlight

• Vernal Equinox – 0o = Equator• Summer Solstice – 23.5oN = Tropic of Cancer

• Sun higher in N. Hemisphere, more hours of daylight, & more intense sunlight

• Autumnal Equinox – 0o = Equator

Section 15.5

Sec 15.5 The Seasons and the Calendar

Section 15.5

Sec 15.5 The Seasons and the Calendar

• Tropical Year – the time interval from one vernal equinox to the next vernal equinox – 365.2422 mean solar days• The elapsed time between 1 northward crossing of

the sun above the equator to the next northward crossing.

• Sidereal year – the time interval for earth to make one complete revolution around the sun with respect to any particular star other than the sun – 365.2536 mean solar days• 20 minutes longer than the tropical year

Section 15.5

Sec 15.5 The Seasons and the Calendar

• Zodiac – the central, circular section of the celestial sphere that is divided into 12 sections

• Each section of the zodiac is identified by a prominent group of stars called a constellation.• Ancient civilizations name constellations for the figure

the stars seemed to form.

• Due to the Earth’s annual revolution around the sun, the appearance of the 12 constellations change during the course of a year.• A particular time of the year is marked by the

appearance of a particular constellation.

Section 15.5

Sec 15.5 The Seasons and the Calendar

Section 15.5

Sec 15.5 The Seasons and the Calendar

• The early Roman calendar consisted of only 10 months; there was no January or February.

• Later January and February were added.• The Julian Calendar was adopted in 45 B.C.

during the reign of Julius Caesar. • Augustus Caesar took over the throne after his

adopted father Julius died.

Section 15.5

Sec 15.5 The Seasons and the Calendar

• The names “July” and “August” were put into use when Augustus Caesar ruled the empire in honor of Julius and Augustus.

• In addition one day was added to August so that it would be as long as July (taken away from February.)

• Julian calendar had 365 days, and during every year divisible by 4, an extra day was added, since it takes approx. 365.25 days for the earth to orbit the sun.

Section 15.5

Sec 15.5 The Seasons and the Calendar

• The Julian calendar was fairly accurate and was used for over 1600 years.

• In 1582 Pope Gregory XIII realized that the Julian calendar was slightly inaccurate.• The Vernal Equinox was not falling on March 21.

• A discrepancy was found. To correct this the Pope decreed that 10 days would be skipped.

• 365.2422 not 365.25 = discrepancy• Every 400 years 3 leap years would be skipped.• This is the calendar we use today.

Section 15.5

Sec 15.5 The Seasons and the Calendar

Section 15.5

Sec 15.6 Precession of Earth’s Axis

• When we spin a toy top, it starts to wobble after a few seconds

• Physicists call this wobble precession.• Earth slowly precesses in a clockwise direction.• The period of precession is 25,800 years. In

other words, it takes 25,800 years for the axis to precess through 360o.

Section 15.6

Sec 15.6 Precession of Earth’s Axis

Section 15.6