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General Physics (PHYS )
Chapter 15
Place and Time
Cartesian Coordinates
Latitude and Longitude
Time
Determining Latitude and Longitude
Wednesday
Seasons and the Calendar
Precession of the Earth’s Axis
Chapter 16: The Solar System and
Planetary Motion
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Place & Time
• In Physical Science events occur at different places and at different times.
• Another way to say it – events are separated by space and time.
• Our five senses make it possible to know about objects and their positions relative to one another.
• Time is a bit more evasive – we relate time to changes we observe in our environment.
Intro
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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 (1596-1550).
Section 15.1
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Cartesian Coordinates – Two Dimensional
• 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
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Latitude and Longitude
• Location on earth is established by means of a coordinate system – latitude & longitude
• Since the earth turns on axis, we can use the geographic poles as north-south reference points.
• Geographic poles – the imaginary points on the surface of the earth where the earth’s axis projects from the sphere
• Equator – an imaginary line circling the earth’s surface half way between the N & S poles – The equator is a “great circle” – a circle on the surface of earth in a
plane that passes through the center.
Section 15.2
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Standard Time Zones
Section 15.3
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Latitude
• 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
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Latitude
• Latitude is also called parallels – – There is an infinite # -- 0o – 90o N or S
• Going from the Equator poles these parallels represent a series of complete circles of which the equator is the largest and they become progressively smaller going N & S
• Only the equator is a “great circle.” All of the other parallels are “small circles,” with the N & S poles being only points .
Section 15.2
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The Equator
Copyright © Bobby H. Bammel. All rights reserved.
Section 15.2
Quito 00° and 78°21′W
French Geodesic Mission visited Ecuadorian territory in 1736
Measured roundness of Earth and latitude at the Equator.
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Longitude
• Longitude - imaginary lines drawn on the surface of the earth running from N to S poles and perpendicular to the equator
• Lines of longitude are also called meridians.
• Meridians are half circles that are portions of “great circles.”
• An infinite number of lines can be drawn as meridians.
Section 15.2
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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
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Standard Time Zones
Section 15.3
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Diagram Showing Latitude and Longitude of Washington, D.C.
Section 15.2
Quito, Ecuador 0
and 78 W
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Great Circle Distance
• The shortest surface distance between any two points on earth is the great circle distance.
• A great circle is any circle on the surface of a sphere whose center is the center of the sphere.
• Nautical mile (n mi) – one minute of arc of a great circle
• 1n mi = 1.15 mi
• 60 nautical miles = 1o Section 15.2
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Maps
• Generally maps are designed for some type of “navigation.”
• Since the earth is nearly a sphere (3-D) and most maps are flat (2-D) they are necessarily ‘projections.’
• The places on a map are shown relative to each other, and the fundamental frame of reference is the lines of latitude and longitude.
• Most with “north” at the top
• Scales are provided to determine distance.
Section 15.2
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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
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Days
• 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
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Solar Day vs. Sidereal Day
• The earth must rotate through 360o to complete one rotation w/ respect to the sun. The Solar Day is 4 min. longer than the Sidereal Day.
Section 15.3
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Days
• 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/24hr 15o/hr 1o/4 minutes
Section 15.3
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Time Measurement
• A 24 hour day begins at midnight and ends 24 hours later at midnight.
• Noon local solar time – when the sun is on the observer’s meridian
• Ante meridiem (A.M.) – the hours before noon
• Post meridiem (P.M.) – the hours after noon
• 12 o’clock should be stated as “12 noon” or “12 midnight.”
• In addition 12 midnight should have the dates “12 midnight, July 26-27.”
Section 15.3
My Trip to Ecuador
Quito 00°9′S 78°21′W
Latitude: 0 degrees,
9-15 minutes south of
equator .
Longitude: 78
degrees, 21 minutes
west of meridian.
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Standard Time Zones
• The earth is divided into 24 time zones, each containing approx. 15o of longitude (east or west of the meridian) or 1 hour. (Remember that the earth rotates 15o/hour = 1o/4! )
Section 15.3
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Standard Time Zones
• 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
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Time Zones of the Conterminous United States
Section 15.3
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Losing and Gaining 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
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Diagram Showing Times and Dates on Earth for Any Tuesday at 10 a.m.
EST
Section 15.3
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“Time Travel”
• Washington, D.C. is located at 39oN latitude.
• At the 39oN parallel the earth is rotating at a speed of approximately 800 mph.
• Therefore if we flew in a plane at 800 mph (along the 39th parallel) we would stay in the same position relative to the sun for as long as we flew!
• Therefore from our position in the plane it would appear that the sun “stood still.”
• In 24 hr we would arrive back in Washington, D.C. at the same time – but a day later!
Section 15.3
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International Date Line
• 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
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Finding the Standard Time and Date at Another Location – An Example
• It is 6 A.M. on March 21 in Los Angeles (34oN, 118oW). What are the time and date in Perth, Australia (32oS, 115oE)?
• Construct a circle with 24 even divisions on it.
• These divisions represent 15o increments of a full circle and each hour of the day.
• Los Angeles falls in the time zone with the 120oW central meridian.
• Perth falls in the time zone with the 120oE central meridian.
Section 15.3
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Finding the Standard Time and Date at Another Location – An Example (cont.)
• We know there are 24 hours in any day. We also are given that it is 6 A.M. in Los Angeles, therefore it is 10 P.M. in Perth.
Section 15.3
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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.
• 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
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Diagrams of Sun's Position (Degrees Latitude) at Four Different Times of the Year
Section 15.4
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Latitude
• 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
Section 15.4
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Finding the Approximate Altitude of the Sun as Observed from Washington D.C. on June 21
• The angle between the sun and the observer is 39o – 23.5o = 15.5o.
• The altitude of the sun is 90o – 15.5o = 74.5o
Section 15.4
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Finding the Approximate Altitude of the Sun as Observed from
Washington D.C. on December 21
Section 15.4
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Around the world in 80 Days
Jule Vernes: 12 min
http://www.youtube.com/watch?v=RhSHHYkGiqI
Section 15.5
