Physical Science chp 15
Chapter 15: Place & Time
Introduction to Space and Time
Physical Science examines events that occur at different places and at different times.
Events can be described as separated by space and time.
Our five senses allow us to perceive objects and determine their positions relative to one another.
Time can be perceived in a more elusive manner; it is often related to observable changes in the environment.
One Dimensional Location
Reference System: Location requires a reference system that consists of one or more dimensions.
One-Dimensional System:
Represented as a straight line extending from positive infinity to negative infinity.
The origin and units of length must be clearly indicated.
Examples of one-dimensional scales include:
Temperature scales.
Left/right distinctions.
Above sea level/below sea level.
Profit/loss measurements.
Cartesian Coordinates
Two-Dimensional System:
Two lines intersect perpendicularly with an assigned origin at the point of intersection.
The horizontal line represents the x-axis.
The vertical line represents the y-axis.
The Cartesian coordinate system is named after the French philosopher/mathematician René Descartes (1596-1650).
Coordinate Definition:
The x-coordinate provides the distance from the y-axis.
The y-coordinate provides the distance from the x-axis.
Many urban layouts, such as cities, are designed in a Cartesian pattern with streets running North-South (N-S) and East-West (E-W).
A point in this system is represented as (x,y).
Latitude and Longitude
Earth's Coordinate System:
Location on Earth is defined using a coordinate system that includes latitude and longitude.
The Earth’s rotation on its axis allows us to utilize the geographic poles as North-South reference points.
Geographic Poles:
Imaginary points on the Earth's surface where its axis extends out into space.
Equator:
An imaginary line encircling the Earth midway between the North and South poles.
Considered a great circle - a circle on the surface of Earth within a plane passing through the center.
Parallels and Meridians
Latitude:
Angular measurement in degrees, specifically the positions north or south of the equator.
Measured relative to the Earth's center from the equator.
Lines of equal latitude are referred to as parallels, forming circles parallel to the equator.
There are an infinite number of parallels ranging from 0° to 90° North or South.
As one moves from the equator towards the poles, the parallels represent smaller circles, with the equator being the largest and the poles being singular points (0°).
Longitude:
Lines drawn on the Earth’s surface from the North to the South poles, perpendicular to the equator.
Also referred to as meridians, they are half circles that form portions of great circles.
Longitude measures angular distance in degrees east or west from the Prime Meridian (0°) located at Greenwich, England.
The maximum value of longitude can reach 180° East or West.
Great Circle Distance
Great Circle:
The shortest distance between any two points on the Earth's surface is measured along a great circle.
A great circle is defined as any circle on the surface of a sphere whose center aligns with the center of the sphere.
Nautical Mile (n mi):
Defined as one minute of arc of a great circle.
Relationship: .
It is also understood that .
Example Calculation:
Determine the nautical miles between locations A (10°S, 90°W) and B (60°N, 90°E). Evaluate the number of degrees between points A and B.
Time Measurement
Concept of Time:
Defined as the continuous forward progression of events.
To measure time continuously, one must use a periodic movement of an object as a reference.
International Unit of Time:
The second has been established as the unit of time, defined by the vibration of the cesium-133 atom, specifically $9,192,631,770$ cycles per second.
Solar Day:
The time interval between two consecutive passages of the same meridian by the sun, typically around 361°.
Sidereal Day:
The time between two successive crossings of the same meridian by a star other than the sun, usually measured at 360°.
Solar Day vs. Sidereal Day
When accounting for the Earth's movement, the Earth needs to rotate through 360° plus 0.985° to complete one full rotation regarding the sun.
This results in the Solar Day being approximately 4 minutes longer than the Sidereal Day.
During one complete orbit around the Sun, the Earth completes 365.25 rotations, but only 360° are completed in one revolution.
As the Earth rotates, it thus moves slightly less than 1° of angular distance each day, calculated as .
Time Zones
A 24-hour day is defined as beginning at midnight and concluding 24 hours later at midnight.
Local Solar Time:
This occurs when the sun is directly overhead an observer’s meridian.
Ante Meridiem (A.M.):
The hours preceding noon.
Post Meridiem (P.M.):
The hours following noon.
Clarification: 12 o'clock should always be stated as either “12 noon” or “12 midnight.”
Standard Time Zones:
Earth's surface is divided into 24 time zones, approximately each covering 15° of longitude or one hour of time (noting Earth’s rotation of 15°/hour).
The first time zone begins at the Prime Meridian and extends roughly 7.5° to both the east and west.
Time zone centers are designated as multiples of 15°.
Traveling West and East in Time Zones
Gaining Time:
Traveling west results in a gain of time; your clock will appear one hour ahead when crossing into a new time zone.
Example: Driving from Texas at noon into New Mexico where the local time is now only 11 A.M.
Losing Time:
Traveling east results in a loss of time; you will lose an hour when crossing into a new time zone.
International Date Line:
Located at the 180° meridian, it is precisely opposite the Prime Meridian.
Crossing the IDL traveling west advances the date into the next day; traveling east subtracts one day from the present date.
Seasonal Variations
Determining Latitude:
During the year, the sun appears to adjust its overhead position between 23.5° N and 23.5° S.
The Tropic of Cancer is at 23.5° N, and the Tropic of Capricorn is at 23.5° S.
As the Earth revolves around the Sun, the sun directly overhead at noon shifts through various latitudes, influenced by the constant 23.5° tilt of Earth relative to the Sun.
Zenith:
This is the position that is directly overhead, always at an angle of 90° from the horizon.
Altitude:
The angle measured from the horizon up to the Sun at noon.
Zenith Angle:
The angle from the zenith to the Sun, calculated as 90° - altitude (it is the complementary angle).
Sun's Position and Seasons
The Sun never has an overhead position greater than 23.5° latitude.
It is always positioned due south at 12 noon local solar time for U.S. observers.
Solstices:
Occur when the Sun is at the farthest point from the equator (“the Sun stands still”).
Summer Solstice occurs at the most northern position (23.5° N).
Winter Solstice occurs at the most southern position (23.5° S).
During an equinox, the sun is directly over the equator, and both day and night are equal in duration worldwide, except at the poles.
Vernal Equinox falls on March 21.
Autumnal Equinox falls on September 22.
Daylight Hours and Yearly Cycles
The distance from the Sun ensures the light rays that reach Earth are parallel, resulting in one half of the planet being illuminated while the other remains in darkness.
However, the number of daylight hours at specific locations depends on both latitude and the time of year.
Yearly Calendar and Time Measurement
Year Definition:
A single complete orbit of the Earth around the Sun is termed a year.
Types of Years:
Tropical Year: The interval from one vernal equinox to the next, approximately 365.2422 mean solar days.
Sidereal Year: This is measured based on Earth's full revolution around the sun in relation to a specific star other than the sun, generally 365.2536 mean solar days.
Historical Calendar Systems
Early Time Measurement:
The most primitive unit for measuring time is probably the day.
The moon cycle (approx. 29.5 solar days) would likely have been humanity's next reference point for time.
The calendar used today can trace back to the Sumerians (3000 B.C.), who divided the year into 12 lunar months of 30 days each.
Roman Calendar:
Initially consisted of 10 months, lacking January and February, which were added later.
Julian Calendar was introduced in 45 B.C. during Julius Caesar's reign.
Augustus Caesar later adjusted the calendar, naming July and August in honor of himself and Julius Caesar, adding one day to August to match July's duration.
The Julian Calendar counted 365 days with an additional day (leap year) for every year divisible by 4, accommodating Earth's actual orbital period being approximately 365.25 days.
Gregorian Calendar
The Julian Calendar was used for over 1600 years but had slight inaccuracies.
1582: Pope Gregory XIII recognized the discrepancy in the calendar due to the Vernal Equinox not landing on March 21.
Hence, 10 days were eliminated to correct this misalignment.
The accurate year length corrected to 365.2422 days led to adjustments where every 400 years, three leap years were ignored; this is the modern Gregorian calendar system used today.