Celestial Coordinate SystemsCelestial Coordinate Systems

Learning ObjectivesLearning Objectives• Know the ultimate goal of celestial navigation.Know the ultimate goal of celestial navigation.• Know the definitions of terms and components Know the definitions of terms and components

associated with the terrestrial, associated with the terrestrial, celestialcelestial, and , and horizonhorizon coordinate systems.coordinate systems.

• Know the relationship between the terrestrial, Know the relationship between the terrestrial, celestialcelestial, and , and horizonhorizon coordinate systems. coordinate systems.

• Apply correct procedures to describe the location of Apply correct procedures to describe the location of a celestial body in reference to the a celestial body in reference to the celestial celestial andand horizon horizon coordinate systems.coordinate systems.

The Goal of Celestial NavigationThe Goal of Celestial Navigation

The solution of spherical triangles of sides The solution of spherical triangles of sides based on the observed positions of celestial based on the observed positions of celestial bodies, in order to determine the position of bodies, in order to determine the position of a vessel.a vessel.

100 years ago, this involved some 100 years ago, this involved some complicated spherical trigonometry.complicated spherical trigonometry.

Today, it requires the use of tables or a Today, it requires the use of tables or a navigational calculator (HP makes one).navigational calculator (HP makes one).

Understanding the Sky By carefully watching the sky, By carefully watching the sky, astronomers learn about how the astronomers learn about how the universe works. By studying eclipses universe works. By studying eclipses and the and the motions of the planetsmotions of the planets, , astronomers eventually realized that astronomers eventually realized that gravitygravity controls the way things move, controls the way things move,

and that gravity was responsible for and that gravity was responsible for the the motionmotion of the Sun, of the Sun, the Moonthe Moon, and , and the stars in our sky as well.the stars in our sky as well.

We now know that the We now know that the Earth's motionEarth's motion is responsible for is responsible for seasonsseasons. .

                                                                                  

                               

•The Sun and the collection of celestial bodies that orbit it. These include the nine planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto) and their 60 moons, the asteroid belt, the comets and the Kuiper belt.

SOLAR SYSTEM

by position by position relative to the Sun: relative to the Sun: innerinner planets planets: Mercury, Venus, : Mercury, Venus,

Earth and Mars. Earth and Mars. outerouter planets planets: Jupiter, Saturn, : Jupiter, Saturn,

Uranus, Neptune and Pluto. Uranus, Neptune and Pluto. The asteroid belt between Mars The asteroid belt between Mars

and Jupiter forms the and Jupiter forms the boundary boundary between the inner solar system between the inner solar system and the outer solar system. and the outer solar system.

by position by position relative to Earthrelative to Earth: : inferiorinferior planets planets: Mercury and : Mercury and

Venus. Venus. • closer to the Sun than Earth. closer to the Sun than Earth. • The inferior planets The inferior planets show show

phases like the Moon'sphases like the Moon's when when viewed from Earth. viewed from Earth.

superiorsuperior planets planets: Mars thru Pluto. : Mars thru Pluto. • farther from the Sun than farther from the Sun than

Earth. Earth. • The superior planets The superior planets

always always appear fullappear full or nearly or nearly so.so.

Like all planets in our solar system, the Earth is in an elliptical orbit around our Sun In Earth's case, its orbit is nearly circular, so that the difference between Earth's farthest point from the Sun and its closest point is very small.

•at perihelion both hemispheres were 147.5 million km from the Sun. •That barely differs from the greatest distance, 152.6 million km in July, which astronomers call aphelion. •Perihelion always occurs near January 4th, while aphelion lands near the 4th of July.

•The Earth travels around the sun in an ellipse.

• If the Earth were to orbit the sun in a circle, the Earth's speed around the sun would be constant. We can think of this as the Earth's average speed.

• However, because the Earth's orbit is elliptical, the speed of the Earth varies throughout the year.

•The speed of the Earth is fastest when it is closest to the sun, in January, and slowest when it is farthest away from the sun, in July.

• In other words, in January it will be moving faster than average, and in July it will be moving slower than average.

Earth's orbit defines a two-dimensional plane which Earth's orbit defines a two-dimensional plane which we call the we call the eclipticecliptic. It takes roughly . It takes roughly 365365 days for the days for the Earth to go around the Sun once.Earth to go around the Sun once.

This means that the Earth is rushing through space This means that the Earth is rushing through space around the Sun at a rate of about around the Sun at a rate of about 67,000 miles per 67,000 miles per hourhour! The time it takes for the Earth to go around ! The time it takes for the Earth to go around the Sun one full time is what we call a year. the Sun one full time is what we call a year.

There are three ways that Earth's orbit changes over time.

•Eccentricity: The shape of Earth's orbit around the Sunbecomes slightly more and then less oval every100,000 years.

•Precession: Earth wobbles on it axis as it spins, completing a fullwobble every 23,000 years.

•Tilt: The angle of the Earth's axis relative to the plane of its orbitchanges about three degrees every 41,000 years.

The Seasonal Merry-Go-Round

                                                                

                                 

The tilt of Earth's rotational axis and the Earth's orbit work together to create the seasons. As the Earth travels around the Sun, it remains tipped in the same direction, towards the star Polaris. This means that sometimes the northern half of the Earth is pointing towards the Sun (summer), and sometimes it is pointing away (winter). These points in the Earth's orbit are called solstices. Notice that when the northern hemisphere is tilted towards the Sun, the southern hemisphere is tilted away. This explains why the hemispheres have opposite seasons. Halfway in between the solstices, the Earth is neither tilted directly towards nor directly away from the Sun. At these times, called the equinoxes, both hemispheres receive roughly equal amounts of sunlight. Equinoxes mark the seasons of autumn and spring and are a transition between the two more extreme seasons, summer and winter.

•The ecliptic is the path the sun appears to take among the stars due to the annual revolution of the earth in its orbit.

•It is considered a great circle of the celestial sphere, inclined at an angle of about 23°26' to the celestial equator, but undergoing a continuous slight change. •This angle is called the obliquity of the ecliptic. •This inclination is due to the fact that the axis of rotation of the earth is not perpendicular to its orbit.

•It is this inclination which causes the sun to appear to move north and south during the year, giving the earth its seasons and changing lengths of periods of daylight.

The two points at which the ecliptic crosses the equator are called equinoxes ( meaning “equal nights”).

When the sun reaches its maximum declination of about 23o 25’ N or S is called solstice (meaning “sun standing still”).

On or about June21, about On or about June21, about 10 or 11 days before 10 or 11 days before reaching aphelion, the reaching aphelion, the northern part of the earth’s northern part of the earth’s axis is tilted toward the sun.axis is tilted toward the sun.

The The north polar regions north polar regions are are having continuous sunlight; having continuous sunlight; the the Northern HemisphereNorthern Hemisphere is is having its having its summersummer with with long, warm days and short long, warm days and short nights; nights;

the the Southern HemisphereSouthern Hemisphere is is having having winterwinter with short with short days and long, cold nights; days and long, cold nights; and the and the south polar regionsouth polar region is in continuous darkness. is in continuous darkness.

This is the This is the summersummer solstice.solstice.

The Summer Solstice Let's pretend, for the moment, that you're the Let's pretend, for the moment, that you're the person standing on the Earth in the picture to person standing on the Earth in the picture to the left, living in Topeka, Kansas, around the left, living in Topeka, Kansas, around 40° N40° N latitudelatitude. The picture on the . The picture on the left shows the view left shows the view from the solar system (upper panel), and from from the solar system (upper panel), and from on the surface of the earth (lower panel).on the surface of the earth (lower panel). Notice that some of the same features are Notice that some of the same features are labelled on each panel. The upper panel shows labelled on each panel. The upper panel shows that on the summer solstice (which occurs that on the summer solstice (which occurs around June 21), the around June 21), the northern half of the Earth northern half of the Earth is tilted towards the Sun. Notice that the Sun is is tilted towards the Sun. Notice that the Sun is north of the equator.north of the equator. For you in Topeka, the For you in Topeka, the altitudealtitude of the Sun at noon is 73.5°, which is of the Sun at noon is 73.5°, which is pretty high in the sky. In fact, that is as high as pretty high in the sky. In fact, that is as high as the Sun ever gets at that latitude. The bottom the Sun ever gets at that latitude. The bottom panel shows how the Sun moves through the panel shows how the Sun moves through the sky for someone standing on the ground in sky for someone standing on the ground in Topeka. Topeka. So in general, the So in general, the northern hemisphere is northern hemisphere is getting more direct sunlightgetting more direct sunlight, which heats the , which heats the Earth most efficiently, than the southern Earth most efficiently, than the southern hemisphere. This is hemisphere. This is summer for people in the summer for people in the northern hemispherenorthern hemisphere. During the summer, the . During the summer, the Sun is also above the horizon longer than it is Sun is also above the horizon longer than it is during the winter. The summer solstice is the during the winter. The summer solstice is the longest day of the yearlongest day of the year. .

                                                    

                                             

on or about on or about December December 22,22, the the

Southern Hemisphere is Southern Hemisphere is tilted toward the sun tilted toward the sun and conditions are the and conditions are the reversereverse of those six of those six months earlier; months earlier;

the Northern the Northern Hemisphere is having its Hemisphere is having its winterwinter,,

and the Southernand the Southern Hemisphere its Hemisphere its summersummer. . This is the This is the winter winter

solsticesolstice..

The Winter Solstice Let's pretend, for the moment, that you're the Let's pretend, for the moment, that you're the person standing on the Earth in the picture to the person standing on the Earth in the picture to the left, living in Topeka, Kansas, around left, living in Topeka, Kansas, around 40° N40° N latitudelatitude. . The The picture on the left shows the view from the solar picture on the left shows the view from the solar system (upper panel), and from on the surface of system (upper panel), and from on the surface of the earth (lower panel).the earth (lower panel). Notice that some of the Notice that some of the same features are labelled on each panel. The same features are labelled on each panel. The upper upper panel panel shows that on the winter solstice (whichshows that on the winter solstice (which occurs around December 21), the northern half of occurs around December 21), the northern half of the Earth is tilted away from the Sunthe Earth is tilted away from the Sun. Notice that the . Notice that the Sun is Sun is south of the equatorsouth of the equator. For you in Topeka, the . For you in Topeka, the altitudealtitude of the Sun at noon is 26.5°, which is pretty of the Sun at noon is 26.5°, which is pretty low in the sky. That is the lowest the Sun gets at low in the sky. That is the lowest the Sun gets at that latitude.. The that latitude.. The bottom panelbottom panel shows how the Sun shows how the Sun moves through the sky for someone standing on the moves through the sky for someone standing on the ground in Topeka. ground in Topeka. So, on the So, on the winter solsticewinter solstice, the , the northern hemispherenorthern hemisphere is getting less direct sunlight than the southern is getting less direct sunlight than the southern hemisphere. This is hemisphere. This is winter for people in the northern winter for people in the northern hemisphere.hemisphere. During the winter, the Sun is also During the winter, the Sun is also above the horizon for a shorter time than it is during above the horizon for a shorter time than it is during the summer (the nights are long). The the summer (the nights are long). The winter winter solstice is the shortest day of the yearsolstice is the shortest day of the year. At this same . At this same time, the southern half of the Earth is tilted toward time, the southern half of the Earth is tilted toward the Sun. the Sun.

                                                            

                                   

about about September 23September 23, the earth, the earth has moved a quarter of the way has moved a quarter of the way

around the sun, but its axis of around the sun, but its axis of rotation still points in about the rotation still points in about the

same direction in space.same direction in space. The sun The sun shines equally on bothshines equally on both hemispheres,hemispheres, and days and and days and nights are the nights are the same lengthsame length over the entire world. over the entire world. The sun is The sun is setting at the Northsetting at the North Pole and rising at the SouthPole and rising at the South Pole.Pole. The Northern Hemisphere is The Northern Hemisphere is having its having its autumnautumn, and the, and the Southern Hemisphere Southern Hemisphere its springits spring. . This is the This is the autumnal equinoxautumnal equinox..

on or about on or about March 21March 21when when both hemispheres again both hemispheres again receive receive equal amounts of equal amounts of sunshine, sunshine,

the Northern Hemisphere the Northern Hemisphere is having is having springspring and and

the Southern Hemisphere the Southern Hemisphere is having is having autumn,autumn,

the the reversereverse of conditions of conditions six months before. six months before.

This is the This is the vernal equinox vernal equinox or or first point of Ariesfirst point of Aries..

The Vernal and Autumnal Equinoxes We're still pretending that you're the person We're still pretending that you're the person standing on the Earth in the picture to the left, living standing on the Earth in the picture to the left, living in Topeka, Kansas, around in Topeka, Kansas, around 40° N 40° N latitudelatitude. The . The picture on the left shows the view from the solar picture on the left shows the view from the solar system (upper panel), and from on the surface of the system (upper panel), and from on the surface of the earth (lower panel).earth (lower panel). Notice that some of the same Notice that some of the same features are labelled on each panel. In the upper features are labelled on each panel. In the upper panel, the Earth's axis is pointing into your computer panel, the Earth's axis is pointing into your computer screen. The screen. The upper panelupper panel shows that on an shows that on an equinox equinox (which occurs around March and September 21),(which occurs around March and September 21), neither half of the Earth points directly towards the neither half of the Earth points directly towards the Sun. In fact, the Sun is at the equator, so both halves Sun. In fact, the Sun is at the equator, so both halves of the Earth are getting about the same amount of of the Earth are getting about the same amount of sunlight. For you in Topeka, the sunlight. For you in Topeka, the altitudealtitude of the Sun is of the Sun is about 50°, in between its altitude on the solstices. about 50°, in between its altitude on the solstices. The The bottom panelbottom panel shows how this looks to someone shows how this looks to someone standing on the ground in Topeka. standing on the ground in Topeka. Equinox literally means "equal night". On the vernal Equinox literally means "equal night". On the vernal (spring) and autumnal (fall) equinoxes, (spring) and autumnal (fall) equinoxes, day and day and night are the same length.night are the same length. Neither hemisphere gets Neither hemisphere gets more sunlight than the other, so both have similar more sunlight than the other, so both have similar seasons (fall in one hemisphere and spring in the seasons (fall in one hemisphere and spring in the other). other).

                                                          

                                       

•Everywhere between the parallels of about 23°26'Nand about 23°26'S the sun is directly overhead at some time during the year.

•Except at the extremes, this occurs twice:once as the sun appears to move northward, and the second time as it moves southward.

•This is the torrid zone. The northern limit is the Tropic of Cancer,

•and the southern limit’s the Tropic of Capricorn.

Tropic of Cancer - The northern parallel of declination, approximately 23o 27’ from the celestial equator, reached by the sun at its maximum northerly declination, or the corresponding parallel on the earth.

Tropic of Capricorn - the southern parallel of declination, approximately 23o 27’ from the celestial equator, reached by the sun at its maximum southerly declination, or the corresponding parallel on the earth.

•The parallels about 23°26' from the poles, marking the approximate limits of the circumpolar sun, are called polar circles.

•The one in the Northern Hemisphere being the Arctic Circle and the one in the Southern Hemisphere the Antarctic Circle.

•The areas inside the polar circles are the north and south frigid zones. The regions between the frigid zones and the torrid zones are the north and south temperate zones.

66o 33’N

Arctic circle

Arctic circle - the parallel of latitude at about 66o 33’ N marking the southern limit of the north frigid zone.

66o 33’ SAntarctic Circle

Antarctic circle - the parallel of latitude at about 66o 33’S, marking the northern limit of the south Frigid zone.