ASTRONOMY

FOR FINALS

The Celestial Sphere

An imaginary gigantic sphere of which heavenly bodies are attached, with an infinite radius whose center is the earth.

Speed of Rotation of celestial sphere

360o 59.14’ per 24 hours

Celestial Poles

are the points on the surface of the celestial sphere pierced by the extension of the earth’s polar axis.

Celestial Axis

is the prolongation of the earth’s polar axis.

Zenith

is the point where the plumb line at the place of observation projected above the horizon meets, the celestial sphere. It is also defined as the point on the celestial sphere vertically above the observer.

Nadir

is that point on the celestial sphere directly beneath the observer, and directly opposite to the zenith.

Great Circle

a great circle of a sphere is the trace on its surface of the intersection of a plane passing through the center of the sphere.

Observer’s Horizon

a great circle of the celestial sphere where a plane, perpendicular to the plumb line at the place of observation and passing through the center of the earth, cuts the celestial sphere.

Observer’s Horizon

This circle is halfway between the observer’s zenith and nadir and is the plane in which azimuth is measured. It is shown by four fixed points (N, E, W, and S), standing for points of the magnetic compass.

Observer’s Vertical

a vertical line at the location of the observer which coincides with the plumb line and is normal to the observer’s horizon.

Celestial Equator

a great circle which is perpendicular to the polar axis of the celestial sphere. It is an extension of the plane of the earth’s equator outward until it intersects the celestial sphere.

Vertical Circle

a great circle passing through the observer’s zenith and any celestial body. Such a circle is perpendicular to the horizon, and represents the line of intersection of a vertical plane with the celestial sphere.

Hour Circle

a great circle joining the celestial poles and passing through a celestial body and whose plane is perpendicular to the plane of the celestial equator.

Meridian

is the great circle of the celestial sphere which passes through the celestial poles and the observer’s zenith. This circle is both a vertical and an hour circle.

North Pole

90d N

Artic Circle

66.5d N

Tropic of Cancer

23.5d N

Equator

0d

Tropic of Capricorn

23.5d S

Antartic Circle

66.5d S

South Pole

90d S

Meridians (Longitude)

is the great circle of the celestial sphere which passes through the celestial poles and the observer’s zenith. This circle is both a vertical and an hour circle.

Vernal Equinox

March 20 0 hours 0° Pisces

Summer Solstice

June 21 6 hours 23.4°N Gemini

Autumnal Equinox

September 23 12 hours 0° Virgo

Winter Solstice

December 22 18 hours 23.4°S Sagittarius

Almucantar

a small circle of constant altitude parallel to the horizon

Parallels of declination

small circles that are parallel to the celestial equator

Circumpolar stars

the stars that never sets.

Upper Meridian Transit (Upper Culmination)

the star reaches the highest point in the sky

Ecliptic

the trace of the sun’s apparent annual journey around the celestial sphere

Obliquity of the ecliptic

the angle between the ecliptic and the celestial equator.

Zodiac

the collective term for the twelve constellations through which the ecliptic passes.

CELESTIAL COORDINATE SYSTEM

Used to define the positions of heavenly bodies and points of reference on the celestial sphere.

HORIZON SYSTEM

Primary reference circle: Horizon ; Secondary reference circle: Vertical Circles

AZIMUTH

a spherical angle and is defined as the angular distance measured along the horizon from the observer’s meridian to the vertical circle through the body

ALTITUDE

is the angular distance above or below the celestial horizon measured along the vertical circle through the body

COALTITUDE/ZENITH DISTANCE

complement of the altitude which is actually 90 degrees minus altitude.

EQUATORIAL SYSTEM

Primary reference circle: Celestial Equator ; Secondary reference circle: Hour circle

DECLINATION

the angular distance above or below the celestial equator measured along the hour circle through the body

RIGHT ASCENSION

the angular distance measured along the celestial equator from the vernal equinox eastward to the hour circle passing through the body.

HOUR ANGLE SYSTEM

Primary reference circle: Celestial Equator Secondary reference circle: Hour Circle

HOUR ANGLE

angular distance measure along the equator from the meridian of reference to the hour circle through the body

TIME

Is a measure in which events can be ordered from the past through the present into the future, and also the measure of durations of events and the intervals between them.

TIME

The daily motion of the stars and their positions within the celestial sphere at any instant are intimately related to time. ➢The measurement of time is directly dependent upon the apparent motion of heavenly bodies caused by the earth’s rotation.

Apparent Solar Time

Apparent time or true solar time is determined with respect to the true sun. It is conveniently measured by means of sun dial.

Apparent Solar Time

The time required for one apparent revolution of the true sun about the earth is called an apparent solar day

Sidereal Time

referred from a star, and it is actually a star time. ➢ It is measured by special clocks which are regulated so as to gain 24 hours a year over ordinarily used time pieces.

Mean Solar Time or Civil Time

Is based from a fictitious body, called the mean sun. ➢ It is assumed to move along the celestial equator at the average or mean rate of motion of the real sun during the year ➢ One complete revolution (+/-365.2422 mean solar days)

Civil Time

refers to statutory time scales designated by civilian authorities, or to local time indicated by clocks

Local Civil Time

based on the central meridian of an observer

equation of time

Apparent and Mean are at all times separated by a constantly changing hour angle called

Greenwich Civil Time

The standard time referred to the Greenwich Meridian is called

Standard Time

Is the mean time at meridians 15d or 1 hour apart, measured either eastward from the Greenwich meridian.

Local Time

Is the time based on the observer’s meridian

Local Civil Time (LCT)

based on the mean solar time, is the hour angle of the mean sun measured from the local meridian plus 12 hours.

Local Apparent Time

based on the true sun, is the hour angle of the sun’s center plus 12 hours

Daylight Saving Time

Time adjusted to achieve longer daylight, especially in summer. Is a way of making better use of the natural daylight by setting the clock forward one hour during the summer months, and back again in the fall

Daylight Saving Time

Is always one hour ahead of standard time. ➢ It is usually adopted in different countries during the summer months.

Spherical Triangle

is the figure formed by joining any three points on the surface of a sphere by arcs of great circles

Point P

is the north pole of the celestial sphere

Point Z

is the observer’s zenith

Point S

is the heavenly body observed which maybe the sun or any other known star such as Polaris

Side PS (p)

Polar Distance or codeclination, (90-Declination)

Side PZ (y)

Colatitude of Z, (90-Latitude)

Side ZS (z)

Zenith distance or coaltitude of the observed heavenly body, (90-Altitude)

Angle Z

True azimuth of the heavenly body.

Angle S

Parallactic angle, it is usually unnecessary to use the value of this angle

Angle t

Meridian angle

degrees, minutes and seconds

the sides and angles of the astronomical triangle are measured in angular units usually in

CORRECTION FOR PARALLAX AND REFRACTION

Correction applied to the measured vertical angle or altitude.

Parallax

difference in direction of a heavenly body as seen from the surface and from the earth.

Refraction

The change of direction or bending of light