OBSERATIONS

ASTRONOMICAL

CelestialSphere

Celestial Sphere For purposes of surveying, an assumption is

made that the stars and other heavenly bodies are all fixed within a gigantic sphere with an infinite radius whose center is the earth called the celestial sphere.

The celestial sphere rotates from east to west about a line which coincides with the earth’s axis.

The speed of rotation of the celestial sphere is 360˚ 59.14’ per 24 hours, thus making slightly more than one revolution per day

An observer is assumed to be at the center of this sphere since the radius is negligible in comparison to the distance to the heavenly bodies within the sphere.

Vertical angles measured to celestial objects are practically the same whether measured at the surface or at the center of the earth.

Surveyors and engineers are not concerned with the distances between celestial bodies. Their observations are more on the determination of angular relations which are measured on earth between celestial bodies or some points on earth and the celestial body being observed.

Hence, the assumption made is that the universe is spherical in shape and that celestial bodies are points on the celestial sphere.

Definition of Terms1. Celestial Poles – are the points on the surface of the

celestial sphere pierced by the extension of the earth’s polar axis.

2. Celestial Axis – is the prolongation of the earth’s polar axis

3. Zenith – is the point where the plumb line at the place of observation projected above the horizon meets the celestial sphere.

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

5. 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.

6. 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. This circle is halfway between the observer’s zenith and nadir and is the plane azimuth is measured.

7. 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.

8. 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.

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

10.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.

11.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.

Observation of Polaris In surveying, the use of true or astronomical

directions has several advantages over the use of assumed or magnetic directions. One reason is that permanence is given to the direction of boundaries of land as compared to magnetic directions which are constantly changing.

True directions may be obtained by sighting on the sun or on one of several thousand stars whose positions are known.

The sun and Polaris (the north star) are the most useful celestial bodies for observations made in the northern hemisphere.

In the southern hemisphere, the Southern Cross is commonly used since there is no bright star located near the south pole.

Polaris is a circumpolar star since it rotates very close to the celestial north pole.

The star is of important significance to engineers and surveyors since it is commonly used to determine the true direction of lines on the earth’s surface.

Relative position of Polaris with respect to the north celestial pole

Polaris is a fairly bright star found about 1˚ from the north celestial pole. It is the last star in the tail of the constellation Ursa Minor (Little Bear) and is located in the sky by first finding the Big Dipper in Ursa Major.

The two stars (Merak and Dubhe) of the dipper farthest from the handle are the Pointers, and Polaris is the nearest bright star along the line through the Pointers.

It is also on the line through the westernmost star of Cassiopeia and the end star of the Big Dipper handle.

Apparent motion of Polaris

From these descriptions of the motions and positions of Polaris it is apparent that, at the moments of elongation, the star’s motion will be nearly vertical and its bearing will change slightly with time.

For an accurate determination of the true direction of a line, the most ideal time to observe the star is when it is at or near one of its elongations.

By sighting Polaris at UC or LC, all that needs to be done is to depress the telescope and set a point on the ground to define a true north direction from the occupied position of the observer to the point set on the ground.

The disadvantage of taking sights on a circumpolar star is that it moves quite rapidly from west to east or east to west at culmination and there is a need to sight on the star at a very precise time.

An appreciably large error in azimuth occurs when a small error is made on the correct time of culmination.

The exact time of UC, WE, LC, and EE for Polaris are provided in an Ephemeris.

Ephemerides

Ephemerides Is an astronomical almanac containing tables

giving the computed position of the sun, the planets, and various stars for every day of a given period.

A variety of ephemerides are available to surveyors for obtaining sun and star positions. Some of the most useful ones are:

1. The Nautical Almanac, published by the U.S. Naval Observatory, Washington, D.C., USA.

2. The Ephemeris of the Sun. Polaris and other Selected Stars, published by the U.S. Naval Observatory, Washington, D.C., USA.

3. Apparent places of fundamental Stars, published by Astromisches Reschen Institute, Heildelberg, Germany.

4. Solar Ephemeris, published by K & E, New Jersey, USA

5. Almanac for Geodetic Engineers, published by Philippine Atmospheric, Geographical and Astronomical Services Administration, Manila, Philippines

Parallels and Meridian Any point on the surface of the Earth can

be systematically located by the use of geographical or spherical coordinates. This coordinate system is based upon two sets of lines called the parallels and meridians

1. Parallels Are lines formed by passing

a series of imaginary planes perpendicular to the axis of the Earth.

Parallels are used to express distances of points above and below the equator in degrees, minutes, and seconds.

A plane intersecting the globe along a great circle divides the globe into equal halves and passes through its center

One such plane which passes through the center of the Earth and halfway between the poles forms on the surface of a great circle is called the equator

2. Meridians Are formed by passing a

series of imaginary planes through the Earth’s poles.

Meridians are numbered from 0 to 180 eastward as well as westward. The 0 to 180 meridians together form a great circle through the poles which divides the Earth into two halves.

The meridian which passes through the former site of the British Royal Observatory near Greenwich England is designated as the 0 meridian

Longitudes are generally used in measuring meridian distances. It is expressed in either arc or time measure.

The following tabulation should serve as a useful summary of time and arc relations

24h = 360o 1m = 15’ 1o = 4m

1h = 15o 1s = 15” 1’ = 4s

CelestialCoordinate System

Celestial Coordinate System Spherical coordinate system are used to define

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

The location of a body is usually expressed in terms of two perpendicular components of curvilinear coordinates.

A primary reference circle is used for referencing one component and the other is reckoned from a secondary reference circle. The coordinates must be referred to an origin somewhere on the primary and secondary circles.

Different celestial coordinate system are adopted and the most common are:

1. Horizon System2. Equatorial System3. Local Hour Angle System

1. HORIZON SYSTEM:► In this coordinate system, the HORIZON is

the primary reference circle and the secondaries are VERTICAL CIRCLES.

The azimuth of a heavenly body is 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.

► The altitude of a heavenly body is the angular distance above or below the celestial horizon measured along the vertical circle through the body.

2. EQUATORIAL SYSTEM:► The primary great circle used is the

celestial equator and the secondaries are those of hour circles. They all have same secondary coordinate called the declination.

The declination of a heavenly is the angular distance above or below the celestial equator measured along the hour circle through the body.

► Within the celestial sphere is an important reference point called the vernal equinox.

Right ascension is reckoned from the vernal equinox and it is used with the declination in defining the location of any heavenly body within the celestial sphere.

The earth as it travels around the sun in its annual revolution defines the plane.

3. HOUR ANGLE SYSTEM:► The primary reference circle in the hour

angle system is the celestial equator; the hour circle through the observer’s zenith is the secondary reference.

The hour angle of any heavenly body is defined as the angular distance measured along the equator from the meridian of reference to the hour circle through the body.

Time, Apparent Time, and Sidereal Time

Definition of Time:► the indefinite continued progress of

existence and events in the past, present, and future regarded as a whole.

It is also considered as a point of time as measured in hours and minutes past midnight or noon.

Different systems used in the determination of time:

1. Apparent Solar Time2. Sidereal Time3. Mean Solar Time4. Standard Time

Apparent Time This method of time determination is resolved

with respect to the apparent sun or the real sun. This method employs the operation of a sun

dial. The time required for an apparent revolution of

the earth around the sun is called as a solar day. It begins at when the true sun starts to appear

on the lower branch of the observer’s meridian. It is also referred to as sun time.

However, the sun is not a good indicator because the length of the apparent solar day is not constant. Due to the following reasons:

The non-constant velocity of the apparent sun on the elliptical path as it moves across the sky.

The amount of time that light is required to travel on varying points on the elliptical orbit of the Earth.

Equinoxes and Solstices

Sidereal Time

A sidereal day at any place on the earth’s surface begins when the vernal equinox is on the observer’s meridian and above the horizon.

This means that after 24 hours the vernal equinox is again at meridian passage and 1 sidereal day passes.

It is considered as a star time. An apparent solar day is 3 minutes and 56

seconds longer than a sidereal day which is 23 hours and 56.1 minutes

At any point on the earth’s surface, the sidereal time is equivalent to the hour angle of the vernal equinox referred to as the meridian of the place.

Sidereal time is measured by special clocks which are regulated so as to gain 24 hours a year over ordinarily used time pieces.

Difference in Solar Time and Sidereal TimeAt time 1, the Sun and a certain distant star are both overhead. At time 2, the planet has rotated 360° and the distant star is overhead again (1→2 = one sidereal day). But it is not until a little later, at time 3, that the Sun is overhead again (1→3 = one solar day). More simply, 1-2 is a complete rotation of the Earth, but because the revolution around the Sun affects the angle at which the Sun is seen from the Earth, 1-3 is how long it takes noon to return.

Mean solar time, Longitudinal and time, Greenwich civil time

SOLAR TIME is a reckoning of the passage of time based

on the sun's position in the sky. The fundamental unit of solar time is the day.

TYPES OF SOLAR TIME Apparent Solar Time (sundial time) Mean Solar Time (clock time)

MEAN SOLAR TIME  time based on the motion of the mean su

n.

MEAN SUN A fictitious body that has been devised

used as an accurate time indicator. an imaginary sun conceived as moving

through the sky throughout the year at a constant speed equal to the mean rate of the real sun, used in calculating mean solar time (an imaginary sun moving uniformly along the celestial equator).

CIVIL TIME It is measured by watches and clocks

and is the hour angle of the mean sun.

MEAN SOLAR DAY Is the time required for one revolution of

the mean sun.

Mean noon

• Begins zero hours or midnight.Mean or civil day

• Instant of time when the mean sun is on the observer’s meridian.

EQUATION OF TIME Is used to make conversions from one kind

of time to other, and can be positive or negative

𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑜𝑓 𝑇𝑖𝑚𝑒=𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑆𝑜𝑙𝑎𝑟 𝑇𝑖𝑚𝑒−𝑀𝑒𝑎𝑛𝑆𝑜𝑙𝑎𝑟 𝑇𝑖𝑚𝑒

The Earth was split into lines of latitude and longitude in order to help with navigation. Longitude lines, or meridians, circle the Earth from east to west. The meridian that passes through Greenwich, in London, is set at 0° longitude for historical reasons.

LONGITUDE AND TIME

At any instant, the difference in local time between two places, whether the time under consideration is sidereal, mean, or apparent solar, is equal to the difference in longitude between the two places expressed in hours.

The PRIME MERIDIAN for figuring out longitudes anywhere in the world passes through Greenwich, England.

The standard time referred to greenwich meridian: Greenwich Civil Time (GCT) Greenwich Mean Time (GMT) Universal Time (UT)

GREENWICH CIVIL TIME

Conversion to greenwich civil time To convert a moment of time, reckoned from

any meridian, to GCT, one hour is added for every 15 degrees of west longitude and one hour is subtracted for every 15 degrees of east longitude.

Standard, Daylight Saving and Local time

Standard Time Standard time is the mean time at meridians 15° or 1 hour

apart, measured either eastward or westward from the greenwich meridian. The adoption of standard time as a system of time measurement was merely a convenience.

Some countries have different time belts such as the united states which is divided into four zones, or sections of standard time. The reference meridian for its zones are, respectively, in the following longitudes west of greenwich: 75°, 90°, 105°, and 120°. Each of theses meridians passes through the center of a zone of standard time.

Daylight Saving Time Daylight saving time (DST) in any zone in

the western hemisphere is equal to Standard time in the zone just to east of it. In the eastern hemisphere it is equal to standard time in the zone just to the west. Thus, daylight saving time is always one hour ahead of standard time. It is usually adopted in different countries during the summer months.

The daylight saving time movement was originated in England by William Willet in 1907 by the publication of a booklet entitled “The Waste of Daylight”. Willet’s scheme aimed at securing more daylight leisure for recreation and lessening the work performed by artificial light during the summer months. It simply meant that during the summer months people should rise an hour earlier than usual in the morning, begin work an hour earlier and finish an hour earlier in the afternoon or evening.

Local Time It is often necessary to convert standard time

into local time or local time into standard time. Local time is the time based on the observer’s meridian. When the standard time is known, the local time at any other place within the same time belt can easily be determined if the longitude of the place is known. When the longitude is given in an arc measure, it must first be converted into its equivalent time measure.

Illustrative Problems

Converting arc measure to time measureChange an arc measure of 85˚ 44’ 36” to time measure by the use of the arc and time conversion table.

Solution:85˚ = 5h 40m 00.0s (equivalent value taken from the conversion table)44’ = 02m 56.0s (equivalent value taken from the conversion table)

36”/15= 02.4s (determined by dividing by15) 5h 42m 58.4s

 Therefore:

an arc measure of 85˚ 44’ 36” is equal to a time of 5h 42m 58.4s

Change a time measure of 8h 40m 55s to its equivalent arc measure by the use of the arc and time conversion table.

Solution:85h 40m = 130˚ 00’ 00” (equivalent value taken from the conversion

table) 52s = 13’ 00” (equivalent value taken from the conversion table) 3s x 15 = 45” (determined by multiplying by15)

130˚ 13’ 45”

Therefore: a time measure of 8h 40m 55s is equal to an arc measure of 130˚ 13’ 45” 

Converting arc measure to time measure

Longitude and timeThe longitude of Washington is 77˚ 04’ 00” West and that of San Francisco is 122˚ 25’ 45” West. Determine the following: a. Difference in solar time between Washington and San

Francisco. b. Time in Washington when it is 9: 03: 00 AM (9h 03m 00s) at

San Francisco.c. Time at San Francisco when it is 7: 54: 30 PM (19h 54m 30s) at

Washington.

SOLUTION:Diff = Longitude of San Francisco – Longitude of Washington= +122˚25’ 45” – (+77˚ 04’00”)= 45˚ 21’ 45” arc measure or 3h 01m 27s time measure

Tw = TSF ± Diff = 9h 03m 00s + 3h 01m 27s

= 12h 04m 27s or 04m 27s

= 0: 04: 27 PM

TSF = Tw ± Diff =19h 54m 30s - 3h 01m 27s

= 16h 53m 03s or = 4: 53: 03 PM

Determining greenwich civil timeWhat is the greenwich civil time (GCT) when at

a given instant the standard or mean time at:

A. 120˚ east longitude is 4: 45 PM?B. 120˚ east longitude is 9: 30 AM?C. 90˚ west longitude is 3: 15 AM?D. 75˚ west longitude is 4: 45 PM?E. 150˚ west longitude is 10:05 PM?

SOLUTION:

a. tm = 4: 45 PM or 1645 H = 16h 45m or 16.75h (Mean or standard time at 120˚E

longitude)TZC = 120˚ ()

= 8h (Time Zone Correction is based on the relationship that 15˚=1h) GCT = tm ± TZC = 16.45h – 8h = 8.75h or 8:45 AM (Equivalent Greenwich Civil Time on the same day)

b. Tm = 9: 30 AM or 0930 H= 9h 30m or 9.50h (mean or standard time at 120˚E

longitude) Tzc = 120˚ ()

= 8h (time zone correction is based on the relationship that 15˚=1h) GCT = tm ± TZC = 9.50h – 8h

= 1.50h or 1:30 AM (equivalent greenwich civil time on the same day)

c. Tm = 3: 15 am or 0315 h= 3h 15m or 3.25h (mean or standard time at 90˚W

longitude)TZC = 90˚ () = 6h (time zone correction is based on the relationship that

15˚=1h) GCT = tm ± TZC = 3.25h + 6h

= 9.25h or 9:15 AM (equivalent greenwich civil time on the same day)

d. Tm = 4: 45 PM or 1645 H= 16h 45m or 16.75h (mean or standard time at 150˚ W longitude)

TZC = 75˚ () = 5h (time zone correction is based on the relationship that 15˚=1h) GCT = tm ± TZC = 16.45h + 5h

= 21.75h or 9:45 PM (equivalent greenwich civil time on the same day)

e. Tm = 10: 05 PM or 2205 H= 22h 05m or 22.083h (mean or standard time at 75˚ W longitude)

TZC = 150˚ () = 10h (time zone correction is based on the relationship that 15˚=1h) GCT = tm ± TZC = 22.083h + 10h

= 32.083h or 8.083h (adjusted equivalent greenwich civil time on the next day)

Standard time and local time

At a place (A) whose longitude is 81˚37’ west, the standard time is 9: 37: 45 AM (9h 37m 45s). Determine the local time of the place at that instant.

Solution:A. Diff = longitude of A – longitude of standard time meridian = +81˚37’ – (+75˚) = 6˚ 37’ arc measure or 0h 26m 28s time measureB. Local time = standard time at 75˚W ± diff

= 9h 37m 45s - 0h 26m 28s

= 9h 11m 17s or 9: 11: 17 AM (local time at A when the standard time at 75˚ is 9: 37:

45 AM)

Thank you for listening !

PREPARED BY GROUP 3{