Field Astronomy

Field Astronomy

Contents

Define the following Astronomical terms: i. The Celestial Sphere and Celestial Horizon ii. Zenith and Nadir iii. Terrestrial Poles and Equator iv. Celestial Poles and Equator v. The Sensible and Visible Horizon vi. Latitude and Co-Latitude vii. Longitude and Altitude 1

Describe the Position of a Celestial body by: i. The Horizon System ii. The Independent Equatorial System iii. The Dependent Equatorial System iv. The Celestial Latitude and Longitude Systems 3

Define the term Nautical mile 4

Recall the Properties and Formulae for Spherical Triangle 4

Describe the Napier’s Rule of Circular Part 6

Describe the following terms: i. Stars at Elongation ii. Stars at Prime Vertical iii. Stars at Horizon iv. Stars at Culmination 7

Define Circumpolar Star 8

Describe the relation between Altitude of Pole and Latitude of Observer 9

Recall the relation between Latitude of Observer & Declination and altitude of Point on Meridian 10

Describe the relation between Right Ascension and Hour Angle 11

Recall the Earth’s Orbital Motion Around the Sun 12

Recall the Units of Time 13

Describe the Equation of Time 14

Recall the Inter Conversion of Local Time to Standard Time 15

Recall the Inter Conversion of Mean-Time Interval to Side Real-Time Interval 16

Recall the Inter Conversion of GST at GMM to LST at LMM 17

Recall the Inter Conversion of Local Mean- Time to SideReal-Time 18

Recall Instrumental and Astronomical Corrections to the Observed Altitude and Azimuth 19

Recall the various Observations of Time for Star/Sun 20

Describe Time of Rising of Setting of a Heavenly body 21

Describe the concept of SunDials 22

Recall the concept of Calendar 23

Describe the following Principal Methods of Azimuth determination: i. By Observations on the Stars at equal Altitudes ii. By Observation on a Circumpolar Star at Elongation iii. By Hour Angle of Star/Sun iv. By Observation of Polaris v. By Ex-meridian observations on Sun/Star 24

Describe the following Methods of determination of Latitudes: i. By Meridian Altitude of Sun/Star ii. By Zenith Pair Observation of Stars iii. By Meridian Altitude of Star at Lower and Upper Culmination iv. By Prime Vertical Transit 25

Describe the following methods of Determination of Longitudes: i. By Transportation of Chronometers ii. By Electrical Telegraph iii. By Wireless Signal 26

Define the following Astronomical terms: i. The Celestial Sphere and Celestial Horizon ii. Zenith and Nadir iii. Terrestrial Poles and Equator iv. Celestial Poles and Equator v. The Sensible and Visible Horizon vi. Latitude and Co-Latitude vii. Longitude and Altitude

i. The Celestial Sphere and Celestial Horizon:

The Celestial Sphere is an imaginary sphere with the observer at its center, on which all celestial objects are projected. It represents the entire universe as seen from the observer’s perspective. The Celestial Horizon is the great circle on the Celestial Sphere that represents the observer’s horizon on the Earth’s surface.

ii. Zenith and Nadir:

Zenith is the point on the celestial sphere that is directly overhead the observer. It is the highest point in the sky and is 90 degrees from the observer’s horizon. Nadir is the opposite of the Zenith and is the point directly below the observer.

iii. Terrestrial Poles and Equator:

Terrestrial Poles are the two points on the Earth’s surface that are 90 degrees from the observer’s position and are located at the Earth’s rotational axis. The North Terrestrial Pole is located in the Arctic region, while the South Terrestrial Pole is located in Antarctica. The Terrestrial Equator is an imaginary circle that lies on the Earth’s surface and is equidistant from the two terrestrial poles.

iv. Celestial Poles and Equator:

The Celestial Poles are two points in the sky, one located near the star Polaris and the other near the star Sigma Octantis, which are 90 degrees from the observer’s position and correspond to the Earth’s rotational axis. The Celestial Equator is an imaginary circle that lies in the sky and is equidistant from the two celestial poles.

v. The Sensible and Visible Horizon:

The Sensible Horizon is the actual visible limit of the Earth’s surface as seen by an observer. The Visible Horizon is the apparent limit of the Earth’s surface as seen by an observer and is influenced by factors such as atmospheric conditions and the observer’s height above the ground.

vi. Latitude and Co-Latitude:

Latitude is a measurement of the observer’s position north or south of the Earth’s equator and is expressed in degrees. The latitude of the Earth’s equator is 0 degrees, while the latitude of the North Pole is 90 degrees North and the latitude of the South Pole is 90 degrees South. Co-Latitude is the complement of Latitude and is expressed as 90 degrees minus Latitude.

vii. Longitude and Altitude:

Longitude is a measurement of the observer’s position east or west of the Prime Meridian, which is an imaginary line that runs from the North Pole to the South Pole and passes through Greenwich, England. Longitude is expressed in degrees. Altitude is the angular distance of an object in the sky above the observer’s horizon and is also expressed in degrees.

Describe the Position of a Celestial body by: i. The Horizon System ii. The Independent Equatorial System iii. The Dependent Equatorial System iv. The Celestial Latitude and Longitude Systems

i. The Horizon System:

The Horizon System describes the position of a celestial body in the sky based on its angular distance from the observer’s horizon. In this system, the observer is at the center of the celestial sphere and the celestial body is described in terms of its altitude, which is the angular distance above the observer’s horizon, and its azimuth, which is the angle between the body’s position and the observer’s north direction.

ii. The Independent Equatorial System:

The Independent Equatorial System describes the position of a celestial body based on its coordinates relative to the celestial equator. In this system, the celestial equator is the reference plane and the celestial body is described in terms of its declination, which is its angular distance from the celestial equator, and its right ascension, which is the angle between the body’s position and the vernal equinox.

iii. The Dependent Equatorial System:

The Dependent Equatorial System is similar to the Independent Equatorial System, but the position of the celestial body is described based on its coordinates relative to the observer’s position on the Earth’s surface. In this system, the observer’s position on the Earth’s surface and the time of observation are used to determine the position of the celestial equator and the vernal equinox, which are then used to describe the position of the celestial body in terms of its declination and hour angle, which is the angle between the observer’s meridian and the body’s position.

iv. The Celestial Latitude and Longitude Systems:

The Celestial Latitude and Longitude Systems describe the position of a celestial body in the sky based on its angular distance from the celestial poles and the celestial equator. In this system, the celestial equator is used as the reference plane and the celestial body is described in terms of its celestial latitude, which is its angular distance from the celestial equator, and its celestial longitude, which is the angle between the body’s position and the vernal equinox. The celestial longitude is equivalent to the right ascension in the Independent Equatorial System.

Define the term Nautical mile

A Nautical Mile is a unit of measurement used in navigation and maritime affairs. It is defined as being exactly 1,852 metres, or approximately 6,076 feet, in length. This unit of measurement was established to provide a consistent and standardised method of measuring distances at sea, and it is commonly used in navigation charts, maps, and related documents. The Nautical Mile is based on the circumference of the Earth and is used to measure both distances between two points and the size of an object or feature on the Earth’s surface, such as a body of water, a coastline, or an island. It is an important tool for seafarers and is widely used in the shipping and maritime industries for navigation and charting purposes.

Recall the Properties and Formulae for Spherical Triangle

There are several properties and formulae associated with spherical triangles that are important to understand and recall. These include:

The Law of Cosines: This formula relates the lengths of the sides of a spherical triangle to the cosine of one of its angles. The formula is given by:

cos C = cos A * cos B + sin A * sin B * cos C

  1. where A, B, and C are the angles of the spherical triangle and a, b, and c are the lengths of the sides opposite the corresponding angles.

The Law of Sines: This formula relates the lengths of the sides of a spherical triangle to the sine of one of its angles. The formula is given by:

sin A / a = sin B / b = sin C / c

  1. where A, B, and C are the angles of the spherical triangle and a, b, and c are the lengths of the sides opposite the corresponding angles.

The area formula: The area of a spherical triangle can be calculated using the formula:

A = R2 * (A + B + C – π)

  1. where R is the radius of the sphere and A, B, and C are the angles of the spherical triangle.
  2. The triangle inequality: In a spherical triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality.
  3. The sum of the angles: The sum of the angles in a spherical triangle is always greater than 180 degrees, which is in contrast to the sum of the angles in a triangle on a flat surface, which is always exactly 180 degrees.

The altitude-to-side formula: This formula relates the altitude of a spherical triangle to the lengths of its sides. The formula is given by:

h = R * sin A

  1. where h is the altitude, R is the radius of the sphere, and A is the angle opposite the corresponding side.

In conclusion, understanding and recalling these properties and formulae is important in solving problems involving spherical triangles, such as calculating distances and directions on the surface of a sphere or determining the location of points based on their angular relationships with known points.

Describe the Napier’s Rule of Circular Part

Napier’s Rule of Circular Parts is a formula used to determine the measure of an angle in a spherical triangle given the measures of the other two angles and the lengths of the sides that contain them. The formula is as follows:

cos C = cos A * cos B + sin A * sin B * cos C

where A, B, and C are the angles of the spherical triangle and c is the length of the side opposite angle C.

The formula is named after John Napier, a Scottish mathematician and astronomer who is credited with its discovery. It is based on the Law of Cosines, which relates the lengths of the sides of a spherical triangle to the cosine of one of its angles.

Napier’s Rule of Circular Parts is used in navigation, astronomy, and geodesy, among other fields, to determine the location of points on the surface of a sphere based on their angular relationships with known points. It is particularly useful when working with large spherical triangles, where it is difficult to measure the angles directly.

In conclusion, Napier’s Rule of Circular Parts is a formula used to determine the measure of an angle in a spherical triangle given the measures of the other two angles and the lengths of the sides that contain them. It is based on the Law of Cosines and is an important tool in navigation, astronomy, and geodesy.

Describe the following terms: i. Stars at Elongation ii. Stars at Prime Vertical iii. Stars at Horizon iv. Stars at Culmination

  1. Stars at Elongation: The term “stars at elongation” refers to the position of a celestial body (such as a planet) in its orbit when it is at its maximum angular distance from the Sun as seen from the Earth. When a planet is at elongation, it is visible in the sky just after sunset or just before sunrise and is at its brightest and easiest to observe. There are two types of elongation: eastern elongation, when a planet is visible in the western sky after sunset, and western elongation, when a planet is visible in the eastern sky before sunrise.
  2. Stars at Prime Vertical: The term “stars at prime vertical” refers to the position of stars in the sky that are exactly 90 degrees from the horizon and 90 degrees from the observer’s meridian (the line connecting the north and south poles of the Earth). The prime vertical is the line that separates the eastern and western hemispheres of the sky. Stars at prime vertical are at their highest point in the sky, directly overhead.
  3. Stars at Horizon: The term “stars at horizon” refers to the position of stars in the sky that are exactly on the observer’s horizon, the line separating the Earth and the sky. When a star is at the horizon, it is at its lowest point in the sky and is just about to set (or has just risen).
  4. Stars at Culmination: The term “stars at culmination” refers to the position of stars in the sky that are at their highest point, directly overhead. When a star is at its culmination, it has reached its maximum altitude above the horizon and is at the zenith (the point directly overhead).

In conclusion, these terms describe the position of celestial bodies in the sky relative to the observer’s horizon and meridian. Understanding these terms is important for navigation, astronomy, and other fields that involve observing the positions of celestial bodies in the sky.

Define Circumpolar Star

A circumpolar star is a star that never sets below the observer’s horizon, as it is always above the horizon and visible in the sky. This is because the star is located near one of the celestial poles (the North or South Pole of the Earth) and its path in the sky appears to be a small circle around the pole, so it never dips below the horizon.

The latitude of the observer determines which stars are circumpolar. For example, a star that is circumpolar for an observer at the North Pole will not be circumpolar for an observer at the equator. Similarly, a star that is circumpolar for an observer at a high latitude in the Northern Hemisphere will not be circumpolar for an observer at a lower latitude.

Circumpolar stars are important for navigation and astronomy, as they are always visible in the sky and can be used for orientation and determining latitude. They are also useful for studying the motion of the Earth and the stars, as their position relative to the observer changes over time.

In conclusion, a circumpolar star is a star that never sets below the observer’s horizon and is always visible in the sky. The latitude of the observer determines which stars are circumpolar, and they are important for navigation and astronomy.

Describe the relation between Altitude of Pole and Latitude of Observer

The relation between the altitude of the pole (the North or South Pole of the Earth) and the latitude of the observer is that the altitude of the pole is equal to the observer’s latitude.

The latitude of an observer is defined as the angle between the observer’s position on the Earth’s surface and the equator. The equator is an imaginary line that circles the Earth at 0 degrees latitude, while the poles are located at 90 degrees latitude (North Pole) and -90 degrees latitude (South Pole).

When an observer is at the equator, the altitude of the pole is 0 degrees, as the observer is located on the equator and the pole is directly on the horizon. As the observer moves north or south from the equator, the altitude of the pole increases. At a latitude of 45 degrees, for example, the altitude of the pole is 45 degrees, as the observer is located halfway between the equator and the pole.

The altitude of the pole is also used to determine the observer’s latitude. By observing the altitude of the pole, the observer can determine their latitude, as the altitude of the pole is equal to their latitude. This method is used in navigation and astronomy, as well as in other fields that involve determining location on the Earth’s surface.

In conclusion, the relation between the altitude of the pole and the latitude of the observer is that the altitude of the pole is equal to the observer’s latitude. The latitude of an observer is defined as the angle between their position on the Earth’s surface and the equator, and the altitude of the pole is used to determine the observer’s latitude.

Recall the relation between Latitude of Observer & Declination and altitude of Point on Meridian

The relation between the latitude of an observer, the declination of a celestial object, and the altitude of the object when it is on the observer’s meridian is determined by the observer’s position on the Earth’s surface and the position of the celestial object in the sky.

Declination is defined as the angular distance of a celestial object north or south of the celestial equator. The celestial equator is an imaginary line that circles the Earth at 0 degrees declination and is perpendicular to the Earth’s rotational axis.

When a celestial object is on the observer’s meridian, it is at its highest point in the sky and its altitude can be determined by the observer’s latitude and the object’s declination. The altitude of a celestial object is defined as the angle between the object and the observer’s horizon.

The formula for determining the altitude of a celestial object on the observer’s meridian is given by:

Altitude = Latitude of Observer + Declination of Object

For example, if an observer is located at a latitude of 45 degrees and a celestial object has a declination of +23 degrees, the object’s altitude when it is on the observer’s meridian will be 68 degrees (45 + 23 = 68).

In conclusion, the relation between the latitude of an observer, the declination of a celestial object, and the altitude of the object when it is on the observer’s meridian is determined by the observer’s position on the Earth’s surface and the position of the celestial object in the sky. The altitude of a celestial object on the observer’s meridian is given by the formula Latitude of Observer + Declination of Object.

Describe the relation between Right Ascension and Hour Angle

Right Ascension (RA) and Hour Angle (HA) are two coordinate systems used in astronomy to describe the position of a celestial object in the sky.

Right Ascension is a coordinate system that measures the position of a celestial object eastward along the celestial equator from the vernal equinox, which is the point where the Sun is located on the first day of spring in the Northern Hemisphere. It is measured in units of time, usually in hours, minutes, and seconds.

Hour Angle, on the other hand, is a coordinate system that measures the position of a celestial object westward from the observer’s meridian, which is an imaginary line that runs from the observer’s location to the celestial pole and intersects the celestial sphere at the observer’s zenith. It is measured in units of time, just like Right Ascension, but is also often measured in degrees.

The relation between Right Ascension and Hour Angle is that they both describe the position of a celestial object in the sky, but from different perspectives. Right Ascension measures the position of an object eastward along the celestial equator, while Hour Angle measures the position of an object westward from the observer’s meridian.

The relationship between Right Ascension and Hour Angle can be described by the following formula:

HA = Local Sidereal Time (LST) – RA

Local Sidereal Time (LST) is the observer’s local time, measured in units of time, relative to the position of the stars in the sky.

In conclusion, Right Ascension and Hour Angle are two coordinate systems used in astronomy to describe the position of a celestial object in the sky. Right Ascension measures the position of an object eastward along the celestial equator, while Hour Angle measures the position of an object westward from the observer’s meridian. The relationship between the two can be described by the formula HA = Local Sidereal Time (LST) – RA.

Recall the Earth’s Orbital Motion Around the Sun

The Earth’s orbital motion around the Sun refers to the path that the Earth follows as it revolves around the Sun. The Earth’s orbit is an elliptical shape, meaning that it is not a perfect circle, but rather an elongated oval. The Sun is located at one of the foci of the elliptical orbit, meaning that it is not at the center of the orbit, but slightly off-center.

The Earth’s orbital motion around the Sun is caused by the force of gravity acting between the Earth and the Sun. The force of gravity pulls the Earth towards the Sun, keeping it in its orbital path. The Earth’s orbit around the Sun takes 365.25 days to complete, which is why we have a leap year every 4 years to account for the extra quarter day.

The Earth’s orbital motion around the Sun is not only responsible for our calendar, but it also has a significant impact on the Earth’s climate and seasons. The Earth’s axis is tilted at an angle of 23.5 degrees, meaning that different parts of the Earth receive different amounts of sunlight throughout the year. This tilt causes the Earth to experience different seasons, with the Northern Hemisphere experiencing summer when the Earth is tilted towards the Sun, and winter when it is tilted away from the Sun.

In conclusion, the Earth’s orbital motion around the Sun refers to the path that the Earth follows as it revolves around the Sun. The Earth’s orbit is an elliptical shape and is caused by the force of gravity acting between the Earth and the Sun. The Earth’s orbital motion around the Sun is responsible for our calendar and has a significant impact on the Earth’s climate and seasons.

Recall the Units of Time

In astronomy, there are several units of time used to measure different aspects of the motion of celestial objects. These units of time include:

  1. Second: The second is the basic unit of time and is used in many other units of time. It is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.
  2. Minute: A minute is a unit of time equal to 60 seconds. It is used to measure small intervals of time, such as the duration of a phone call or the time it takes to travel a short distance.
  3. Hour: An hour is a unit of time equal to 60 minutes or 3600 seconds. It is commonly used to measure the duration of an event or the time it takes to complete a task.
  4. Day: A day is a unit of time equal to 24 hours or 86,400 seconds. It is used to measure the duration of one complete rotation of the Earth on its axis.
  5. Year: A year is a unit of time equal to 365.25 days or 31,536,000 seconds. It is used to measure the duration of one orbit of the Earth around the Sun.
  6. Julian Year: A Julian year is a unit of time equal to 365.25 days. It is used in astronomy to describe the length of one average year, based on the time it takes the Earth to orbit the Sun.
  7. Sidereal Day: A sidereal day is a unit of time equal to the time it takes the Earth to complete one rotation on its axis relative to the stars. A sidereal day is shorter than a solar day by about 4 minutes.

In conclusion, there are several units of time used in astronomy to measure different aspects of the motion of celestial objects. These units of time include the second, minute, hour, day, year, Julian year, and sidereal day. Each unit of time is used to measure a different aspect of time, such as the duration of an event, the rotation of the Earth, or the orbit of the Earth around the Sun.

Describe the Equation of Time

The Equation of Time is a term used in astronomy to describe the difference between the mean solar time and the apparent solar time. The mean solar time is a measure of time based on the average length of a solar day, while the apparent solar time is a measure of time based on the actual position of the Sun in the sky.

The Equation of Time can be represented as the difference between the two times, with the mean solar time being ahead of the apparent solar time by some amount. This difference is due to several factors, including the elliptical shape of the Earth’s orbit around the Sun and the tilt of the Earth’s axis relative to its orbit.

The Equation of Time can be represented graphically on a sundial, where the difference between mean solar time and apparent solar time can be observed by the discrepancy between the position of the shadow cast by the gnomon (the vertical rod on a sundial) and the actual time.

In conclusion, the Equation of Time is a term used in astronomy to describe the difference between mean solar time and apparent solar time. This difference is caused by several factors, including the elliptical shape of the Earth’s orbit and the tilt of the Earth’s axis, and can be represented graphically on a sundial.

Recall the Inter Conversion of Local Time to Standard Time

The conversion of local time to standard time is a process by which the time in a specific location is adjusted to align with a standardised time reference. This standardised reference is usually the time at a certain longitude, often referred to as the “time zone meridian.”

Local time refers to the time in a specific location as determined by the position of the sun in the sky. This time can vary by several minutes from one location to another, even within the same time zone.

Standard time, on the other hand, is a uniform and consistent time reference that is used to synchronise clocks and schedules across a large geographic region. This is necessary to ensure that communication, transportation, and other activities are coordinated and operate smoothly.

The conversion of local time to standard time involves adjusting the time in a specific location to align with the standardised time reference. This can involve adding or subtracting an hour or more, depending on the location’s position relative to the time zone meridian.

In conclusion, the conversion of local time to standard time is the process of adjusting the time in a specific location to align with a standardised time reference. This allows for consistent and coordinated timekeeping across a large geographic region, and helps ensure smooth communication, transportation, and other activities.

Recall the Inter Conversion of Mean-Time Interval to Side Real-Time Interval

The conversion of mean time to sidereal time is a process by which the time in a specific location is adjusted to align with the position of the stars in the sky. This conversion is used in astronomical observations and calculations, as the position of the stars is a more constant and uniform reference than the position of the Sun.

Mean time is a measure of time based on the average length of a solar day. This time is used in everyday life and is the basis for standard time, which is synchronised across a large geographic region.

Sidereal time, on the other hand, is a measure of time based on the position of the stars in the sky. This time is calculated by observing the position of a star relative to the observer’s location and the position of the vernal equinox (the point where the Sun’s path crosses the celestial equator at the start of spring in the Northern Hemisphere).

The conversion of mean time to sidereal time involves adjusting the time in a specific location to align with the position of the stars in the sky. This can be accomplished by subtracting the mean time from the sidereal time to find the difference, which is known as the equation of the equinoxes.

In conclusion, the conversion of mean time to sidereal time is a process by which the time in a specific location is adjusted to align with the position of the stars in the sky. This conversion is used in astronomical observations and calculations, and allows for more accurate and consistent timekeeping based on the position of the stars in the sky.

Recall the Inter Conversion of GST at GMM to LST at LMM

The conversion of Greenwich Mean Time (GMT) to Local Mean Time (LMT) is a process by which the time in a specific location is adjusted to align with the local time zone. GMT is a standardised time used as a reference across the world, while LMT is a measure of time based on the longitude of a specific location.

The conversion of GMT to LMT involves adjusting the time in a specific location to align with the local time zone. This can be accomplished by subtracting the longitude of the location from the longitude of the Prime Meridian (0°), which is located at Greenwich, England, and then multiplying the result by 4 minutes per degree of longitude. This gives the difference in minutes between GMT and the local time, which can then be added or subtracted from GMT to give the local time.

Similarly, the conversion of Greenwich Sidereal Time (GST) at the Greenwich Meridian to Local Sidereal Time (LST) at a specific location is a process by which the time in a specific location is adjusted to align with the position of the stars in the sky. GST is a measure of time based on the position of the stars relative to the Greenwich Meridian, while LST is a measure of time based on the position of the stars relative to a specific location.

The conversion of GST to LST involves adjusting the time in a specific location to align with the position of the stars in the sky. This can be accomplished by subtracting the longitude of the location from the longitude of the Greenwich Meridian, and then multiplying the result by the sidereal day (the time it takes for one rotation of the Earth relative to the stars). This gives the difference in seconds between GST and LST, which can then be added or subtracted from GST to give LST.

In conclusion, the conversion of GMT to LMT and GST to LST are processes by which the time in a specific location is adjusted to align with the local time zone and the position of the stars in the sky, respectively. These conversions allow for more accurate and consistent timekeeping based on the location and the position of the stars in the sky.

Recall the Inter Conversion of Local Mean- Time to SideReal-Time

The conversion of Local Mean Time (LMT) to Local Sidereal Time (LST) involves adjusting the time in a specific location to align with the position of the stars in the sky. LMT is a measure of time based on the longitude of a specific location, while LST is a measure of time based on the position of the stars relative to that location.

The conversion of LMT to LST can be accomplished by subtracting the equation of time, which accounts for the discrepancy between solar time and mean time, from LMT. This gives the solar time, which can then be converted to LST by adding the longitude of the location in seconds of time to the local solar time.

The equation of time is the difference between solar time and mean time and can be calculated using a formula that takes into account the elliptical shape of the Earth’s orbit and the tilt of the Earth’s axis. Solar time is the time based on the position of the sun in the sky, while mean time is based on the average position of the sun over the course of a year.

In conclusion, the conversion of LMT to LST involves adjusting the time in a specific location to align with the position of the stars in the sky. This conversion allows for more accurate and consistent timekeeping based on the location and the position of the stars in the sky.

Recall Instrumental and Astronomical Corrections to the Observed Altitude and Azimuth

Instrumental and astronomical corrections are adjustments made to the observed altitude and azimuth of celestial objects in order to accurately determine their true positions in the sky. These corrections take into account various factors that can affect the accuracy of the observations, including the position and orientation of the observer, the instruments used, and atmospheric conditions.

Instrumental corrections are adjustments made to the observed altitude and azimuth due to the inaccuracies or limitations of the instruments used. For example, the bubble level in a sextant can be tilted, causing an error in the observed altitude. The index error, which is the difference between the position of the index arm and the actual position of the celestial object, can also cause inaccuracies in the observations.

Astronomical corrections are adjustments made to the observed altitude and azimuth due to the positions and movements of celestial objects. For example, the parallax correction accounts for the difference in position of a celestial object as seen from the Earth’s surface and from the observer’s position. The refraction correction takes into account the bending of light in the Earth’s atmosphere, which can cause celestial objects to appear higher in the sky than their actual position.

In conclusion, instrumental and astronomical corrections are important adjustments made to the observed altitude and azimuth of celestial objects to accurately determine their true positions in the sky. These corrections take into account various factors, including the position and orientation of the observer, the instruments used, and atmospheric conditions, and allow for more accurate and consistent navigation and celestial observations.

Recall the various Observations of Time for Star/Sun

In navigation, it is important to accurately determine the time, which can be done through various observations of celestial objects such as the stars and the sun. The following are some common observations of time for stars and the sun:

  1. Stellar time: Stellar time is determined by observing the passage of stars across the meridian, which is an imaginary line that runs from the North Pole to the South Pole and passes directly overhead. The time at which a star crosses the meridian can be used to determine local time.
  2. Solar time: Solar time is determined by observing the position of the sun in the sky. The sun’s highest point in the sky, known as solar noon, can be used to determine local time.
  3. Chronometer time: A chronometer is a high-precision timekeeping instrument, such as a quartz crystal clock or a mechanical clock. Chronometer time can be used to determine local time by comparing the local time to the time kept by the chronometer.
  4. Time signals: Time signals are radio signals that transmit accurate time information, such as the Coordinated Universal Time (UTC). Time signals can be used to determine local time by comparing the local time to the time kept by the signal.

In conclusion, there are several methods for determining time in navigation, including observing the passage of stars across the meridian, observing the position of the sun, using a chronometer, and receiving time signals. Accurately determining time is important for navigation and helps to ensure that position fixes and other navigation calculations are accurate and consistent.

Describe Time of Rising of Setting of a Heavenly body

The time of rising and setting of a celestial body, such as the sun, moon, or a planet, refers to the moment when the body appears on the eastern horizon (rising) or disappears below the western horizon (setting) as observed from a specific location. The time of rising and setting is significant in navigation because it helps to determine the position of a celestial body in the sky and the observer’s location relative to it.

The time of rising and setting depends on several factors, including the observer’s latitude, the celestial body’s declination, and the time of year. Declination is the angular distance of a celestial body north or south of the celestial equator and it changes over time as the Earth orbits the sun. The observer’s latitude is important because it determines the observer’s position relative to the celestial equator and affects the angle at which the celestial body rises and sets.

The time of rising and setting can be calculated using astronomical tables, computer software, or mathematical models based on the observer’s latitude, the celestial body’s declination, and the time of year. Knowing the time of rising and setting of celestial bodies is important in navigation because it helps to determine the observer’s longitude, which is the angular distance east or west of the prime meridian. This information is useful in fixing a ship’s position and determining its course and speed.

In conclusion, the time of rising and setting of a celestial body is an important concept in navigation. It helps to determine the position of a celestial body in the sky and the observer’s location relative to it, which is useful in fixing a ship’s position, determining its course and speed, and performing other navigation calculations.

Describe the concept of SunDials

A sundial is a device that uses the sun’s rays to determine the time of day. The basic principle of a sundial is that the shadow cast by an object changes position with the position of the sun in the sky. In the case of a sundial, the object is a gnomon, which is typically a vertical rod or pillar. The shadow of the gnomon will fall on a flat surface, such as a plate or a sundial face, which is marked with the hours of the day.

Sundials were used for thousands of years as a way to determine the time without the need for a clock or other timekeeping device. They were commonly used in ancient times, especially in Greece and Rome, and remained in use for many centuries. With the advent of accurate timekeeping devices such as clocks and watches, sundials fell out of common use, but they are still used today in some places as a way to determine the time in a traditional and aesthetically pleasing way.

The design of a sundial can vary widely, but the basic principle of using the shadow of a gnomon to determine the time remains the same. The shape, size, and orientation of the gnomon will affect the accuracy of the sun dial, as will the latitude of the location and the time of year. Sundials can also be designed to correct for the equation of time, which is the difference between mean solar time and apparent solar time.

Recall the concept of Calendar

A calendar is a system of organising days and weeks into months and years to keep track of time. The Gregorian calendar, which is widely used today, is based on a year of 365 days with an additional day added to the month of February during leap years (29th February). This calendar is divided into 12 months, each with a specific number of days. The Gregorian calendar is used for civil purposes, such as scheduling appointments, holidays, and other events, and for astronomical purposes, such as determining the timing of eclipses and other astronomical events. Different cultures and religions have their own calendars that reflect their specific beliefs and traditions.

Describe the following Principal Methods of Azimuth determination: i. By Observations on the Stars at equal Altitudes ii. By Observation on a Circumpolar Star at Elongation iii. By Hour Angle of Star/Sun iv. By Observation of Polaris v. By Ex-meridian observations on Sun/Star

The Principal Methods of Azimuth determination are various methods used to determine the azimuth, or the horizontal direction, of a celestial body in relation to the observer.

i. By Observations on the Stars at equal Altitudes: In this method, two observations of the same star are taken, one when the star is at its lower transit and one when it is at its upper transit. The difference between the two altitudes gives the observer’s latitude, and the average of the two observations gives the azimuth.

ii. By Observation on a Circumpolar Star at Elongation: In this method, the observer measures the altitude and azimuth of a circumpolar star at elongation, which is when the star is at its greatest distance from the celestial pole. By knowing the observer’s latitude, the azimuth of the star can be determined.

iii. By Hour Angle of Star/Sun: In this method, the observer determines the hour angle of a star or the sun by observing its right ascension and declination and converting it to local sidereal time. The observer’s longitude and latitude can then be used to determine the azimuth.

iv. By Observation of Polaris: In this method, the observer determines the azimuth of Polaris, the North Star, which is located almost exactly at the celestial North Pole. The observer’s latitude can be determined from the altitude of Polaris.

v. By Ex-meridian observations on Sun/Star: In this method, the observer takes two observations of a celestial body, one when the body is on the observer’s meridian (directly overhead) and one when the body is on the observer’s east or west horizon. The difference in the two observations gives the observer’s longitude, and the average of the two observations gives the azimuth.

These methods are used by astronomers and navigators to determine the positions of celestial bodies and to navigate on the Earth’s surface.

Describe the following Methods of determination of Latitudes: i. By Meridian Altitude of Sun/Star ii. By Zenith Pair Observation of Stars iii. By Meridian Altitude of Star at Lower and Upper Culmination iv. By Prime Vertical Transit

The determination of Latitude is an important part of astronomical navigation. Latitude is a measure of the location of a point on the Earth relative to the equator, expressed in degrees north or south of the equator. The following are the four main methods used for determining Latitude:

  1. By Meridian Altitude of Sun/Star: The observer measures the highest point of the sun or a star as it passes overhead, called the culmination. The latitude can be calculated from the altitude of the object and the observer’s position.
  2. By Zenith Pair Observation of Stars: The observer measures the altitude of two stars at the same time, one of which is closest to the observer’s zenith, while the other is at the same altitude but on the opposite side of the sky. The latitude can be calculated from the difference in altitude between the two stars.
  3. By Meridian Altitude of Star at Lower and Upper Culmination: The observer measures the altitude of a star at its lower and upper culmination, and the latitude can be calculated from the difference in the star’s altitude between the two observations.
  4. By Prime Vertical Transit: The observer measures the altitude of a star as it passes the observer’s prime vertical, which is the direction from the observer to the east or west horizon. The latitude can be calculated from the star’s altitude at this time.

Describe the following methods of Determination of Longitudes: i. By Transportation of Chronometers ii. By Electrical Telegraph iii. By Wireless Signal

The three methods of determination of longitudes are:

  1. By Transportation of Chronometers: The method of determination of longitudes using transportation of chronometers involves carrying a clock (chronometer) that is highly accurate and free from significant variations due to temperature and other environmental factors. The time difference between two points on the Earth’s surface is used to calculate the difference in longitudes between these two points. The accuracy of this method is highly dependent on the accuracy of the chronometer.
  2. By Electrical Telegraph: The method of determination of longitudes using electrical telegraph involves transmitting the time signal from a known location to the location whose longitude is to be determined. The difference in time between the transmitted signal and the received signal is then used to calculate the difference in longitudes.
  3. By Wireless Signal: The method of determination of longitudes using wireless signals involves receiving and measuring the time of arrival of signals from a known location using a wireless receiver. The difference in time between the transmission of the signal and its reception is then used to calculate the difference in longitudes. This method was developed after the electrical telegraph method and is more accurate and reliable than the previous method.