This document contains information from Vijay Parmar's YouTube channel on astronomy and related topics. It includes definitions of key terms like astronomy, longitude and latitude, spherical trigonometry, and astronomical terms. It also discusses celestial coordinate systems, the astronomical triangle, and different units of time used in astronomy like sidereal time, solar time, mean solar time, and atomic time.

2. VIJAY PARMAR
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https://www.youtube.com/channel/UCyNyseeSPe
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Astronomy : is the branch of science which deals with celestial objects,
space, and the physical universe as a whole.

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The Earth
Radius : 6371 km

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Longitude and Latitude
the angular distance of a place east or
west of the Greenwich meridian, or
west of the standard meridian of a
celestial object, usually expressed in
degrees and minutes.
"at a longitude of 2° W"
the angular distance of a place north or
south of the earth's equator, or of the
equator of a celestial object, usually
expressed in degrees and minutes.
"at a latitude of 51° N"

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Longitude and Latitude

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Longitude and Latitude

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Spherical Trigonometry
Spherical trigonometry is the
branch of spherical geometry that
deals with the relationships
between trigonometric functions
of the sides and angles of the
spherical polygons (especially
spherical triangles) defined by a
number of intersecting great
circles on the sphere.

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Spherical Trigonometry
Sine rules
Cosine rules

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Spherical Trigonometry
Half-angle and half-side formulae

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Spherical Trigonometry
Napier's analogies

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Astronomical Terms

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Astronomical Terms

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Astronomical Terms
Celestial sphere : An imaginary sphere of infinite
radius with the earth at its centre and other celestial
bodies studded on its inside surface is known as
celestial sphere.
Great Circle (G.C) : The imaginary line of
intersection of an infinite plane, passing through the
centre of the earth and the circumference of the
celestial sphere is known as great circle.
Zenith (Z) : If a plumb line through an observer is
extended upward, the imaginary point at which it
appears to intersect the celestial sphere is known as
Zenith. The imaginary point at which it appears to
intersect downward in the celestial sphere is known
as Nadir (N).
Vertical circle : Great circle passing through zenith
and nadir is known as vertical circle.

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Astronomical Terms
Horizon: Great circle perpendicular to the line
joining the Zenith and Nadir is known as
horizon.
Poles : If the axis of rotation of the earth is
imagined to be extended infinitely in both
directions, the points at which it meets the
celestial sphere are known as poles. The point
of intersection in the northern hemisphere is
known as north celestial pole and that in the
southern hemisphere as south celestial pole.
Equator : The line of intersection of an infinite
plane passing through the centre of the earth
and perpendicular to the line joining celestial
poles with the celestial sphere.
Hour circle : Great circle passing through
celestial poles is known as hour circle, also
known as declination circle.

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Astronomical Terms
Meridian : The hour circle passing through
observer's zenith and nadir is known as
(observer's) meridian. It represents the North-
South direction at observer station.
Altitude (h) : The altitude of a celestial body is
the angular distance measured along a vertical
circle passing through the body. It is
considered positive if the angle measured is
above horizon and below horizon, it is
considered as negative.

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Astronomical Terms
Azimuth (A) : The azimuth of a celestial
body is the angular distance measured
along the horizon from the observer's
meridian to the foot of the vertical circle
passing through the celestial body

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Astronomical Terms
Azimuth (A) : The azimuth of a celestial body is
the angular distance measured along the
horizon from the observer's meridian to the
foot of the vertical circle passing through the
celestial body

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Astronomical Terms

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Astronomical Terms

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Astronomical Terms

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Astronomical Terms
Declination (d) : The declination of a
celestial body is the angular distance
measured from the equator to the
celestial body along the arc of an hour
circle. It is considered positive in North
direction and negative in South.
Ecliptic : The great circle along which
the sun appears to move round the earth
in a year is called the ecliptic.
Equinoctial points : The points of
intersection of the ecliptic circle with
the equatorial circle are known as
equinoctial points. The point at which
the sun transits from Southern to
Northern hemisphere is known as First
point of Aeries (g) and from Northern to
Southern hemisphere as First point of
Libra (W).

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Astronomical Terms
Right ascension : The right ascension of
a celestial body is the angular distance
along the arc of celestial equator
measured from the First point of Aeries
(g) to the foot of the hour circle. It is
measured from East to West direction
i.e., anti-clockwise in Northern
hemisphere.
Prime meridian : Reference meridian
that passes through the Royal Naval
Observatory in Greenwich, England is
known as prime meridian; it is also
known as Greenwich meridian.

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Astronomical Terms
Longitude (l) : The longitude of an
observer's station is the angular
distance measured along the equator
from the prime meridian to the
observer's meridian. It varies from zero
degrees to 180° E and 0° to 180° W.
Latitude (f): The latitude of an
observer's station is the angular
distance measured along the observer's
meridian from the equator to the zenith
point. It varies from zero degree to 90°
N and 0° to 90° S.

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Astronomical Terms
Hour angle (HA) : The hour angle of a celestial body
is the angle at the equatorial plane measured
westward from meridian to the hour circle passing
through the celestial body.
Local hour angle (LHA): The angular distance of a
celestial body measured westward from the point of
intersection of the equator and the meridian of the
observer to the foot of the hour circle passing
through the celestial body.
Greenwich hour angle (GHA) : Angle at the
equatorial plane measured westward from the
prime (Greenwich) meridian to the hour circle
through the celestial body.
Spherical triangle: Triangle formed by the
intersection of three arcs of great circles (on the
surface of the celestial sphere) is known as
spherical triangle.

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Astronomical Triangle
The spherical triangle formed by arcs of
observer's meridian, vertical circle as well as
hour circle through the same celestial body is
known as an astronomical triangle. The
vertices of an astronomical triangle are
Zenith point (Z), celestial pole (P) and the
celestial body (S) and thus termed as ZPS
triangle. In each astronomical triangle, there
are six important elements. Three of them
are the three sides and other three are the
three angles of the triangle. It is important to
know these elements as some of these will
be required to be observed in the field and
others are to be computed to find the
position / direction of celestial body.

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Astronomical Triangle

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Astronomical Triangle

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Astronomical Triangle
Polar distance (PS or p) : The angular distance from the celestial pole (P) to the celestial
body (S) along the hour circle is known as polar distance. It is also known as co-
declination and is designated by p (= 90°- d), where d is the declination of the celestial
body, S.
Zenith distance (ZS or z) : The angular distance from observer's zenith (Z) to the celestial
body (S) along the vertical circle is known as zenith distance. It is also known as co-
altitude and is designated by z (= 90°- h), where h is the altitude of the celestial body, S.
Co-latitude, ZP : The angular distance from observer's zenith (Z) to the celestial pole (P)
along the observer's meridian is known as co-latitude and is given by (90°- f), where f is
the latitude of the observer.

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Astronomical Triangle

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Astronomical Triangle

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Astronomical Triangle
Angle Z : The angle at the zenith (A) is measured from the
observer's meridian to the vertical circle passing through the
celestial body in a plane parallel to the observer's horizon. It is
nothing but the azimuth of the celestial body. It is measured
clockwise from the observer's meridian and its value ranges
from zero to 360°.
Angle P : The angle at the pole (P) is measured from the
observer's meridian to the hour circle passing through the
celestial body in a plane parallel to the equatorial plane. It is
nothing but (360°– H, hour angle of the celestial body). Hour
angle is measured clockwise from the upper branch of the
observer's meridian.
Angle S : angle at a celestial body between the hour circle and
the vertical circle passing through the celestial body. It is
known as the parallactic angle.

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ASTRONOMICAL / CELESTIAL COORDINATE SYSTEM

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CELESTIAL COORDINATE SYSTEM
1. Horizontal system
2. Equatorial system
3. Ecliptic system
4. Galactic system
5. Super-galactic system
6. Spherical coordinate system

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CELESTIAL COORDINATE SYSTEM
1. Horizontal system :
The horizontal coordinate
system is a celestial coordinate
system that uses the observer's
local horizon as the
fundamental plane. It is
expressed in terms of altitude
(or elevation) angle and
azimuth.

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CELESTIAL COORDINATE SYSTEM
2. Equatorial system :
The equatorial coordinate system is a celestial
coordinate system widely used to specify the
positions of celestial objects. It may be
implemented in spherical or rectangular
coordinates, both defined by an origin at the
center of the Earth, a fundamental plane
consisting of the projection of the Earth's
equator onto the celestial sphere (forming the
celestial equator), a primary direction towards
the vernal equinox, and a right-handed
convention.

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CELESTIAL COORDINATE SYSTEM
3. Ecliptic system :
The ecliptic coordinate
system is a celestial
coordinate system
commonly used for
representing the positions
and orbits of Solar System
objects.

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CELESTIAL COORDINATE SYSTEM
4. Galactic system :
The galactic coordinate system is a
celestial coordinate system in
spherical coordinates, with the Sun
as its center, the primary direction
aligned with the approximate
center of the Milky Way galaxy, and
the fundamental plane parallel to
an approximation of the galactic
plane but offset to its north.

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CELESTIAL COORDINATE SYSTEM
4. Super-galactic system :
Supergalactic coordinates are
coordinates in a spherical
coordinate system which was
designed to have its equator
aligned with the supergalactic
plane, a major structure in the local
universe formed by the preferential
distribution of nearby galaxy
clusters towards a (two-
dimensional) plane.

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CELESTIAL COORDINATE SYSTEM
6. Spherical coordinate system :
To define a spherical coordinate
system, one must choose two
orthogonal directions, the zenith
and the azimuth reference, and an
origin point in space. These
choices determine a reference
plane that contains the origin and
is perpendicular to the zenith.

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TIME IN ASTRONOMY
Hour Angle :
In astronomy and celestial navigation,
the hour angle is one of the coordinates
used in the equatorial coordinate
system to give the direction of a point
on the celestial sphere. The hour angle
of a point is the angle between two
planes: one containing the Earth's axis
and the zenith (the meridian plane),
and the other containing the Earth's
axis and the given point (the hour circle
passing through the point).
LHA – local hour angle
GHA – Greenwich hour angle

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TIME IN ASTRONOMY

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TIME IN ASTRONOMY
UNITS OF TIME :
1. Sidereal Time
2. Solar Apparent Time
3. Mean Solar Time
4. Standard Time
5. Universal Time
6. Atomic Time
7. Astronomical Time

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TIME IN ASTRONOMY
1. Sidereal Time :
sidereal time is a "time scale
that is based on Earth's rate of
rotation measured relative to
the fixed stars" rather than the
Sun.

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TIME IN ASTRONOMY
2. Solar Apparent Time :
Solar apparent time is a
calculation of the passage of
time based on the Sun's position
in the sky. The fundamental unit
of solar time is the day.

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TIME IN ASTRONOMY
3. Mean Solar Time :
• Mean solar time is the hour angle
of the mean Sun plus 12 hours.
• The duration of daylight varies
during the year but the length of a
mean solar day is nearly constant

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TIME IN ASTRONOMY
4. Standard Time :
Standard time is the synchronization of clocks within a geographical area or region to a
single time standard, rather than using solar time or a locally chosen meridian (longitude)
to establish a local mean time standard.
INDIA = GMT+5.5

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TIME IN ASTRONOMY
5. Universal Time:
Universal Time (UT) is a time standard based on Earth's rotation. It is a modern
continuation of Greenwich Mean Time (GMT), i.e., the mean solar time on the Prime Meridian at
Greenwich, London, UK.
INDIA = GMT+5.5

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TIME IN ASTRONOMY
6. Atomic Time :
• Atomic Time is a high-precision
atomic coordinate time standard
based on the notional passage of
proper time on Earth's shape. It is
the basis for Coordinated
Universal Time (UTC), which is
used for civil timekeeping all over
the Earth's surface, and for
Terrestrial Time, which is used for
astronomical calculations.

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TIME IN ASTRONOMY
7. Astronomical Time :
• Astronomical Time is based on
the repetition of astronomical
events for setting frequency
standards. For example, the
occurrence of day and night is
caused by the rotation of the
Earth, and seasons by the Earth
revolving around the Sun.

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