Chapter 5
Spheres and Coordinates
Abstract In observational astronomy, we are dealing with the celestial sphere, which
is non-Euclidean. Hence, astronomers use the non-Cartesian Alt-Az and equatorial
coordinate systems to point telescopes and identify objects. The non-Euclidean nature
of our observations means that we have to use spherical geometry when measuring
the position of objects in the sky.
5.1 Introduction
For thousands of years, people thought of the sky as a hollow crystal sphere with
the Earth at the centre to which the stars were attached. Although we know that
this concept is incorrect, the idea is not entirely without its merits. The stars do not
change position relative to each other over a human lifetime, and they appear as
point sources, with no parallax discernible to the human eye. The consequence of
this is that stars appear in the same position in the sky relative to each other for all
observers on Earth. We can, therefore, make a representative map of the stars as seen
from Earth using a sphere with the stars placed on its surface and the observer located
at its centre, with the Earth’s equator and meridian lines projected onto the sphere.
This sphere is known as the celestial sphere.
For an observer, the current position of a stellar object in the visible sky is governed
by several factors: the location of the observer on the Earth, the time, and the position
of the object on the sphere of fixed stars in relation to established reference points.
All of these depend on spherical geometry.
Let us consider a sphere. Extend a line of diameter vertically, both up and down,
through the surface of the sphere. For rotating bodies such as the Earth, we make this
the axis of rotation. For purposes of orientation we shall call the uppermost point of
interception the north pole and the lower the south pole, although this is entirely
arbitrary. We draw a circle intercepting both the north and south poles so that this
circle has the same circumference as the sphere. Such a circle is known as a great
circle, and if we used it to bisect the sphere, it would do so through the centre. We shall
call this great circle the meridian. We now draw a second great circle perpendicular
© Springer Nature Switzerland AG 2020
M. Gallaway, An Introduction to Observational Astrophysics,
Undergraduate Lecture Notes in Physics,
https://doi.org/10.1007/978-3-030-43551-6_5
53
Spheres and Coordinates
Abstract In observational astronomy, we are dealing with the celestial sphere, which
is non-Euclidean. Hence, astronomers use the non-Cartesian Alt-Az and equatorial
coordinate systems to point telescopes and identify objects. The non-Euclidean nature
of our observations means that we have to use spherical geometry when measuring
the position of objects in the sky.
5.1 Introduction
For thousands of years, people thought of the sky as a hollow crystal sphere with
the Earth at the centre to which the stars were attached. Although we know that
this concept is incorrect, the idea is not entirely without its merits. The stars do not
change position relative to each other over a human lifetime, and they appear as
point sources, with no parallax discernible to the human eye. The consequence of
this is that stars appear in the same position in the sky relative to each other for all
observers on Earth. We can, therefore, make a representative map of the stars as seen
from Earth using a sphere with the stars placed on its surface and the observer located
at its centre, with the Earth’s equator and meridian lines projected onto the sphere.
This sphere is known as the celestial sphere.
For an observer, the current position of a stellar object in the visible sky is governed
by several factors: the location of the observer on the Earth, the time, and the position
of the object on the sphere of fixed stars in relation to established reference points.
All of these depend on spherical geometry.
Let us consider a sphere. Extend a line of diameter vertically, both up and down,
through the surface of the sphere. For rotating bodies such as the Earth, we make this
the axis of rotation. For purposes of orientation we shall call the uppermost point of
interception the north pole and the lower the south pole, although this is entirely
arbitrary. We draw a circle intercepting both the north and south poles so that this
circle has the same circumference as the sphere. Such a circle is known as a great
circle, and if we used it to bisect the sphere, it would do so through the centre. We shall
call this great circle the meridian. We now draw a second great circle perpendicular
© Springer Nature Switzerland AG 2020
M. Gallaway, An Introduction to Observational Astrophysics,
Undergraduate Lecture Notes in Physics,
https://doi.org/10.1007/978-3-030-43551-6_5
53