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import numpy as np
import matplotlib.pyplot as plt
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from IPython.display import HTML
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In this chapter we present the positional astronomy we will need to comprehend interferometry. We discuss three useful astronomical coordinate systems in this chapter.
Astronomical coordinate systems
• the equatorial coordinate system in $\S$ 3.1 ➞: the equatorial coordinate system enables us to create
star map catalogues, so that we can easily relocate celestial objects in the night sky.
• the horizontal coordinate system in $\S$ 3.3 ➞: The horizontal coordinate system is used to point a telescope to a specific location in an observer's local sky.
• the direction cosine coordinate system in $\S$ 3.4 ➞: The direction cosine coordinate system is used to make local sky-maps around a direction of interest. It is also important in radio interferometry as it allows us to define a Fourier relationship between the sky brightness and the interferometric measurements (see $\S$ 4 ➞).
There are two additional concepts that are also discussed: hour angle and local sidereal time.
Hour angle
The equatorial coordinate system is static, i.e. the positions of the stars changes very slowly. The longitude equivalent equatorial coordinate is known as right ascension. The stars do however move across the sky of an earth-bound observer all the time, we therefore need a mutable longitude equivalent equatorial coordinate if we wish to keep track of the stars from earth. This is exactly what the hour angle provides. The hour angle is discussed in more detail in $\S$ 3.2.1 ➞.
Local sidereal time
The local sidereal time, is the current star time of a local observer. We need a separate "star" clock as our normal civil clocks keep track of the Sun. The Sun and an arbitrary star take different amounts of time to reappear at the same position in the sky. We discuss this in greater detail in $\S$ 3.2.2 ➞. We use the local sidereal time to obtain the hour angle of a source from its right ascension coordinate.
In general, we do not explicitly reference any outside material in this chapter, but the reader is referred to Practical Astronomy with your calculator or spreadsheet ⤴ as it provides an in depth review of astronomical coordinate systems. It is the main (mostly silent) reference of this chapter.