Chapter 4 — Coordinates

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Project Bluestar

5 min readApr 18, 2021

Introduction

Coordinates is something we learn in middle school that sticks with us for quite a lot of time but what exactly are their applications? What use do we get from plotting points on an x-y coordinate system and how exactly do they help us? We’re going to find that out today

I think the universe is pure geometry — basically, a beautiful shape twisting around and dancing over space-time.
Antony Garrett List

x-y coordinate systems

While it may seem fundamental, we might as well cover the basics of an x-y coordinate system just for revision. The coordinate system we use most commonly is the Cartesian Coordinate System.

A typical coordinate system is split into four parts also known as quadrants. Each quadrant is represented using a roman numeral.

We can let the x and y axis be any quantity. We could let the x axis equal time and the y axis equal position or velocity or whatever. The point 0 is known as the origin.

We represent a point in the coordinate system in the form (a, b) where a is the x axis value of that point and b is the y axis value of that point. You can plot many points on the same coordinate system and create graphs.

Sometimes a 2 dimensional plane isn’t enough for calculations and a z axis is added.

A point in space is represented like this: (a, b, c) where a is the x axis value, b is the y axis value and c is the z axis value.

Coordinates on Earth

A coordinate system seems pretty abstract, how can we flatten a 3D sphere onto a two dimensional plane or how can we fit everything into a 3D space. The answer is we don’t do that. Instead we use latitudes and longitudes to specify a position on Earth.

We split the Earth in half at the equator. The top half is known as the Northern Hemisphere and the bottom half is the Southern Hemisphere.

The equator is said to be 0⁰. We then draw parallel lines to the Equator, these are known as parallels of latitude.

At 90⁰, we have the North Pole and at -90⁰ we have the South Pole.

We now need to use a set of lines perpendicular to these for intersections, we take Greenwich in the UK to be 0⁰. These lines are called meridians of longitude.

The intersection of the meridians of longitude and parallels of latitude give us a coordinate system on Earth.

Chennai is about 13⁰ N and 80⁰ E while London is about 50⁰ N and 0.12⁰ W. It may not be as easy to visualise as in a 2D coordinate system but it works and has been used for a very long time.

Equatorial Coordinate System

Now how do we measure the location of other objects in space? We can’t use the longitude and latitude system as we would have to have really small increments in angles and it’s just awkward to work with. Instead we use a slightly more confusing system that’s functional nevertheless. What we do is we stretch out the North and South pole like this:

These poles are renamed the North celestial and South celestial pole respectively. These retain their angle as per the ones on Earth, 90⁰ and -90⁰ respectively. The North Celestial Pole is also called the Zenith while the South Celestial Pole is called the Nadir. I won’t use these terms so you don’t get bogged down with all these new words.

We basically stretch out the latitudes but we don’t call them latitudes anymore because Astronomy!!! Instead we call them ‘declination’. We however do not stretch out longitude because we just can’t. Again Astronomy!!! Nah I’m joking there’s a reason for this. It’s because the Earth is constantly rotating on its own axis. Therefore 0⁰ is constantly changing and that means the location of each object in space would change everytime the Earth rotates which gets kinda annoying.

However we humans are smart and decide to use a different system for longitudes. Instead we take the path of the Sun also known as the ecliptic as the main longitude line. The point at which the ecliptic intersects with the celestial equator. This is known as the vernal equinox and is taken as 0⁰. However now we don’t use degrees as our unit for longitudes, we use hours because the Earth takes 24 hours to rotate on its own axis.

These are not called longitudes but are instead called hours of Right Ascension. We can now join the Right Ascension and the Declination to form a coordinate system. Polaris is located roughly at 2h 40 min RA and 89⁰ Dec. Again not easy to visualise but it works.

Conclusion

This is the idea of the celestial coordinate system at a very simple level. There is more to it but I feel that a blog isn’t exactly the most conducive way for someone to learn it through. I will be linking some resources for you to learn more about it. One flaw of the celestial coordinate system is that it doesn’t let you measure the distance of the celestial object from the Earth. For that we’d have to use the parallax method or other methods of measurement which we’ll get into a bit later.

Resources:

Images can be found at:

“Geospatial Activities.” GSP 270: Latitude and Longitude, gsp.humboldt.edu/olm/Lessons/GIS/01%20SphericalCoordinates/Latitude_and_Longitude.html.

2. “Latitude and Longitude.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., www.britannica.com/science/latitude.

3. “What Are Circumpolar Constellations?” Quora, www.quora.com/What-are-circumpolar-constellations.

Chapter 4 — Coordinates

Written by Madhav Menon