Tag: India

I started shooting star trails last year and observed that their pattern varies depending on the direction in which the camera is focused. The curiosity to understand the star trails led me to an interesting phenomenon – the Celestial Equator. Hence, during the trek to Singalila Ridge (near Darjeeling, India) in Oct’18, my key objective was to record the Celestial Equator in my pictures.

Firstly, let me answer the most common question asked, “Can we see the star trails?”

Answer is No! Human eye is very powerful but cannot record a scene while a camera can do so on a photo film or digital sensor. As per my settings, a star trail picture is a composite image of minimum 60 frames where each frame has a time exposure of 30 secs. All such frames are shot continuously without disturbing the camera position and settings. Each frame captures the apparent movement of a star due to Earth’s rotation in 30 secs. Individual frames are then stitched together in a photo processing software in ascending order of time sequence to build a single star trail image.

Let’s now take a magnetic compass and explore the night sky….

A) Focus on the North direction as shown by the compass

Earthlings in the Northern Hemisphere are lucky to have a clearly visible star Polaris or North Star about 323 light-years away from Earth. The position of North Star in the sky is aligned with Northern end of Earth’s axis of rotation. It means if the observer is standing at the North Pole, North Star will be seen in the sky vertically above the observer’s head i.e. at the ‘Zenith’.

Now, imagine our observer standing at the North Pole (Latitude = 90 degrees North) starts walking downwards towards the Equator (Latitude = 0 degree). As he moves away from the North Pole, he will see that the North Star is now not visible at Zenith above his head. It actually has shifted down the Zenith towards the horizon.

How much will be the displacement of North Star’s position in sky?

For every 1 degree of latitude walk from North Pole to Equator, North Star will be visually displaced by 1 degree away from the Zenith of the observer’s location and towards the Northern horizon. From the observer’s location, North Star’s position in the sky will be as follows:

• From the Zenith = Number of Latitude degrees observer is away from the North Pole or From the Zenith = 90 – Latitude of the observer’s location
• From the Horizon = 90 – number of Latitude degrees observer is away from the North Pole or From the Horizon = Latitude of the observer’s location

When the observer reaches Kalapokhri (my location at Latitude = 27 degrees North of Equator) on India-Nepal border then North Star will appear:

• From the Zenith = 90 – Latitude of the observer’s location  = 90 – 27 = 63 degrees (angle between Zenith→Observer→North Star)
• From the horizon = Latitude of the observer’s location = 27 degrees (angle between Horizon→Observer→North Star)

Ok! So, we have identified the angle of view for North Star. Now, let’s check the star trails in the North sky.

Earth rotates from West to East around its axis which is aligned from North Pole to South Pole. Also, North Star is visible at the Zenith of the North Pole. Thus, due to Earth’s rotation, stars in Northern Hemisphere appear to wheel around the North Star in anti-clockwise motion. This makes the North Star as the centre of circular star trails. North Star appears to be stationary because it is aligned along the rotational axis (North-South) of Earth. It implies that irrespective of the observer’s location on Earth, if the North Star is visible then its position indicates the North direction. This is the reason why North Star is so important for navigation.

At the Equator (Latitude = 0 degree), the angle between Horizon→Observer→North Star = 0 degree. Thus, North Star will not be visible. The star trails will appear like semi-circles centred around the position at the horizon below which lies the North Star.

At the North Pole (Latitude = 90 degrees North), the angle between Horizon→Observer→North Star = 90 degrees. Thus, North Star will be visible overhead at the Zenith. The star trails will appear overhead as circles centred around the North Star and parallel to the horizon. Anywhere in the Southern Hemisphere, North Star will not be visible as it will be below the horizon.

B) Focus on the South direction as shown by the compass

As explained for Northern Hemisphere, all stars in Southern Hemisphere also appear to move around South Pole but in clockwise motion. There is an equivalent to North Star known as Polaris Australis but it is barely visible.

In the above picture, you can see that centre of concentric circular star trails is not visible and appears to be at the far-left bottom of the frame. That’s because Sandakphu is in the Northern Hemisphere and South Pole is below the horizon. Now, if we focus towards East or West there should be vertical star trails. Yes, but the magnitude and the angle of vertical trails again will depend on the location of the observer. This brings us to the Celestial Equator!

C) Focus on the West direction as shown by the compass. It should be real geographical West and not the point on West horizon where the Sun sets!

Assume that the observer is standing on the Equator with his arms stretched sideways from left to right and parallel to the ground. If he moves his hand to meet at the top of his head, it results in a semi-circular trajectory. Let’s extend this trajectory up in the sky. This imaginary circular trajectory with an infinite radius in the sky, parallel to the Equator from East horizon to Zenith to West horizon is the Celestial Equator.

The Celestial Equator divides the visible sky anywhere on Earth into Northern and Southern Hemispheres. Thus, at the Equator, one half of the sky towards North of Equator is Northern Hemisphere and the other half of the sky towards South of Equator is Southern Hemisphere. This division of the sky in two equal parts will occur only at the Equator.

What about the other locations on Earth?

To find the answer, let’s ask our observer to face South and walk backwards towards the North Pole. For every 1 degree of latitude walk from Equator to North Pole, the imaginary line dividing the sky called as the Celestial Equator will fall by 1 degree from Zenith towards Southern horizon. This fall is because of the spherical shape of Earth. The portion of the sky North of Celestial Equator will be in Northern Hemisphere and that to the South of Celestial Equator will be in Southern Hemisphere.

Star trails in the Northern Hemisphere will be concentric with the North Star aligned with North Pole and the stars in the Southern Hemisphere will be concentric with the Polaris Australis aligned with South Pole. All stars at or near the Celestial Equator will appear to be moving in almost straight trajectories parallel to the Celestial Equator.

The Celestial Equator will intersect the horizon exactly at the geographical East and West points for the given location. Let’s take the West intersection point and draw an imaginary line from this point to the Zenith. Now, from the observer’s location,

• the angle between Zenith→Intersection point on Horizon→Celestial Equator = Latitude of the observer’s location or (90 – number of Latitude degrees observer is away from the North Pole)
• the angle between Horizon→Intersection point on Horizon→Celestial Equator = Number of Latitude degrees observer is away from the North Pole or (90 – Latitude of the observer’s location)

Let’s check the results when the observer reaches Kalapokhri (my location at Latitude = 27 degrees North of Equator) on India-Nepal border.

In the Figure 3, it is observed that,

• angle between Zenith→Intersection point on Horizon→Celestial Equator = 27 degrees
• angle between Horizon→Intersection point on Horizon→Celestial Equator = 90 – 27 = 63 degrees

Wow! This observation for the intersection angle of Celestial Equator at Kalapokhri is as per the theoretical explanation given above.

When he reaches the North Pole, the Celestial Equator will be located along the horizon (90 – 90 = 0 degree). Thus, the entire sky will be in Northern Hemisphere.

This phenomenon is also applicable when we move towards South Pole from Equator. The Celestial Equator will move towards North by 1 degree from Zenith for every 1 degree latitude walk towards South Pole from Equator.

To summarize, for any location on Earth:

1. The Celestial Equator divides the visible sky anywhere on Earth into Northern and Southern Hemispheres.
2. The Celestial Equator will intersect the horizon at geographical West and East points. Its angle of intersection relative to Horizon and Zenith will be same for all observers located at the same latitude anywhere on Earth.
3. All star trails will be parallel to the Celestial Equator.
4. All stars in the Northern Hemisphere sky (North of Celestial Equator) will form anti-clockwise star trails with the North Star at North Pole as the centre.
5. All stars in the Southern Hemisphere sky (South of Celestial Equator) will form clockwise star trails with the Polaris Australis at South Pole as the centre.
6. At the Equator,
   • star trails in Northern Hemisphere will appear like semi-circles centred around the position at the horizon below which lies the North Star aligned with North Pole.
   • star trails in Southern Hemisphere will appear like semi-circles centred around the position at the horizon below which lies the Polaris Australis aligned with South Pole.
   • star trails in the East and West directions will appear perpendicular to the horizon.
7. At the North Pole, all star trails will appear parallel to the horizon with centre as North Star visible at Zenith of North Pole.
8. At the South Pole, all star trails will appear parallel to the horizon with centre as Polaris Australis located at Zenith of South Pole.

Today, we have sophisticated technology to understand various cosmic phenomena. However, modern science is built on the work of our ancestors who identified these concepts by meticulous observations and calculations. I bow to them!

Please visit Image Gallery : With Stars at Singalila

Click Celestial Equator for a time lapse video that clearly shows the Celestial Equator with the star trails i.e. Clockwise (in Southern hemisphere – left side of the video directed towards South), Straight (along Celestial Equator) and Anti-clockwise (in Northern hemisphere – right side of the video directed towards North).