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A Sphere with Infinite Radius

Abhilasha Rajan

Time Seeds of Universe – 3

What is the perspective of the observer, and what is the reference frame of observation? Observing the sky from earth, the sky appears to be moving- Sun, Moon, Planets, and stars all appear to be moving in their own rhythm. Where are these objects and how are they moving? These objects are moving inside a celestial sphere, which represents our Earthling’s view of the universe.

Position on Earth

The observer’s position on Earth holds significance in the reference frame of observation. My position on Earth is defined by the coordinates of latitude and longitude. The timing of morning and evening, the length of day and night, the objects visible in the night sky, and even the temperature and rainfall in my location are all influenced by latitude and longitude. Before contemplating the vast sphere outside of Earth, it is important to firmly establish one’s position on the Earth’s surface and understand where they are located. In my case, I am situated in the northern hemisphere, above the Tropic of Cancer, but I also spend a significant amount of time in places close to the equator. My longitude is east of the Prime Meridian, and my hometown is even farther east, resulting in a significant time difference between these two places.

Understanding my location on Earth led to an interesting discovery about the length of shadows and zero shadow days. It reminded me of the childhood horror stories that ghosts do not have shadows, and one can quickly identify their presence when they appear! However, there are days when we live without our shadow (created by the Sun). Not all places on Earth have the luxury of witnessing zero shadow days; only latitudes between the Tropic of Cancer and the Tropic of Capricorn experience them. Alok Mandavagane has created a mobile app to help find zero shadow days on Earth. (Link: Find Zero Shadow Days app)

It was intriguing to revisit the arbitrariness of the current Prime Meridian, Greenwich, and recognise that geopolitical power dynamics play a critical role in standardising scientific concepts. Further exploration into the history of assigning meridians revealed a Pandora’s box of information. Indians had their own Prime Meridian at some point, located near the Tropic of Cancer, currently known as Ujjain. This topic deserves independent exploration.

A Sphere with Infinite Radius

Returning to the celestial sphere, imagine a colossal sphere surrounding the Earth, so vast that its radius is infinite! It encompasses everything that exists now, ever existed, or will ever exist, both manifested and unmanifested. All celestial objects moving in the sky have their own paths within this celestial sphere. The sphere is concentric with the Earth, and its pole and equatorial plane coincide with those of the Earth. We can describe the location of objects in the sky using celestial coordinates: declination (DEC) and right ascension (RA), which are equivalent to latitude and longitude on Earth, respectively.

Declination represents the angular distance of a point north or south of the Celestial Equator, ranging from +90°N to -90°N, similar to the latitude of the North and South Poles.

Celestial South Pole = -90° declination

Celestial Equator = 0° declination

Celestial North Pole = +90° declination

Right ascension measures the angular distance of an object measured eastward from the First Point of Aries (named after the Aries constellation), also known as the Vernal Equinox. RA is typically measured in hours, minutes, and seconds rather than degrees. Since the sky appears to turn 360° in 24 hours or 15° in one hour, an hour of RA corresponds to 15° of sky rotation.

Now, let’s transition from the large sphere to the big circle known as the ecliptic or ecliptic plane. The ecliptic represents the orbital plane of the Earth around the Sun, inclined at an angle of 23.4° from the celestial equator. The great circle marking the intersection of the celestial sphere with this ecliptic plane is where the Sun and planets appear to move in the sky. This great circle is also where the Sun and Moon cross paths during solar and lunar eclipses, which explains its name.

But what about eclipses? Drawing the large sphere helped me visualize the movement of various celestial objects in the sky, and learning about eclipses proved to be a surreal experience that left more questions unanswered than answered. I realized that relying solely on the internet was not enough for a comprehensive understanding.

Time Seeds of Universe is a series on understanding time. TimeSeeds of Universe: A Sphere with Infinite Radius is part 3 in this series. Following are the link to other blogs of this series : 

Time Seeds of Universe- 1 : A Journey of Self-Discovery

Time Seeds of Universe- 2- It is about Reference Frame

Time Seeds of Universe- 4: Path, Light and Shadows

Time Seeds of Universe – 5: Quest for Salvation in the Wonders of Nature