By: Dr. Lim Ju Boo
Date: July 6, 2021
The heavens declare the glory of God; and the firmament sheweth his handywork. Day unto day uttereth speech, and night unto night sheweth knowledge (Psalm 19:1 - 2)
It is he that sitteth upon the circle of the earth, and the inhabitants thereof are as grasshoppers; that stretcheth out the heavens as a curtain, and spreadeth them out as a tent to dwell in (Isaiah 40:22)
A fortnight ago I was talking with a doctor colleague of mine on the Covid-19 pandemic, its origin and the direction we are taking for good or for the worse.
Before long I thought the Universe we are in is so immensely vast that anything is possible out there including our origin and our fate in the millennium ahead.
I then thought I should immerse myself writing out a small thought about our size and all humanity on Earth, the Sun, the stars, the galaxies till the Observable Universe containing roughly 70 billion trillion (7 x 10 ^22) stars, each of them like our own Sun as a grain of sand across a vast cosmic seashore.
How do those dimensions work out? Let’s check this out.
Before we do that, let’s have a look at some data about the size of our Sun, Earth and us before it is possible to proceed.
1. Radius of Sun 696,340 km (696 340 000 meters)
2. Diameter of Sun 1,392,680 km (1,392,680,000 meters)
3. Radius of Earth 6,371 km (6,371,000 meters)
4. Diameter of Earth 12,742 km (12,742,000 meters)
5. Diameter of Sun to Earth 109.3
Volume of sphere = 4/3 pi r^3
Radius of sphere ∛(3Vol / 4 pi)
Volume of Sun = 1.41^18 cubic km = 1.41^27 cubic meters
Volume of Earth = 1.08^12 cubic km = 1.08^21 cubic metres
Volume Sun compared to Earth = 1,305,555
Miniaturization:
The Sun has a diameter of 1 392 680 000 metres (1,392,680 km). its volume would be 1.41^18 cubic km (1.41^27 cubic meters).
If we were to scale down the Sun as a grain of sand 1 cubic millimeter in volume, its diameter would be 1.24 millimetre or 1240 microns.
We shall use a grain of sand to represent our Sun as an average star as our scale all through for comparison.
The volume of Sun would be 1,305,000 times that of Earth, and the Earth in comparison is 7.6 ^ -7 times that of Sun or 7.66^-7 cu millimetre (766 cubic micron) in size.
The radius of Earth then is 5.7 ^ -3 millimeter, and its diameter is 0.01135 mm (11.35 micron).
The average density of a human body is equal to 1 010 kg/m³.
In an average person with a mass of 65 kg its body volume would be 0.064 cubic metre. (Vol = wt / density)
The volume of man would be 0.064 cubic metre, and his diameter is 0.50 metre.
The volume of man compared to that of the Sun would be:
4.5 ^-29 (0.0,000,000,000,000,000,000,000,000,00045) cubic metre or 4.5 ^ - 11 cubic micron.
The human body would be reduced to a teeny-tiny dot in comparison with a diameter of only 4.4 ^-10 meter across (0.00044 micron).
The Sun’s diameter in comparison with that of Earth would be 109 larger, but it will be 2,800,000,000 times that of a human.
Conversely, the diameter of a human body to that of the Sun would be shrunk to 3.6 ^ -10 in reverse.
The volume of human body compared to Earth would thus be:
5.9 ^-23 (0.000,000,000,000,000,000,000,059).
Our Purpose:
Whichever way we like to present it, in their actual or in their miniaturized ratios, the result is exactly the same, as the purpose of this comparison is to show how insignificant and infinitesimal teeny-tiny we are, as much as our entire world in a cosmic ocean of sands, each grain representing a star or a sun. We shall go into that later.
Let us now turn to the stars in our galaxy, and the distance between them as two grains of sand.
Let's check this out.
We are located somewhere about two-third the way out from the center of our Milky Way Galaxy in one of the spiral arms called the Orion Arm.
In this location is our Solar System consisting of eight planets along with untold numbers of comets, asteroids and large sub-planetary bodies like dwarf planet, planetoid, meso-planet, quasi-planet. Dwarf planets are the smallest planets, not the largest sub-planets.
The Universe is not just our Solar System, but contains an unspeakable 70 billion trillion (70,000,000,000,000,000,000,000 other stellar systems.
The Universe is so vast across at 93 billion light-years in diameter or 8.8×10 ^ 23 km (880 yotta metres) that it is not possible to estimate a representative distance that separates each star let alone their planets.
It is difficult as we do not have sufficient safe sample sizes in such an immensely huge population of stellar systems to represent them all to measure their central tendency by dividing the sum of the values by their numbers.
However, we shall discuss other options below
We know the star density in the center of globular clusters is high. In the densest globular-cluster cores, it is so highly dense that we cannot resolve the individual stars let alone their distances of separation.
For instance the M15's center packs approximately 4 million stars per cubic parsec. That means their densities are more than 75 million times denser than the region around the Sun.
This works out on an average of only 0.013 light-year, or 860 astronomical units between the stars.
(An astronomical unit is the average Earth-Sun distance of about 1.496e+8 km = 149,600,000 km)
Most galaxies, such as M31 in Andromeda, M33 in Triangulum, and the Milky Way have central densities close to this value. This means the average separation of each star is about 0.013 light-year or 123 billion km.
But some galaxies pack stars even tighter. M32, one of the Andromeda Galaxy's satellites, has the highest measured stellar density of any nearby galaxy, and has around 20 million stars per cubic parsec or 20 million stars per 2.9 x 10^40 (29 followed by 39 zeros) cubic km in its core!
One parsec is a larger unit used professionally than a light year for measuring the distances to the stars and galaxies. It is the distance at which the radius of Earth's orbit subtends a parallax angle of one second of arc, and is equal to 3.086e+13 or 30,860,000,000,000 km. But we shall use light years instead to make it easier for our lay readers.
In the centre of a galaxy the separation of stars may be at least half a light year or 4.7 ^ 12 km (4,700,000,000,000 km) from each other, so vast between them that even if two galaxies were to collide at some point, it is hardly likely for any star colliding with each other even at their centers. Towards the edges of a galaxy the stars are paced even further apart.
However, since we are two-thirds the way out from the centre of our Milky Way Galaxy, we are in a location neither too packed nor too sparse.
Even if we use this example as the average distance of separation between every grain of sand found in this world, this works to be 5.5 ^ 13 km which is 55 trillion (55,000,000,000,000) km from each other.
This is how vast this Universe of ours is, and later we shall show how small both our Earth and ourselves are.
On an average, the distance between stars in outer parts of the Milky Way is about 5 light years. But in the core, where the density is more, the average distance is only 0.013 light years (1.2 ^ 11 km), or 120,000,000,000 km apart.
We make our estimate of 5 light years (47 trillion km) as our stellar separation using our nearest star, Proxima Centauri that lies 4.2 light-years away since the average stellar density here in the galactic disk is one star every 19 cubic parsecs.
We shall then use 5 light years scaled down to 42 km to represent the average distance between the sands on the seashores and deserts in our world, even though the numbers of stars in the Universe with different distances from each other are far more than all the sands on Earth.
See this article:
https://scientificlogic.blogspot.com/search?q=number+of+sands
Let us now look at the dimension of our own Milky Way Galaxy
The Milky Way Galaxy is a barred spiral galaxy estimated to have a visible diameter of 100,000–200,000 light years across. Scaling down its diameter similar to the dimension of its average star or our sun to the size of a grain of sand, this works out to be (8.4 km x 100,000) to (8.4 x 200,000) = 840,000 km - 1680,000 km across.
This means standing on a seashore between these two dimensions to represent only our own Milky Way galaxy, and not the entire Universe.
Such a localized seashore will still stretch 2.2 - 4.4 times the Earth to the Moon distance, since the average Earth- Moon distance is 384,399 km.
But the Milky Galaxy also has several satellite galaxies as part of the Local Group of galaxies, which form part of the Virgo Supercluster, which is itself a component of the Laniakea Supercluster, and we have not even considered them.
Recent simulations suggest that the Milky Way may stretches beyond with a dark matter disk containing some visible stars. This suggests the Milky Way diameter may extend to as much as almost 2 million light-years. This works out at 16,800,000 km of seashores of sands.
The Milky Way is estimated to contain 100–400 billion stars and at least that number of planets or more.
This implies the seashore and deserts of sand, each grain as the stars in the Milky Way extend to far more than just 2 - 4 times the Earth to Moon distances.
This size when miniaturized is only for our Milky Way galaxy. It is estimated there are 125 billion (1.25×1011) galaxies in the observable universe.
Cosmic Flickering Yardsticks to the Stars:
The closest known galaxy to us is the Canis Major Dwarf Galaxy. It lies at 236,000,000,000,000,000 km (25,000 light years).
But how far are each galaxy apart from each other?
Leavitt discovered that the period of oscillation of Cepheid stars, a type of variable stars, is related to their intrinsic brightness.
Over a period of between 1-70 days, a Cepheid progresses through a complete cycle from maximum brightness to minimum and then back to maximum again.
She discovered the brighter Cepheids take longer to complete their oscillation cycle.
The difference between observed and actual brightness is known as “period-luminosity relation" gives the distance.
We shall not go into the details on this as it is not the aim of this essay, but simply put, by finding Cepheids on other galaxies and measuring their oscillation period allows us to determine their distances from their apparent brightness.
Leavitt used the flickering Cepheids as the cosmic yardsticks to the stars and galaxies.
Beyond our Milky Way Galaxy:
Let us now look at some galaxies beyond ours. But before that we need to scale down their distances.
If we scale down one light year of 9.461e+12 km (9.461 ^ 15 meters) or 9.462 ^ 18 millimeters into its distance in km proportionally to a grain of sand at 1.24 mm across compared to that of the Sun, it works out to be 1.24 mm / 1,392,680 km x 9.461e +12 km = 8,423,787 mm or 8.4 km.
We shall now use 8.4 km to present a light year to look at just 6 examples of our nearest galaxies with their scaled-down distances in km in parenthesis.
1. Wolf-Lundmark-Melotte (WLM) – 3,064,500 light years (25,741,800 km)
2. Sagittarius Dwarf at 0.81 million light years (6,804,000 km)
3. Andromeda Galaxy (M31) at 2.538 million light years (21,320,000 km)
4. Sculptor Galaxy (NGC 253) at 11.40 million light years (95,760,000 km)
5. Messier 81 at 11.74 million light years (98,616,000 km)
6. Centaurus A 12.01 million light years (100,884,000 km)
Let us now go further beyond.
The furthest galaxy MACS0647-JD discovered is a galaxy with a redshift of about z = 10.7, equivalent to a light travel distance of 13.26 billion light-years (4 billion parsecs).
This distance is equivalent to a scaled down 1.11384 ^ 11 km (111.4 billion km) away.
This galaxy is believed to be formed about 427 million years after the Big Bang. Its diameter is less than 600 light-years wide (equivalent to 5,040 km) and contains roughly a billion stars.
Having said all that, it is hardly possible for us to imagine a seashore with sands stretching out 112 billion km to represent the further galaxy. But that’s not all. We need to go further.
Beyond the Furthest:
By measuring the number and luminosity of observable galaxies, astronomers put the current estimate on the total number of stars within the Observable Universe roughly at 70 billion trillion (7 x 10 ^22), again each of them a grain of sand like our own Sun.
The diameter of the Observable Universe is put at 93 billion light years. Scale this down, it puts our seashores at 7.81 ^ 11 or 781 billion km across, or 390.5 billion km all around.
This is how vast this Universe of ours is, and later we shall show how small both our Earth and ourselves are.
Let us now return to ourselves in such immensity.
Can we be Seen?
A light microscope allows us to see an object between a millimetre (10-3 m) to as small as 0.2 micrometres (0.2 thousands of a millimeter (2 ^-4 mm) or 2 x 10^ - 7 m).
The most powerful electron microscopes allow us to see objects as small as an atom (about one ten-millionth of a millimetre or 1 angstrom or 10-10 m).
Some can go down below 5 ^ -10 metres which is 0.5 angstrom (50 picometres), enabling magnifications above 50 million times. But we shall take 10 ^ - 10 m as the limit.
This means if our Sun as a grain of sand 1 cubic millimeter in size, we can still see it with our naked eye.
The Earth at 0.0227 (227 ^ -4) millimetre across is invisible to our naked eyes that can only see an object about 0.1 millimeter across, but can still be seen with a light microscope at high magnifications.
But the diameter of a man at only 3.6 ^-10 millimetre can no longer be seen even by the most powerful electron microscope.
What about if we put ourselves together in one spot. Can we still be visible?
Let’s have a look.
The world population currently on June 2021 is 7.9 Billion (2021).
Hence if we gather all humans together side-by-side in one spot as a blob on Earth, leaving completely no space in between, the total human volume compared to the size of a grain of sand one cubic millimeter the volume would be:
(7.9 ^ 9) x 4.5 ^ -29 = 3.6 ^ -19 cubic metre (0.36 micron)
Our total diameter as a blob works out to be 8.8 ^ -7 meter
At this collective human diameter we can be seen only with the world’s most powerful electron microscope that can resolve an object almost the size of an atom. Our collective size would be only about 880 times larger than an atom.
This only shows how infinitesimally insignificantly small we are.
We talk about space. What about our existence in time? This is another separate problem that requires lengthy write-up. Very briefly put:
The Age of this Universe is estimated at 13.8 billion years. At maximum, our life span lasts only 100 years in comparison.
Translated, our extremely transient life lasts just 6.3 x 10^ -4 second (0.00063 second). We can mull over this again and again.
We can chew this over and muse ourselves with this mind boggling dimensional scenario long as we like, and good luck to our imaginations.
Thank you for reading.
Jb Lim
Scales used:
1 metre = 1000 mm
1 km = 1000 000 mm
1 millimeter = 1,000 micrometer (1,000 micron)
1 micrometer (micron) = 1e-6 meter (0.000 001 m).
1 m = 1/0.000 001 = 1 000 000 micrometer
1 cubic meter = 10 ^9 cubic millimeter
10 ^ 9 cubic meter = 1 cubic km
1 ^ 9 cubic millimeter = 1 cubic micrometer
1 cubic mm = 1 ^ 9 micron
1 cubic micron = 1e-18 cubic meter
1 cubic millimeter = 1^9 cubic micron