The Universe in Perspective

 

4: Welcome Home

 

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"It suddenly struck me that that tiny pea, pretty and blue, was the Earth. I put up my thumb and shut one eye, and my thumb blotted out the planet Earth. I didn't feel like a giant. I felt very, very small." - Neil Armstrong

 

 

Stylized SunWelcome Home: Earth


Earth is our home: an astronomical object, a massive ball of rock. It is a planet orbiting a sun in the vast cosmos. It is the only astronomical body of which we all have personal detailed knowledge.

Naturally, then, it is our stepping stone to understanding Universal scales.

Our planet is a massive sphere(oid). Even though it is not a perfectly symmetric sphere treating it like one is close enough for our purposes.

We'll take in the scale of Earth using a progression through the three dimensions: first is linear (length) measurements. Earth has a radius of 6,371 km, and so more than 6 million meters from the surface of the Earth to its center.

From a personal point of view this is quite a distance. And this is just the radius, the diameter, of course, is twice as far.

How big is 6371 km? Were we to stand on the equator and, wherever we are, draw a line straight north, these cities would be (approximately) 6400 km away:

Inverness, Scotland

Arendal, Norway

Stockholm, Sweden

Moscow, Russia

Neryungri, Russia

Juneau, Alaska USA

Fort McMurray, Canada

For those living in southern climes, same thing but a line due south instead:

360 km. south of Ushuala, Tierra del Fuego

Between Puerto Toro & Villa Las Estrellas, Chile

1600 km south of Hobart, Tasmania, Australia

We can also look at it the other way. Stand at the South Pole and draw various lines of lenght 6400 km straight north and you find these cities:

Durban, S. Africa

Perth, Australia

Cordoba, Argentina

La Serena, Chile

Rosario, Argentina

Pelotas, Brazil

And, for those living in Northern climes, same thing but standing at North Pole and drawing various 6400 km lines due south:

Casablanca, Morocco

Tripoli, Libya

Alexandria, Egypt

Tel Aviv, Israel

Baghdad, Iraq

Kandahar, Afghanistan

Rawalpindi, Pakistan

Amritsar, India

Xian, China

Shanghai, China

Nagasaki, Japan

San Diego, CA USA

Dallas, TX USA

Shreveport, LA USA

Charleston, SC USA

If those don't help you visualize Earth's 6400 km radius perhaps some distances between cities:

Lisbon, Portugal to Dubai

London, UK to Karachi, Pakistan

London, UK to Kampala, Uganda

Cape Town, S. Africa to Jeddah, Saudi Arabia

Moscow, Russia to Pyongyang, N. Korea

Baghdad, Irag to Beijing, China

Melbourne, Australia to Kuala Lumpur

Darwin, Australia to Patna, India

Anchorage, AK USA to Miami, FL USA

Seattle, WA USA to Bogota, Columbia

Bogota, Columbia to Puerto Arenas, Chile

These distances are straight-line geodesics on the world; that is, the shortest distance on a sphere between these cities. These are "as the crow flies", or, more modern-ly, as the jet airplane flies, straight lines. If you look these up on say google maps you will see they bend. That is because 3d geometry doesn't plot all that well on a 2d flat map surface. So some of these paths will be over ocean, or even the poles, contrary, sometimes, to "common sense".

On a more personal note: A Marathon race is 42.195 km (26.2 miles). To move yourself a distance equal to one Earth radius would reguire you to run (or walk very very briskly) a Marathon each day for 151 days, or about 5 months. And this is just Earth's radius, its diameter is, of course, twice as long.

The radius / diameter is not the Earth's only "linear" dimension, it also has a circumference. And that, at the equator where the Earth bulges a bit due to its rotation, is 40,075,017 meters (40,075 km). This is about 6.28 times greater than the radius and so Marathons each day around the equator would take you 948 days, or 2 years and 7 and a half months.

Earlier we talked about millions and billions and trillions, which are huge. So, it is easy to lose sight of just how big 6,000 anythings are, at least on our small human scale.

To put Earth's linear dimensions in perspective: A tennis ball is 6.7 centimeters wide (0.067 m). One kilometer relates to our radius of 6,371 km as one tennis ball relates to a line of tennis balls 427 m long.

And one kilometer relates to our circumference of 40,074 km as one tennis ball relates to a line of tennis balls 2.58 km long.


Everest-EarthSlice Quiz Pic

A small pop quiz for you all. This is a slice through the Earth. Mt Everest is shown at the top, some place in the Pacific Ocean at the bottom.

In the world of PC's and smart phones the size of this picture is going to vary depending on your screen size. So let's say Everest here (using the mark shown) is 2 cm tall. your task is guess how tall this picture would have to be to show Everest in (semi)accurate scale to Earth's diameter?

Answer below.


Earth slice

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The picture would have to be about 28 and a half meters tall.


 

I now introduce here some "personal" measures, ones that relate to you personally.

First our personal linear measurement. It is common knowledge that men are generally taller than women, and both of these are, generally, taller than children.

After careful consideration I declare that an average human height is 1.67 meters.

This is, in this book, your height.

The Khufu pyramid (the "Great" Pyramid in Gaza, Egypt) is 147 m tall. Everyone has seen a picture of that with myriads of little people wondering about. If not here are some I snapped myself:


Yet another set of Pyramid Pictures

A few years ago I had the opportunity to visit Cairo and took these pictures of Khufu as a momento. Please note all the people and note that, for the purposes of this book, each one of them is 1.67 m tall.


Khufu from corner

Khufu from front

 

Khufu can hold a stack of 88 of 1.67 m tall you's.

Mt. Everest the highest mountain in the world (the tallest is Mauna Kea, Hawaii) has its tip at 8,848 meters above sea level.

To match Everest's height we would have to stack 60.2 Khufus.

And we would have to stack 720 Everests to match Earth's radius of 6,371 km.

From another viewpoint (the old "shrink to 1 meter" trick):

•  Were we to shrink Khufu so that it was only 1 meter tall:

you would be 1.14 cm tall.

 

•  Were we to shrink Everest to 1 m tall:

Khufu would be 1.7 cm

you would be 0.2 mm.

 

•  Were we to shrink Earth so it's diameter is 1 m long:

Everest would be 0.7 mm tall

Khufu would be 0.012 mm tall

you would be 0.00013 mm (0.13 µm)

 

 


 

Now let's move on to surface area, two dimensions. The Earth's surface area is 5.10072 × 1014 m2, this is equivalent to 510,072,000 km2.

Easy, we just have to know how big a square kilometer is! So do you have an image of the size of a square kilometer in your brain? No? Let's build one.

First we need a concept of personal area (you-area). I declare this to be 4 m2. This means you live in a square 2 m on a side. This is enough to lay down and sleep (remember you are 1.67 m tall), stretch your arms out and spin around, kick your leg out, and break dance. What more do you need?

A tennis court has an area of 260.87 m2. This would 65.25 you-areas.

A football (also known as Soccer) field has an area of 7,140 m2. This would hold: 27.4 tennis courts and 1,785 you-areas.

Khufu has a base footprint of 53,100 m2. It would hold: 7.4 football fields, 203 tennis courts, and 13,275 you-areas

A square Kilometer has an area of, well, 1 km2. This is equivalent to 1,000,000 m2 (106 m2).

So a square Kilometer would hold: 18.8 Khufus, 140 football fields, 3,833.3 tennis courts, and 250,000 you-areas

So now we have an idea how big a square kilometer is and we simply compare that to the 510,072,000 km2 of Earth...

...Nope. Still doesn't capture the imagination does it?

At least it indicates that the more than a half billion square kilometers of Earth's surface is impressive. We need to make this more personal. And we will do that with horizons.

Unlike Fame and Fortune everyone has an horizon. This is, of course, the distance you can see. The best place to see unimpeded is from a shore line or on a boat on the sea, otherwise city structures, hills, forests, etc. get in the way.

You, being 1.67 m tall, have a horizon of about 4.6 km.

It all depends on your height, or rather, the height of your eyes from the surface of Earth.

Take a person that is 1 m taller, a bit taller than the tallest professional Basketball player, and her horizon would be 5.6 km, a full kilometer more.

This gives us a (semi) significant area. The horizon distance is, of course, the same in all directions, again assuming an unimpeded view. So this means the horizon distance is the radius of the circle of the portion of the Earth's surface you can see.

For you this horizon circle has a radius of 4.6 km and so its area is 66.5 km2. This is equivalent to 254,914.5 tennis courts. This is your personal horizon-area.

Our super-giant, 1 meter taller, Basketball player's horizon-area would be 98.5 km2 equivalent to 377,580 tennis courts.

An interesting side note: The Large Hadron Collider (CERN), the worlds largest machine, in Switzerland/France has a radius of 4.5 km. This means if you stood at the center of the circle the LHC circumscribes the LHC would run all around you at the very edge of your horizon, that's how big it is!

Your personal horizon-area is nice but we need more I'm afraid.

Khufu pyramid is, as mentioned, 147 m tall. Were you stand on its peak your horizon distance would be 43.3 km which translates to 5890.1 km2.

And there is no reason to stop here. The highest natural height a person can achieve is the summit of Mt. Everest, 8,848 m up. Your horizon distance here would be 335.8 km translating to 354,251 km2.

Note: The calculation of horizon distance is actually not a simple thing, and the usual method to calculate it will break down, more or less, the higher you go. I'm assuming this error is not enough to cause us any mental harm, and all these figures are approximately correct.

So here is our new area scale:

•  Khufu horizon-area holds:

88.6 you horizon-areas

 

•  Everest horizon-area holds:

60 Khufu horizon-areas

5,327 you horizon-areas

 

•  Earth's surface area holds:

1,440 Everest horizon-areas

86,598 Khufu horizon-areas

7,670,256 you horizon-areas

 


Everest Horizon-area Examples

A few years ago I had the opportunity to visit the Moon and I took this picture...

Nah, I'm kidding. The red dot is (very) approximately the size of the Mt. Everest Horizon area compared to Earth's surface. The Indian continent is at the center, the red dot is over the Himalayas.

I made this picture using Blender and Earth map files (land, bump, and ocean mask) provided by NASA.

Now, the human eye is fooled by circles and spheres so following this are the areas as squares, one overall and one zoomed in. Black is Earth, yellow is Everest-horizon-area, green is Khufu-horizon-area, and red is personal-horizon-area.

You may want to compare this with the same area on the Moon.


Everest horizon area compared to earth

Earth Everest areas as squares

Earth Everest areas as squares zoomed


 

Now we come to adding the third, and final, dimension and talk about volume.

Ok, everyone here who has a good understanding of just how big a cubic kilometer is raise your hand.

Hmmm. Just as I thought.

To begin our journey to the cubic kilometer we need a you-volume. And, since you are 1.67 m tall, this seems like a great diameter for your personal volume bubble. Your you volume goes from the bottom of your feet to the top of your head with a diameter of 1.67 meters, so the volume will be 2.44 m3.

First lets get an idea of how big your you-volume is.

A ping pong ball (radius 0.02 m) has a volume of 3.4 × 10-5 m3.

A football (soccer ball), radius 0.11 m, has a volume of 0.0056 m3.

So a football volume can hold 167 ping pong ball volumes.

Your you-volume can hold 436 football-volumes and 72,800 ping pong ball volumes.

An Olympic regulation swimming pool is 50 m × 25 m surface area. I'm assuming here there pools are 2 m deep and that translates to a volume of 2500 m3. It can hold 1025 you-volumes. 446,429 football-volumes. And 73,529,412 ping pong ball-volumes.

The actual structure of Khufu, just the structure of stones, has a volume of 2.6 × 106 m3. This volume can hold: 1040 pool-volumes -- 1,065,574 you-volumes -- 464,285,714 football-volumes -- 7.6 × 1010 ping pong ball-volumes.

Now for the cubic kilometer which is, uh, 1 km3 (a cube with sides of 1 km), which is equal to 109 m3. It can hold: 385 Khufu-volumes -- 400,000 pool-volumes -- 409,836,066 you-volumes -- 1.79 × 1011 football-volumes -- 2.94 × 1013 ping pong ball-volumes.

Now for the punchline: Earth's volume is 1.08 × 1012 km3 (this is equivalent to 1.08 × 1021 m3). This is simply HUGE. Consider, for a moment, these steps and what you know about numbers in the trillion and quadrillion range...

...ok. Now that we "know" how big a cubic Kilometer is we can see the coming fail of using personal volumes as any type of comparision.

We will turn back to horizons for this, using the various horizon distances as the radii of spheres.

So your you-horizon-volume, based on your horizon distance of 4.6 km, is 407.7 km3.

Re-capping this for our small volumes, but just for your new you-horizon-volume of 407.7 km3:

 

156,964 Khufu-volumes

163,080,000 pool-volumes

1.67 × 1011 personal you-volumes

7.3 × 1013 football-volumes

1.2 × 1016 ping pong ball-volumes.]

 

Continuing with horizon volumes...

...Using Khufu again, but this time we want the volume based on its horizon distance of 43.3 km, we find that Khufu-horizon-volume is 340,057 km3.

And finally using Everest's horizon distance of 335.8 km we get an Everest-horizon-volume of 158,610,044 km3.

With these more appropriate monster volumes we get:

•  Khufu horizon-volume holds:

834 you-horizon-volumes

 

•  Everest horizon-volume holds:

466 Khufu horizon-volumes

389,036 you-horizon-volumes

 

•  Earth's volume of 1.08 × 1012 km3 holds:

6,809 Everest horizon-volumes

3,175,938 Khufu horizon-volumes

2.65 × 109 you-horizon-volumes

 


Everest Horizon-volume Examples

Here are a few diagrams to illustrate the volume differences. Each has an overall view and a zoomed view.

As before, circles and spheres can fool our eyes and braims, so cubes are also presented. The color schemes are the same: black is Earth, yellow is Everest-horizon-volume, green is Khufu-horizon-volume, and red is personal-horizon-volume. Larger versions can be seen here: first  second  third  fourth


Earth Everest volumes

Earth Everest volumes zoomed

Earth Everest volumes as cubes

Earth Everest volumes as cubes zoomed

 


 

The next major property of Earth, and any astronomical object, is its mass.

If you are unsure about the concept of mass you can see this mass footnote, it has a return link to here.

There is no need to create a system of comparisons for mass because mass is tied to volume in a very specific way: Density.

So first let's talk about density.

Density is simply the amount of mass in a specified volume. The average density of Earth is 5.515 g/cm3 (equivalent to 5,515 kg/m3). This simply means that if you take a random, average 1 cubic centimeter sample of Earth, it will have a mass of around 5.515 grams.

So, since density tells the mass per unit volume we just need to multiply this average density times the Earth's volume to get Earth's mass.

Note: it was actually (historically) done the other way round. Search the internet for "determing Earths mass" if you are interested.

Earth's mass, using the figures I've used so far in the book, is: 5.956 × 1024 kg.

Note: NASA's figure for Earth's mass is: 5.9723 × 1024

That is because they use more precise figures (ie., more decimal points) for Earth's volume than I do in the book.

1024 is a lot, that number makes my eyes water considering that it is 5 billion (5 × 109) times bigger than the montrous quadrillion (1015) we talked about earlier.

Interestingly, 1015 kg is about the mass of your personal-horizon-volume.

Let me explain, but first we need to agree on units. We used cubic kilometers earlier because it was convenient and made the perspective a bit easier to understand. But kilometers are rarely used in science.

There are two often used "systems" in Science: the "cgs" and "mks" system. "cgs" stands for centimeters, grams, seconds; and "mks" stands for meters, kilograms, seconds.

So from now on, for the most part, we will use either grams and centimeters or kilograms and meters. Densities are, then, usally written as g/cm3 or kg/m3.

So let's take our test volumes from earlier and see how much they would weigh (on Earth) if they had an average Earth density of 5.515 g/cm3 - 5,515 kg/m3.

A ping pong ball's worth of "average" density Earth is 0.19 kg (almost 200 grams), akin to a stone or pebble.

A football's (Soccer) worth is 30.9 kg, akin to a large stone.

And your personal-volume's worth (the sphere based on your 1.67 m height) is 13,456.6 kg, akin to a boulder.

So now we will use your personal-horizon-volume based on your horizon distance of 4.6 km. Earlier we found this volume to be 407.7 km3. But km3 no more! This volume is equivalent to 4.077 × 1011 m3. And this volume's worth of average Earth is 2.25 × 1015 kg (2 quadrillion kg).

Now, just for fun, we'll do the same volumes but using air, which has a density, at sea level, of 1.22 kg/m3:

Ping Pong ball: 0.04 g

Football (the spherical one): 6.8 g

Your personal-volume: 3 kg

Your personal-horizon-volume: 5 × 1011 kg


 

Before we move on it would be nice to use some practical object to compare Earth with.

There are three astronmical objects that everyone knows: the Earth, the Sun (which we'll get to later), and the Moon. Let's use the Moon.

Some may argue that the Moon doesn't belong in the chapter on the Earth. But the Earth and Moon travel together around the Sun and through space. It's not just a technicality, they really are the same system, both revolving around each other.

The Moon is special. It is not the largest moon in the Solar System, Jupiter's Ganymede takes that honour. But it is the largest moon in relation to its host planet.

The Moon is also special in that it is spherical, like a ball. Many moons are not spherical. Sphericity of an astronomical object comes about when that object is massive enough to have a substantial gravity. Once this mass is achieved that object must be spherical because gravity won't let mountains, ridges and so on grow past a certain height. Gravity is strong enough to pull them inward, towards the center of the object.

On Earth, Mt. Everest is close to this limit where the rock is strong enough to support its own weight. Not too much taller and the rock, under the enormous pressure of the weight of itself, starts to become elastic and flows out at the base of the mountain. In this way, really massive objects must be spherical.

So the Moon is interesting because it is relatively large and massive enough to be ball-shaped. How does it compare with Earth?

The Moon's radius is 1,737 km.

Were we to center the Moon inside Earth, the Moon's surface would be 4,600 km below your feet.

Running the Moon's radius, one Marathon each day, would take 42 days (Earth's radius "Marathon" time is 151 days by comparison).


Earth Moon Comparison

Here is a depiction of the Earth and Moon sitting next to each other.

They are in (approximate) scale to each other and so show the relative sizes of each to each other.


Earth Moon comparison


 

The Moon's surface area is 3.79 × 107 km2, a bit bigger than the African continent.

It would take take about 13 and a half Moon surfaces (or Africa surfaces) to cover Earth's surface completely.

The Moon holds (Earth equivalent in parentheses):

109 Everest horizon-areas (1440)

6,434 Khufu horizon-areas (86,598)

569,925 you horizon-areas (7,670,256)


Everest horizon area on the Moon

Were you to build an Everest high observation tower on the Moon, this is the area of the Moon you could see, approximately.

You may want to compare this with the same area on Earth.


Everest area on the Moon


 

The Moon's volume is 2.2 × 1010 km3, it takes about 49 Moon volumes to equal Earth's volume.

The Moon's volume would hold, again Earth comparisons in parentheses:

138.7 Everest horizon-volumes (6,809)

64.695 Khufu horizon-volumes (3,175,938)

53,961,246 you-horizon-volumes (2.65 billion)

The Moon's average density is 3,344 kg/m3, notice this is quite a bit less than Earth's 5,515 kg/m3, the Moon is made of lighter materials overall. Still its mass is 7.35 × 1022 kg, about a hundredth of the Earth's mass.

The Moon orbits, on average, 384,400 km away from Earth. Running a Marathon a day it would take you 9,100 days (24 years, 11 months) to travel this distance. But this is extremely close by astronomical standards.


Earth, Moon, and Moon Distance to scale

Here you see, very approximately, the scale of the Earth and Moon and the distance between them. The line is marked off in kilometers.

Since I don't know how your browser will handle differing sized pictures, I put two here, you may need to scroll.

You can see a larger depiction here, depending on your browser you may need to click it to bring it to full size. The link will open in a new window.


Earth, Moon, Distance to scale


 

While we're here let's do one more characterization of the Earth-Moon system. The Earth and the Moon are literally companions moving through space and comprise a single system.

About 100 km over our heads is the "official" beginning of "outer space". The operative word here is "space". There is a lot of space.

For a quick idea of it let's consider the Earth-Moon system to be a bubble of space, a sphere, whose radius is the Earth-Moon average distance: 384,400,000 meters.

This makes an "Earth-Moon Volume" of 2.4 × 1026 m3.

The volume of the our total home system can hold over 218,000 Earth volumes or 10,800,000 Moon volumes.

Our local "home" volume is 99.9995% empty space. Were we looking at a silverware drawer with the same percentage we would say it is completely empty except for that sesame seed in the corner.

And yet Earth, our home, seems quite substantial, at least to us, in any case.

Oh, and before I forget. You may have noticed the big, burny thing, upper left corner of each page. That is, as you've probably guessed, the Sun.

The large black circle (with the 2/4 thingy next to it) is the planet Jupiter, in approximately the correct scale. The 2/4 thingy is the old alchemical/astrological symbol for Jupiter.

And the small dot above Jupiter (with the ⊕ symbol) is, in approximately correct scale, the Earth.


 

There. We've characterized and perspectivized (is that a word?) our first astronomical objects. We're ready to move on, but first I just wanted to mention that I'm keeping this chapter to a minimum and focusing on only the major properties of the planet. But Earth is fascinating and there is so much more to know and appreciate.

If you have the desire, and are not already familiar with these topics, I'd like to recommend some further directions to go in the library or internet.

The structure of the Earth is complex, the density we gave only an average, so maybe check out more about Earth's structure. Really cool is "plate tectonics". And don't forget to read up on the Atmosphere and the Oceans.

Oh, And it is only planet we know of with life, so you may also want to check out stuff about Biology. Quick, before arrogant humanity eliminates it.

Now, on to the Solar System.


 

 

 

Footnote 1: Mass and Weight.

The Universe is, at the simplest level, divided into two major regimes: matter and radiation/energy.

Radiation/energy is seemingly insubstantial: for example, light and heat. We talk much more about energy in later chapters.

Matter is the term for "stuff". Physical, real world stuff you can touch. Matter boils down to atoms of elements (more on those in later chapters) which combine in myriad ways to make up all the things around you. Including you.

A property of matter is that it has mass, that is it has substance, heft. And a volume. This, in all normal circumstances, can never be taken away. It will have this mass whether it is at the surface of the Earth, the surface of the Moon, or in deep outer space.

In all those locations it will "weigh" different amounts, weighing nothing in outer space, because weight depends on gravity.

Consider you yourself, for example. You are made of matter, therefore you have a mass. Were you to be transferred to the Moon you would weigh less, yes, but you haven't shrunken or evaporated, you are still 1.67 m tall and the substance of you, your mass, is still there with you. You weigh less on the Moon simply because your mass is just attracted less by the smaller gravity of the Moon.

A mass never changes (normally), while weight varies according to where the object is: Earth, Moon, outer space.

Return to where you were.

 

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