Countries in the Sky

A spot on Earth is a spot in the sky.

Every “spot” on Earth has a corresponding “spot” in the sky. For instance, on the spot where you are now, directly overhead, is the zenith. There is only one zenith where you stand. No two spots share the same zenith. Every spot on a sphere “points to” a different location in the sky. Nobody shares your zenith.

Your Zenith is Unique

Imagine the boundary of your country as a set of these spots. These locations can be projected onto the celestial sphere. Projecting shapes of countries onto the sky can help you really “see” how large or small a country is. Seeing countries from the inside out helps to understand the shape of the Earth as a sphere.

That Star is Someone’s “First Star I See Tonight.”

When you see a star rising you are actually seeing a star that someone 6 timezones east of you sees directly overhead.

Sirius rises just before dawn (heliacal rising) in mid August (at latitude 40˚N). It rises earliers and earlier each day until by November it is rising at midnight. When people on the east coast of the USA see Sirius rising, people in Western Europe see the same star Sirius high in the sky at the meridian.

How Fast is the Earth Moving? – A Quiz

A family views the visible orbit path of the earth.
A family views the visible orbit path of the earth.

“How fast?” means “What is our velocity?” Velocity is a speed combined with a direction. We can figure out our speed and our direction on the Earth by looking at these 6 motions and directions…

But, before you read these, try to think of the 6 different motions that the Earth has.

Just putting some space in here to give you time to think about the Quiz.

_________________________________________________

The answer:

  1. Rotation of Earth (cycle) – 0.5 km/sec
  2. Orbit around Sun (cycle) – 30 km/sec
  3. Solar System through Galaxy (cycle) – 200 km/sec
  4. Milky Way Galaxy moving toward Andromeda within the Local Group (non-cyclical toward Andromeda)- 109 km/sec
  5. Local Group motion inside Virgo Supercluster (non-cyclical toward “overdense” regions) – 300 km/sec
  6. Cosmic Void repulsion (non-cyclical) – 600 km/sec

Earth’s Overall motion = 368 km/sec +/- 30 km/sec depending on season

Our overall direction of motion? The Cosmic Microwave Background (CMB) tells us generally which direction we are moving in: towards the “overdense” regions of the Cosmic Void.

References

Thanks for Ethan Seigel for gathering all the relevant data points for this quiz.

https://www.forbes.com/sites/startswithabang/2017/06/16/how-does-earth-move-through-space-now-we-know-on-every-scale/#4a1dd5d4861f

Super Simple Earth Model

Super Simple Earth Model

Physical Astronomy by Daniel Cummings

Stand outside on a sunny day or in a room with only one light. If you are inside the light should be at eye level when you are standing up. This will be your Sun.

Stand up, make sure there is space around you – things might get messy if you start spinning like the earth and there are things to bump into.

Turn to the left and begin a slow leftward spin. This is the direction that the Earth rotates (as “seen” from above the north pole).

Your head is like the earth. Your eyes are like two different people on the surface of the earth. They are looking straight out from the earth toward the sun.

As you spin in your leftward rotation, wink your left eye shut. Observe how your left eye can see the light before your right eye. This is like the east and west coasts of the USA. The east coast is a few hours ahead. Observe how when you continue to spin and your eyes turn away from the light source it is like night.

Spin a few times more to feel yourself as the Earth model. 29-31 spins makes a month. 365 spins makes a year. Multiply your age in years by 400 and that’s about how many days you’ve been riding on the earth – give or take a few hundred.

Galaxy Horizon – 4/20 at Midnight

On April 20th (4/20) at midnight Earth’s horizon (in northern latitudes) lines up perfectly with the plane of the entire Milky Way galaxy. The galaxy “wraps around” our view of the sky and we can see into and through the plane of the galaxy.

Starinastar.com galaxy horizon visualization. Shows the galaxy plane lined up with the local horizon at midnight on April 20th. This happens every year.
The Milky Way galaxy lines up perfectly with your local horizon view on April 20th (4/20) at midnight each year.

At this moment when you look out around you at the horizon, you are looking into the plane of the Milky Way galaxy.

How to See the Milky Way Galaxy Plane

Look southward (and a little bit east) and you are looking toward the center of the galaxy. Look northward (and a little bit west) and you are looking toward the outer edges of the galaxy.

Why does the galaxy line up with the horizon?

Each year on 4/20 the galaxy lines up with the horizon – an “event” I call the Galaxy Horizon. In fact, this “event” occurs every day! It’s just an interesting coincidence that the alignment happens on 4/20 at midnight. Each day the galaxy lines up again with the horizon but it happens 4 minutes earlier.

Earth Map in the Sky

Earth Map in the Sky – Landforms as Constellations

Learn how to see the map of Earth in the starry sky.

Stars help us find our way. Stars are like a giant map in the sky that tells us where we are on the surface of the Earth. Sailors use them as a “map” to navigate the world. For thousands of years, the stars were stationary markers of latitude and longitude.

We are going to learn to map something new onto the sky: locations on the Earth! We can create an exciting new set of “constellations” out of the shapes of the continents on the Earth.

We live on a sphere so we can see half of the sky (a hemisphere) at any one moment. It’s easy to imagine half the Earth mapped onto half the sky. Keep reading to learn how.

A new way to experience life on a sphere. It’s an Earth map projected onto the starry sky. Image created by: Daniel Cummings

Zenith Stars

Wherever you are on the Earth, when you look straight up (toward your zenith), you might see one star, but there are a bunch of other stars within view. All of the stars you see in the sky are directly overhead some other place on the Earth. Every place on Earth has their own set of stars directly overhead – their “zenith stars.”

Look up at any star in the night sky; that star is directly over some place on Earth. There are hundreds of “faraway zeniths” up there.

World Zeniths – See the Map of the Earth in the Sky

Every star maps to a location on Earth and every location on Earth maps to a star.

If you live in the western hemisphere, you can learn to look up and “see” the land borders of the North American and South American continents visible, projected into the sky like a giant painting on a curved ceiling. You can learn to see even more landforms in the sky – you can learn to see the entire western half of the Earth projected in the sky.

Visualize Countries in the Sky

We can learn to see country outlines in the sky. The key is to imagine yourself at the center of the Earth looking out into space “through” a translucent Earth surface.

Here is a good way to visualize these countries-in-the-sky even when you are on the surface. Imagine that you can look up and see your location at the zenith.

When I do this, I see southern New York state, Long Island jutting out into the water like a long pier, and the wide Hudson River emptying past New York City. Eastward is the dark expanse of the Atlantic Ocean and low on the eastern horizon are the countries of Europe and West Africa.

Westward in the sky, I can see the outline of the west coast of the US. Then, there is a big blank space of the Pacific Ocean and a spot near the western horizon that is Hawaii.

The Map of the Earth in the Sky is Reversed

Map of Earth landforms as they map to the starry sky. Map is reversed because it is projected into the sky. The places named at the cardinal directions (N, E, S, W) are the locations where New York horizon stars are zenith stars. Image created by: Daniel Cummings

There is one odd thing about the map as you see it in the sky… it’s reversed – as if seen in a mirror! This happens because we project the map lines outward into space toward the stars. When we look at the map this way it’s as if we are “inside” the Earth looking outward.

The map of the USA covers about 58˚ of sky from east-to-west. 58˚ is about 2x pinky-to-thumb (spread out all your fingers of both hands and touch thumbs). Your left pinky tip should be on your zenith. If you are in New York or somewhere on the east coast, the right pinky tip will indicate the approximate western edge of the USA.

Physical Astronomy – Stars Map to Places on Earth

Physical Astronomy Activity Instructions to learn to see the Map of the Earth in the Sky. Faraway Zenith stars help us visualize what it is like to live on the surface of a sphere. Image created by: Daniel Cummings

Learn to see the zenith map in your sky using this Physical Astronomy technique.

Exercise 1: face south and point high in the sky.

Face south. Then, reach both hands straight up over your head and point above your head with both pointer fingers. You are pointing at your zenith. Now, bring both arms down until they are pointing one due east and one due west. You are pointing at two points in the sky that are zeniths for someone else.

When I do this exercise in New York, my left hand (the eastern) points at a spot in the starry sky that is the zenith star for someone in the country of Nigeria in West Africa. This is a location on the globe that is 6 time zones east. My right hand (the western) points at a spot in the sky that is the zenith for someone in the island state of Hawaii in the middle of the Pacific Ocean. This location is 6 time zones west of New York.

So, when I look at the eastern horizon sky I am looking at the starry sky that is already directly above a place 6 time zones ahead of me. I am looking at someone else’s zenith stars.

Exercise 2: Repeat exercise 1. But this time, face east.

Face east, point up. Now, bring your arms down and point toward the north and the south directions. This time your right hand points south and your left hand points north. Your right hand points at a spot in the sky that is over the city of Cuzco, Peru (the closest city to Machu Pichu) and your left hand points to sky that is over Yekaterinburg, Russia – the 4th largest city in Russia.

Secret! You Can See a Star That Another Person Can’t

If you do this physical astronomy exercise right after sunset, the eastern and southern zenith locations are in night, but the western and northern sky points are over Earth locations that still have daytime.

This means that you can see the star that is at their zenith, but they cannot see that star. For example, Seattle still has 3 hours of sunlight left in their day so stars are invisible behind blue sky. The city of Yekaterinburg is on the opposite side of the world and just after sunset in New York it faces the Sun and has a bright daytime sky!

We are on the night time side of the Earth and we can see the current zenith stars of Seattle and Yekaterinburg – but people who live in these cities cannot see them! They have to wait to rotate to the night time side of the Earth to see stars.

The Math – How High Up is the Zenith Map?

Guy Ottewell’s illustration from Astronomical Companion (page 8). This schematic shows how we experience the celestial sphere – the array of stars in the sky. It shows zenith, cardinal direction points, the meridian, the celestial equator, the ecliptic, and the viewer – you, in England – sitting on the globe at latitude 40˚ north, looking up at the sky. Credit: © 2016 Guy Ottewell – UniversalWorkshop.com – used with permission.

Project an imaginary map of the Earth into the sky. The map has to be the correct size so that when it is viewed from a distance it “covers” the same distances.

If a map is too close, it is just the same size as the territory. So, we have to choose the correct distance to project the zeniths. As the zenith map “projector screen” moves away from the Earth we see more of the borders of the Earth. But, at some point the distance of the map corresponds exactly to the faraway zeniths.

Our question is: “How far away from the Earth do you have to be so the landforms (like the continents) have an angular diameter that is equivalent to their “actual size” in the sky?” How far away does our imaginary zenith map USA (about 3000 miles wide) image have to be to cover 58 degrees of arc in the sky?

To answer this we need math.

The Zenith Map Distance from Earth

Earth map showing close up of Algol passing over New York City while Gorgonea Tertia approaches Washington DC. Almach is the Zenith Star somewhere near Chicago, IL. The Earth’s rotational speed at this latitude makes the stars appear to travel a little bit faster than the speed of sound. They will be Zenith Stars for a location about 800 miles west in 1 hour. Image created by: Daniel Cummings

The Earth is approximately 24,901 miles in circumference at the equator. If we can see half the sky from any point on the Earth, then we can “see” half the Earth projected onto the sky by the zenith map. That means that for 180˚ of sky we can “see” about 12,450 miles of the Earth’s surface projected into space. 12,450/180 = 69 miles. When 1 degree of arc spans 69 equatorial miles the image is “at” the correct distance.

1 Degree of Sky equals 69 Miles

So, at the equator every degree of sky covers about 69 miles in every direction. As you go towards the poles the longitude degrees (east and west) cover less and less zenith map distance, but the latitude degrees (north and south) always stretch 69 miles. Every 15˚ of sky equals about 1035 (69*15) miles.

The distance between your pointer finger and your pinky (when you hold your arm and hand stretched out in front of you) is 15˚ – so you are measuring about 1035 miles on Earth with that sky measurement. One pinky width is equal to 1˚, which is 69 miles of zenith map!

The Math – Inverse Tangent and Angular Diameter

There is a simple calculation that helps us determine how far away something needs to be to fill just 1˚ of the sky. Here we use just a tiny drop of trigonometry to discover the “tangent of 1 degree.”

The tangent of 1˚ is 0.017455. The inverse of something is when you divide 1 by the number you want to invert. So, the inverse of 0.017455 (1/0.017455) is 57.29. The inverse of the tangent of 1˚ helps us figure out the distance something has to be to appear to be 1 degree angular diameter.

This page explains how to calculate distance from a known angular size. “When an object’s distance is 57.29 times its size, it has an angular size of 1 degree.”

So, 57.29 * 69 miles = 3,953 miles away! This is how far away the “map” has to be to show you your hemisphere of the Earth map. 3,953 miles is higher than low Earth orbit (LEO) satellites (lower than 1200 miles); it’s closer than geosynchronous satellites (at about 23,000 miles); and it’s about 1/60 the way to the Moon.

So, imagine that the Earth map is projected onto a screen – an imaginary celestial sphere, shell-shaped – that is quite close to the Earth and encircles us. It shows us our Earthen landforms and the oceans beside, superimposed in the sky.

Summary

We live on a sphere. When we look at out night sky we are able to see stars low on our horizon that are visible directly above someone else – one-quarter the way around the around the world in all directions.

If you live within 6 time zones of someone that means that you share some “simultaneous sky.” Anyone living further than 6 time zones away sees a completely different sky – unless you can see circumpolar stars that dip under the North Star. That means that you can see countries past the North Pole and down the other side of the globe.

Your zenith is yours – it is unique and changing all the time. Not even someone standing right beside you shares your zenith. You can use this idea of the zenith stars to comprehend the vast and mysterious experience of life on a sphere.

References

A list of extreme geographic points in the USA – Wikipedia – https://en.wikipedia.org/wiki/List_of_extreme_points_of_the_United_States

Feel the Earth spin

Many people ask “Why can’t I feel the Earth spinning?” Or “Why don’t we feel the rotation of the Earth?”  The answer is that the Earth is so large and we are so small in comparison that we just get carried along for the ride. 

We humans are tiny so we don’t notice that everything on Earth moves along with us. Until we look up and we see the Sun speeding through the sky – then the questions start to fly: “Why does the Sun move across the sky?”, “How big is the Earth?”, “How fast is the Earth spinning?”

If the Earth is spinning why can't I feel it? The Earth is Gigantic. Humans are tiny.
Q: If the Earth is spinning why can’t we feel it? A: The Earth is gigantic and we are tiny.

It’s hard to imagine just how large the Earth is and just how fast it is carrying us around in its daily motion. How fast is the earth spinning?

You are about to learn the answer and learn how to experience this speed!

We are too small to see the illusion

The Earth spins at about 1000 mph (1609 kph) at the equator. But we can’t feel it. This illusion of non-motion happens for several reasons:

  1. Because the Earth is enormous compared to us, and
  2. Everything around us moves in the same direction and speed, and 
  3. Our inner ear is not sensitive enough to feel the gradual changes in momentum caused by Earth’s constant turning.

Imagine riding in a fast car that has no windows. The car cruises on a smooth highway at 100 kph (62 mph). Inside the car we chat with our friends, the seats are comfortable, and maybe a hot drink sits placid in a cup holder. We don’t feel the motion at all unless the car turns or speeds up or slows down.

Everything seems to be staying still but this stillness is an illusion. All of this stuff in the car is moving along with us at the same speed. But, if you could open a window in the car you would see the motion of the other objects not in the car.

The sky is our open window to find those other objects that are not “on the Earth.” We will use them to explore the Earth’s speed and movement.

Motion senses don’t feel the motion

Another reason that we can’t feel the Earth spinning is because our sense of balance. We get this sense from organs of the inner ear. We know what it feels like to move. We can feel a car accelerate and turn – but these sense organs don’t help us feel the Earth’s changes in speed and constant turning.

It’s easy to feel and then believe that the Earth stays still and everything else moves around us; the Earth doesn’t seem to be moving. The idea of a moving Earth seems preposterous. It’s no wonder it took humans so long to figure out that the Earth is spinning and moving!

However, you can learn a surprising way to feel the rotation of the Earth – and it has to do with the speed of sound. You can “feel the Earth spin under your feet” and all it takes is a little bit of imagination.

Speed of sound is the speed of day

The speed of sound in air is 1235 kph (767 mph). This is really fast, but it is still a visible and imaginable speed. 

The speed of the Earth’s rotation at the equator is faster than the speed of sound! But, because of the Earth’s shape, the Earth’s rotation speed is exactly equal to the speed of sound at two latitudes on the Earth: 42.97 North and 42.97 South.

What does this mean for you and your approach to physical astronomy? You have to train your brain to see the speed of sound, then you will be able to feel the Earth spinning. You will understand that the speed of sound is the speed of day.

7 ways to see the speed of sound

We can train our brains to “see” the speed of the Earth’s rotation (I’ve named this speed the “Speed of Day“). This is possible because “the speed of sound = the speed of Earth spinning.” 

Lightning and thunder can help you see the speed of sound.
You see lightning before you hear thunder because of the speed of sound. Credit: FreePhotos
  1. The fastest plane you’ve ever seen is traveling a bit slower than the speed of sound. Imagine the fastest jet plane you have ever seen. Unless you were watching a fighter jet, that jet was not going at the speed of sound. Commercial jet planes travel about 250-350 mph below the speed of sound.
  2. Echoes, echoes, echoes… The speed of sound can be heard and easily visualized by exploring sound echoes that bounce off walls, fences, hillsides, and other objects.
  3. Large fields. Go to a large field (as big as a football field or bigger) with a friend and ask them to clap. You will see your friend’s hands clapping and then hear the clap.
  4. Stadium concerts. You can experience the speed of sound at big stadium concerts where you can see the drummer hit the drums but the sound is not in synch with what you see.
  5. Lightning and Thunder. You can feel the speed of sound when you see the flash of distant lightning and you don’t hear the boom of thunder for several seconds. Every 5 seconds is about 1 mile.
  6. Fireworks. You can witness the speed of sound when you are watching fireworks and you hear the bang of the explosion after you see the light of the explosion.
  7. Videos. Finally, there are several good videos online that can help you visualize the speed of sound (links below – includes a clever piece from the Exploratorium in San Francisco).

The speed of rotation of the Earth

How fast is the Earth spinning? Once you have a clear idea of how fast sound goes, you can get a clear idea of how fast the Earth is spinning – and by experiencing this speed you can easily imagine just how incredibly large the Earth is.

A gigantic bell rings, “Races the day”

The Earth's surface spins at the speed of sound at 43 north and 43 south latitude.
Bell, Sun, Mountain – the speed of sound is the speed of day. Credit: vasocardin

One way of visualizing the speed of the Earth’s rotation is to imagine that a gigantic bell rings each time the Sun enters a new time zone. Imagine that there is no sound loss over distance and the sound of that bell can be heard across the whole time zone (up to 1000 miles).

When this bell rings, the sound takes time to travel. It will travel at the speed of sound: 767 miles per hour.

Sound = 767 miles / hour

Bangor, ME and Detroit, MI – two American cities on opposite ends of the eastern US timezone – are 1183 km (735 miles) apart. The sound of our imaginary bell takes about 1 hour to travel between these cities.

Earth surface = 767 miles / hour

Since these cities are near 42.97 N latitude, the Earth takes about 1 hour to spin underneath the Sun.

Wonder why we can't feel the Earth spinning? The Earth is huge and humans are tiny. The Earth's surface spins at different rates depending on what latitude you are living at.
Why can’t we feel the Earth spinning when it is moving faster than the speed of sound?

Sound, which seems quite fast, is actually slow enough to “see” it moving. Once you can see the speed of sound you have seen the speed of the surface of the Earth.

Summary

The Earth rotates once per day. People at the equator are moving at faster than the speed of sound, people near the poles are moving slower than the speed of sound. People living at latitude 42.97 N and 42.97 S are moving at exactly the speed of sound.

References

Editor’s Note: Credit goes to Bob Berman (aka SkyManBob) for first pointing out the latitude/speed of sound correspondence to me. I first learned about this idea in his fantastically engaging book Zoom – How Everything Moves. It has a footnote in Chapter 5 that says people at Coney Island are moving at 795 mph – just over the speed of sound. It got me wondering… how can people experience this speed? The result is this article. Thanks, Bob! 

Editor’s Note: Another Bob (aka AstroBob) gets credit for helping me refine this article with insights about our common perception of motion.

List of cities at 43˚N latitude.

Calculations showing speed of rotation at different latitudes on the surface of the Earth.

Video showing how to use your video camera to measure the speed of sound – good science fair project!

Video by the Exploratorium visualizing the speed of sound in a very creative way – Clapping Speed of Sound.

A visualization of the Earth’s surface rotation speed at each latitude.

A general audience article discussing how we experience the motion of the Earth.

GPS uses Quasars

GPS uses Quasars to work

GPS uses quasars to get its own position
GPS satellite in low Earth orbit. Credit: NASA artist’s impression
The Global Positioning System (GPS) is precise.

That precision originates in a mind-blowing place!

GPS signals tell billions of people where they are each day.

GPS helps pilots land planes and captains steer ships.

GPS signals stamp locations onto millions of photos.

GPS gives you driving directions.

But, where does GPS get its own GPS?

The GPS for GPS

How does GPS know where a GPS satellite is?Click here to continue reading…

Merry-Go-Round Earth shows Seasonal Constellations

The Earth is like a Merry-Go-Round

Merry-Go-Round Earth model demonstrating how the seasonal constellations work
A Merry-Go-Round is a good model of daily Earth rotation.

The Earth is like a merry-go-round showing us seasonal constellations

That iconic childhood ride. Round and round each day we go, round and round each year we go, where we stop nobody knows! When we look out from the edge of the ride we can see the space beyond. Sometimes the Sun occupies that space, and sometimes that space is the night sky filled with stars.Click here to continue reading…

Walk to Mintaka

Physical Astronomy by Daniel Cummings

Mistakable rises toward the zenith as you walk toward the equator
As you walk toward the equator, Mintaka appears to rise higher in the sky.

In this post we will learn how to use one bright star of Orion’s belt to visualize the Earth’s equator.

Mintaka is a Star in Orion’s Belt

When you look up at the winter sky in the northern hemisphere, Orion and his famous belt are impossible to miss. The belt is made up of three stars of equal brightness.

One of these stars is called Mintaka and it is a guidepost for finding the Earth’s equator in space. Click here to continue reading…

Tilt Head to Tilt Earth – Seasons are caused by a tilted Earth

Physical Astronomy by Daniel CummingsTilt your head to tilt the earth and experi nice the seasons

Seasons are caused by a tilted Earth

Use this technique to understand how seasons happen on the Earth. The Earth is tilted. When the northern part (your forehead and eyes) tilts away from the Sun the season is winter. When the northern part tilts toward the Sun the season is summer.

The Earth is tilted as it spins daily – it is not straight up and down like a top, but more like the Leaning Tower of Pisa (if the tower could spin!). As it goes through its yearly orbit, the Sun hits the northern and then the southern parts of the Earth.

Tilt your head to tilt the Earth

In this model, when the northern part (your forehead and eyes) tilts away from the Sun the season is winter. When the northern part tilts toward the Sun the season is summer.

Did you like this season model? Any questions? Type in the comments to send me a message.