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 – – 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.


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.


A list of extreme geographic points in the USA – Wikipedia –

10 ways to wear a Moon Hat

Wear the Moon Hat – have fun!

The Moon Hat is no ordinary hat. 

The Moon Hat keeps your head warm – yes!  And, every day it gently reminds you to be curious about the Moon. It reminds you to observe what usually stays hidden. It reminds you to #doscienceeveryday.

There are many ways to wear a Moon Hat. You can wear the Moon Hat in at least 10 different ways. The Moon Hat is made of soft stretchy fleece with small embroidered Moon phase images placed all around the brim.

The Moon Hat fabric is flexible and foldable.

10 ways to wear the Moon Hat

  • Moon Finder – where is the Moon right now
  • Phase Reminder – what is the Moon phase right now
  • Hidden Moon outside – hide the moons outside
  • Hidden Moon inside – hide the moons inside
  • Tidal Shores no tag – longshoreman style
  • Tidal Shores show tag – longshoreman style
  • Moon Slouch – Moon Finder, pull the fleece backward
  • Moon Beret – Moon Finder, pull the fleece forward
  • Moon Disk – Hidden Moon inside, show one embroidered disk
  • Moon Peeker – Hidden Moon inside, peek one embroidered disk
  • Halfsies (Bonus #11) – Hide half the phases, wear the hat straight

#1 – The Moon Finder

The Moon Hat style The Moon Finder. This is the standard style for wearing the Moon hat. The phases are oriented in the correct way and you can face the Sun and find the Moon using the Moon Hat moon phase images.

The standard way to wear the Moon Hat with the new Moon image in front. This creates the model of the Moon, Earth, Sun relationship and helps you understand how the motions of the Moon create the phases that we see from Earth.

Get the current Moon phase. Put the hat on with the New Moon image on your forehead. Face the Sun. Now, all of the Moon phase images point to where the Moon is in the sky. Amazing!

#2 – The Phase Reminder

The Moon Hat style The Phase Reminder This is another standard style for wearing the Moon hat. The current phase is oriented to the front and you can face the Moon and find the Sun using the Moon Hat New Moon phase image.

This everyday style is for people who want to remind themselves of the phases of the Moon and how they change over the 29 and a half days of the cycle. Just choose a Moon phase and put it at the front.

This is a subtle way to keep track of the Moon phases and learn their sky location. Before you put on the hat, pause for a second and consider which phase to wear. And, it doesn’t feel like a Moon phase quiz – it’s fun to put your thinking cap on!

#3 – Hidden Moon outside

Man wearing the Moon Hat hiding all the embroidered images of the Moon Phases. Sometimes you just want to wear a cap.

Don’t want any Moon phases to show? Just fold up the brim toward the outside of the hat and all of the Moon phase images disappear.

Sometimes a hat is just a hat.

#4 – Hidden Moon inside

Moon phase images are all hidden by folding the brim of the Moon Hat inside the hat. It gives a slightly exotic look to the cap.

Another way to hide the Moon phase images… tuck the brim of the Moon Hat towards the inside. All the Moon phase embroidery is now hidden and you have a sleek cap.

Looking for a unique style? The Moon Hat is flexible.

#5 – Tidal Shores no tag

The Moon Hat style the Tidal Shore No Tag - the hat starts inside out and the brim is folded up to reveal the images. This is another standard style for wearing the Moon hat. The New Moon image is oriented to the front and you can face the Sun and find the Moon using the Moon Hat New Moon phase image.

This is the longshoreman style. Turn the Moon Hat inside out and then fold the brim outward. The brim should be wide enough to both show the Moon phase images and hide the instruction tag.

A close-fitting style that uncovers your ears.

#6 – Tidal Shores show tag

The Moon Hat style the Tidal Shore Show Tag - the hat starts inside out and the brim is folded up to reveal the images. This is outre style for wearing the Moon hat because the tag is showing. The Full Moon image is oriented to the front and you can face the Full Moon and find the Sun using the Moon Hat New Moon image.

Just like the Tidal Shores no tag, but the brim of the hat is folded thinly so that the tag is revealed. You can wear the tag on the side, or the back, or if you are feeling daring, on the front!

This style makes a strong statement – show off the instruction tag.

#7 – Moon Slouch

Man wearing the Moon Hat in slouch style. The hat is loosely bunched and then pulled backward to give a relaxed ring of Moon phase images that are carried above the ear.

This is the Moon Finder style, but pull the Moon Hat upwards to get some amount of fabric standing up away from your head and then pull it backward and flatten it for a sleek look

You can easily wear the Moon Hat pulled up above your ears.

#8 – Moon Beret

Man wearing the Moon Hat in beret style. The hat is loosely bunched and then pulled forward to give an intense ring of Moon phase images that are carried above the ear.

This is the Moon Finder style, but pull the Moon Hat upwards to get some amount of fabric standing up away from your head and then pull it forward and flatten it for an intense look.

Folding and bunching the fabric in the hat leads to a renaissance or jester look.

#9 – Moon Disk

A single Moon Phase image shows at the back of Man's head but hiding all the other phases.

The Moon Disk style starts with the Hidden Moon inside, but then you pull the embroidered disk of your favorite Moon phase and place it somewhere – it could be centered on your forehead or placed round the side of your head just behind the ear, or all the way at the back. It’s your choice.

This style lets you show an individual Moon image disk.

#10 – Moon Peeker

This is the same as the Moon Phase disk, but more discreet. Just a tiny Moon phase image disk peeks out from just in front of the right ear.

This style is the same as the Moon Disk, but pull the Moon phase under the fabric of the brim until it is just peeking out. This style looks particularly good when the disk is just in front of your left or right ear.

This look makes a sly statement.

#11 – Halfsies 

Half the Moon Hat brim is folded upwards to hide a set of embroidered moon phase images. Hat is adjusted to make it look symmetrical.

Fold down half the Moon Hat brim to hide 4 of the phases, then adjust, and angle the hat so that it looks like it is sitting flat on your head.

An alternative way of hanging your hat.

Go out and play with the Moon Hat

This is a fun and flexible bit of fabric with lots of science and a mountain of style potential. Hide and show the Moon phase images, fold and flex the fabric. Get outside and get curious about the Moon and its motion.

See Mercury and Venus orbits during the day

Your hands and arms help you see the orbits of Mercury and Venus and the shape of solar system

Question: If you could see the orbit of Venus would it fill the whole sky?

The answer might surprise you!

You can use your hands and arms to see the size of the orbits of the solar system’s inner planets: Mercury and Venus.

Imagine (as pictured below) if the orbit of Mercury were visible as a red oval and the orbit of Venus were visible in green.

Use your hands and elbows to see Mercury and Venus orbits any time of day or night. The orbits of Mercury and Venus can be seen.
Two hand spans show the orbit of Mercury, elbows show the orbit of Venus.

Physical Astronomy – see Mercury and Venus orbits

Caution! Do not look directly at the Sun without proper solar safety glasses on.

Turn toward the Sun, hold your arms out straight, hands up in the air with fingers spread wide and thumbs touching. Your pinky fingers now span the width of the orbit of Mercury and your elbows span the width of the orbit of Venus.

Both of the entire orbits of Mercury and Venus orbits would be visible in the sky all at once – if they could be made visible during the day.

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