“I am close the the Moon but not as close as I can be.” This Astronomy Koan invites the reader to consider all of the ways which an Earth-bound observer might get as close to the Moon as humanly possible – without leaving the surface of the Earth.
The Earth and Moon are moving, I am moving
The Moon and the Earth are two oblate spheroids interacting in complex ways.
The Earth-bound observer is able to move around on the surface of the Earth while we calculate the “closest” point of the Moon to be the surface point that is closest to a surface point on Earth.
The goal of the Earth-bound observer is to find the location and time where they will be physically closest to the Moon.
Motions of the Moon that bring the Moon closer and further to your “closest personal point”
Daily apparent revolution – every 24h 50m wherever we are on the Earth surface, the Moon transits (crosses the meridian) and reaches the “closest personal point” at that time.
The apsides of the Moon’s orbit – the Moon’s orbit is slightly elliptical and has an apogee (furthest point from Earth) and a perigee (closest point to Earth). If a perigee coincides with a Moon transit, this brings the Moon even closer to the surface of the Earth. Approximately 357000km (perigee) and 406000km (apogee)
The inclined orbital track of the Moon. Close to the ecliptic, but an additional 5 degrees offset, this gives the Moon an opportunity to be closest to people located on the surface of the Earth who are slightly north (up to 5.14 degrees) of the Tropic of Cancer and south of the Tropic of Capricorn.
The Moon’s orbit is slowly moving away from the Earth (by 3.8cm per year, about 38km in 1million years) – so the longer you wait, the further away it will be!
Surface of the Moon orientation toward my location – East-west libration moves the “orientation” of the Moon as it relates to the Earth
The surface of the Moon has crater walls and valleys. The closest point would be at the height of a crater wall or central peak. Hipparchus crater or Triesnecker crater seem like likely candidates because they are “central”, but this is beyond my understanding of the topology of the Moon surface and how it might interact with the orientation changes caused by libration, nutation, and the inclined orbit.
My motions on the Earth that can get me closer to the Moon
The transit can be made closer by moving closer on the surface of the Earth to the current declination of the Moon. Generally speaking, that involves going toward the equator, but it get complicated by the fact that the orbit is inclined to the equator and ecliptic.
The transit can be made closer by going to a higher elevation
The transit can be made closer by going to the top of a mountain close to the equator (Mt. Chimborazo as opposed to a tall mountain like Everest that is not near the Equator)
The “ideal” situation that would bring a human on the surface of the Earth as close as can be to the Moon would be
Stand at the top of Mt. Chimborazo, at the moment of Moon transit, at the exact orbital perigee, with Hipparchus crater wall oriented toward Mt. Chimborazo, as soon as possible!
We looked at all of the ways that the Earth and Moon approach and recede from each other. The goal is to understand more directly when I am close to the Moon and observe the motions that change that distance.
Please let me know if I have missed anything here! Add in comments below.
NASA Moon page: https://svs.gsfc.nasa.gov/5048 – has “an animated diagram of the subsolar and sub-Earth points for 2023” Indicates the general sweep of the “closest Moon-Earth point” as it traces out irregular shapes on the surface of the Moon.
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 earlier 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.
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.
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.
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 – 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.
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
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
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.
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?
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
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.
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.
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?”
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:
Because the Earth is enormous compared to us, and
Everything around us moves in the same direction and speed, and
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.”
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.
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.
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.
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.
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.
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.
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”
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.
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.
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.
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.
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…