How far away from the earth do we have to be to know that the earth is round, and how far away can we see the entire earth?

This is a question that many netizens are confused about. Some even think that the earth is flat when viewed from the ground. Even if the earth is round, water should be flat, right? Because the so-called "level" of an object requires it to be flat, right?

First of all, let me reiterate that the earth is round.

In fact, the earth is round, not only the land is round, but also the water, which is the result of gravity. Because the mass of the planet is large enough, the gravity is enough to overcome the rigid body force of the object and achieve hydrostatic equilibrium. What is hydrostatic equilibrium? In layman's terms, it makes the object become a spherical shape.

It has long been common knowledge that the earth is round, and it seems indisputable. But there are some people who insist that the earth is flat. A group of people in a certain country even set up an organization to prove their "truth". To this end, they are collecting donations everywhere and want to build a rocket to fly to the sky, so that they can see it for themselves. They just don't believe what modern science has already proven, and think that scientists all over the world are liars.

But they have been raising money for more than ten years, but they still haven't raised enough money for a plane ticket around the world. Because almost everyone looks at these people strangely, as if they are seeing a group of monsters.

But this world is so strange. There are many things that have long been proven by science, but some people just don’t believe them. They also make wild assumptions based on their imaginations, thinking that scientists have the same brains as them. How could they come up with such unexpected high technologies?

If you don't believe it, we can see it in the comments section of various popular science articles, and there are quite a few such people. Although these people have already believed that the earth is round, their cognition is just a little different from those who don't believe that the earth is round. They often get entangled in some scientific common sense that has long become a consensus, chattering endlessly and denigrating it at will.

Now let’s get back to the topic and talk about how far away you need to be to know that the earth is round and how far away you need to be to see the entire earth.

Evidence that the Earth is round surrounds us

If I tell you that you don’t need to go far to know that the earth is round, just by standing on the earth, would you believe it?

None of us need to leave the Earth to feel that the Earth is round. You stand on a plain and can see the wilderness or grassland in front of you, but how far can you see? If the Earth is flat, theoretically you can see the end of the world, of course, provided that the world has an end.

Even though distant objects cannot be seen clearly, they can be seen with a large telescope. Has anyone seen it? No.

This is because the earth is a sphere. The ground beneath our feet is not flat, but arc-shaped. The ground in the distance bends and falls below our sight, so all we can see is the horizon.

What is the horizon? It is the range of the curved surface that you can see at a certain height on a sphere. The radius of the earth is about 6371km (kilometers or kilometers), so we assume that the earth is a perfect sphere (in fact, it is not, the equatorial radius is slightly larger than the polar radius), and the curvature of the earth is about 1/6370.

This is the degree of curvature of the earth, which is especially important for aviation. When an aircraft flies parallel to the ground, the change in curvature must be taken into account, especially when flying at low altitudes. If the curvature is not taken into account, it will crash into the ground.

It is because the earth is round that we can see farther from the top.

Anyone who has climbed a mountain or taken a plane has had this experience: the higher you go, the farther you can see. When sailing on the high seas, far away from the coast, the waves on the sea are endless. When we look around, we feel like we are in the center of a big disk. As far as we can see, the sea and the sky are one color. Where the sky and the sea meet is the horizon, which is the farthest point of the curvature of the earth that we can see from that height.

When we see a ship approaching us in the distance, we always see the smoke from the mast or chimney first, and then we can see the hull. This is because the earth is round, the water surface is also round, and the ship in the distance slowly rises from the horizon of people's vision.

This is why we can know that the earth is round without leaving the surface of the earth. But if we want to see the arc of the earth more intuitively and see that our world is a beautiful blue planet, we have to go to a higher place.

Relationship between altitude and visual distance

For a perfect sphere, how far you can see is proportional to the height of observation. So how far can you see on Earth? Based on the principle of the above figure and combined with geometric knowledge, we can easily derive the following formula:

d^2=（R+h）^2-h^2

Here, d represents the visible distance; r is the radius of the earth, which is 6371km; and h is the height of the observer. Based on this formula, we can easily calculate how far the earth's curved surface is seen at different altitudes. For example, on a 1,000-meter mountaintop, we can see a range of about 113km; if we fly at an altitude of 10,000 meters, we can see a range of about 341km.

From the International Space Station, at an altitude of 400km above the Earth's surface, you can see a range of about 2292km. This is only the range that the human eye can see. Unlike a camera, the human eye has a wider viewing angle than a lens and can scan in all directions like a video recorder. The human eye has a 120-degree viewing angle, so people can fully see the entire Earth at an altitude of 1000km.

We have experienced this when taking photos: the entire landscape or a building that the human eye can see may not be fully framed by the camera's viewfinder. At an altitude of 1,000 kilometers, except for stitching together multiple photos, the camera cannot fit the entire earth into a single frame. It takes an altitude of 12,000 kilometers to capture the entire earth.

Of course, whether it is direct observation by humans or photos taken with cameras, the so-called "full picture" is only the half of the earth facing the observer, and it is always only close to half.

Because the earth is spherical, and objects are at an angle when viewed from the front, theoretically, to see 50% of the earth's hemisphere, you have to be infinitely far away. But humans can never achieve infinite distance, so the half of the earth's spherical surface that is photographed can only be infinitely close to 50% of the entire spherical surface, and can never reach the true 50%.

Just like when a satellite or spacecraft photographs the Earth, at an altitude of 36,000 kilometers, the entire shape of the Earth can be photographed, but only about 45% of the Earth's total surface area can be seen; from the moon, 384,000 kilometers away from the Earth, only 49.5% of the Earth's total surface area can be photographed. The farther away from the Earth, the closer the round surface seen is to 50% of the total area.

Well, this is the answer to how far away you can see that the earth is round. What do you think? Welcome to discuss, thank you for reading.

The copyright of Space-Time Communication is original. Infringement and plagiarism are unethical behavior. Please understand and cooperate.