Where you need to be to see the entire earth

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

15 October 2017

How far away from earth do you need to go in order to see the entire planet? To find the answer, we need to know the size of the field of view of a human being. That is, when looking straight ahead, how wide is the area that you can see?

Now, if you Googled the phrase “human field of view”, you will get nice diagrams showing the angle of view. It is about 110 degrees from side to side and 120 degrees from top to bottom. If you know some geometry, you can then use these numbers to calculate the relationship between the width of the visible zone (in metres) and the distance away.

However, some things are easier done experimentally instead of relying on Dr. Google! So this is what I did…

I stood in front of a wall and marked an “X” on a spot at eye level using a pencil. Then I took two pencils (one in each hand) and spread my arms out horizontally.

I then stood about one metre away from the wall looking at the “X” mark. In this position, I brought my arms in slowly towards the front until they both came into my field of view. Then I walked gently to the wall (with my eyes fixed on the “X”) until the two pencils touched the wall.

I made two more marks, one on the left, and the other on the right. Then I measured the distance between these two new marks and also that from the wall to my eyes. The result was that my eyes were 30cm (about one foot) from the “X” and the two marks were 160cm apart.

The field of view is the ratio of the visible width to the distance away; that is 160:30, or 160/30 = 5.3. In other words, when I am one unit of distance away, I see a field that is 5.3 units wide (horizontally).

I repeated the experiment for the vertical field of view and found that, when my eyes are 40cm from the wall, the two pencil marks are 120cm apart (top to bottom). The vertical field of view comes to 120/40 = 3.

Clearly then, the vertical field of view is smaller than the horizontal one. If I need to see the entire earth, I must go far enough for it to fit in my vertical field of view. The ratio of height to distance is 3; therefore, since the “height” of the earth is 12,700km (its polar diameter diameter), then I need to be about 12,700 x 3 = 38,100km away.

It turns out, then, that astronauts at the International Space Station cannot see the entire earth. At just 400km above the earth’s surface (13,200km from the centre of the planet) they are too close. But if some one went to a Geostationary Communications Satellite, 42,000km from earth, they would be able to see the planet in full.

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**NB: There's a fundamental error in the above calculation. A correction is available in the article of 22nd October 2017.