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# How high above the equator does one have to be to see both of the poles?

Question #58240. Asked by Arpeggionist. (Jul 10 05 1:03 AM)

gmackematix

I presume you mean seeing both poles directly at the same time.

If planes tangential to (just touching) the North and South Poles are parallel then surely it is impossible to view both poles from anywhere at the same time. They won't be exactly parallel but I imagine that the angle between them is so slight it will be light years into space before the planes meet and both poles can be seen at once.

 Jul 10 05, 6:07 AM

As the poles are (theoretically) exactly opposite eachother on the globe, any tangents drawn from them would of neccessity be parallel in at least one axis. As parallel lines never converge, you cannot be positioned so as to see both poles at the same time without visual aid, i.e. mirrors or cameras.
The one theoretical exception would be if your eyes were more than 12,714km apart. It would then be a function the ratio between the earth's polar diameter and your visual parallax.

 Jul 12 05, 7:47 AM
Arpeggionist

So then, how come half of the Earth is exposed to sunlight?

 Jul 12 05, 3:34 PM

Because the sun's diameter is greater than that of the earth (very much greater). If I hold a card vertically between my eyes, I can see both sides of the card at the same time. This is because the distance between my eyes is greater than the thickness of the card. Likewise the sun and the earth.

 Jul 13 05, 6:24 AM
Arpeggionist

And there's no distance from the earth at which the distance between a person's eyes could give that person a direct line of vision at both sides of a sphere?

 Jul 13 05, 12:33 PM
gtho4

The south pole is not at sea level, so there must be a point where both poles are visible. Is there an actuary in the house, who can finish this calc?

The circumference of the earth at the equator is 24,901.55 miles (40,075.16 kilometers). But, if you measure the earth through the poles the circumference is a bit shorter - 24,859.82 miles (40,008 km). This the earth is a tad wider than it is tall, giving it a slight bulge at the equator. This shape is known as an ellipsoid or more properly, geoid (earth-like).

The south pole has an elevation of 9,301 feet, and the north pole has an elevation of zero.
http://www.joanmyers.com/Jnlinset.htm">http://www.joanmyers.com/Jnlinset.htm

The apparent horizon at the south pole is 129.8 miles away.
http://www.boatsafe.com/tools/horizon.htm">http://www.boatsafe.com/tools/horizon.htm

 Jul 13 05, 5:49 PM
someothername

In three dimensions, infinitesimal points require an infinity of distance to almost touch. In a wonky two dimensional oblate spheroid it depends on the topology. Pythagorus knows if it is a circular plane.

 Jul 13 05, 10:03 PM
Arpeggionist

Well, the problems arise when you take into account the elevation of the south pole, and the fact that it is located between Antarctic mountains (or so I've read, my source might be wrong). Either way, even an elevation of 9,000 feet is hardly noticable when you're relating it to the planet's circumference or area.

 Jul 14 05, 1:00 AM

It is as simple as this: no matter how far away from the Earth you are, your eyes will never be farther apart FROM EACHOTHER and it is this separation, not that from the earth, that determines the parallax.

Try a simple experiment: take two balls, one for ping-pong and one for basketball. Place two small dots, exactly opposite from eachother on each ball and observe.

Using one ball at a time and starting with it pressed right against the bridge of your nose, attempt to distinguish both dots on the ball simultaneously.

Push the ball farther and farther away until you are able to distinguish both dots.

I recommend you try the ping pong ball first as you should be able to see both dots quite quickly. The basketball will take considerably longer -- forever.

Try it and let us know how you get on.

 Jul 14 05, 5:36 AM

### Other Similar Questions & Answers

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