Opposite Cities

Geometry Level 2

Nobody on earth can see the North Pole and the South Pole at the same time.

Is it possible for a satellite to capture an image that contains both of them?

Note: For the purpose of this problem, assume that the earth is a perfect sphere. Effects of optical phenomena such as refraction are to be neglected.

Yes No

3 solutions

Agnishom Chattopadhyay
Jul 19, 2017

Suppose the two cities are two points on the equator. And you are an astronaut above the north pole, who is gradually increasing his altitude.

The further you go, the further of the earth's surface you see. But it is never enough to see the entire equator.

In this figure, A and B are the two cities. Suppose C is the astronaut

Maxime Weill
Aug 8, 2017

the problem isn't very well stated, you could imagine the satellite being larger than the earth, in this case it could see both pole.

Do you think that it would have been better for me to have clarified that the satelite is only a pinhole camera?

Agnishom Chattopadhyay - 3 years, 10 months ago

yes it would be clearer

maxime weill - 3 years, 10 months ago

Juvin Abayon
Jul 20, 2017

If the cities had not been diametrically opposite to each other, the tangent lines drawn would not be parallel to each other, and that the point of intersection would be the place where the astronaut should be in order to see both cities simultaneously. The otherwise has been the case, however, implying that it would not be possible.

would not be parallel to each other

I think you meant would be parallel to each other.

Agnishom Chattopadhyay - 3 years, 10 months ago

I have been confused in my statement, my apologies.What I meant was that the tangent lines would intersect if they're non parallel. Thanks for the correction. :D

Juvin Abayon - 3 years, 10 months ago

Opposite Cities

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