What altitude do I have to be to see the solar terminator?
Short answer: You’d want to be at least a few kilometers high, and the higher the better.
Long answer: This is a really good question that won’t have an exact answer, but with some reasonable guesses we can probably come up with an estimate.
The angular size of the sun in the sky is about 0.5 degrees. This means that there is a sliver on earth, 0.5 degrees longitude thick, were people can see the sun intersect with the horizon. I’ll call the width of this band the width of the terminator. If the earth’s equator is 40,075 km long, then the terminator will be
(0.5/360)(40,075 km) = 55 km
55 km thick, but atmospheric effects will further smear this out. I expect that in order to get a clear view of this you’d want to be able to see at least 100 km. The distance to the horizon is easy to calculate from a given height ; at a height of about 1 km the horizon is 113 km away. The biggest skyscrapers in the US are about 500 m tall, so you could try going up one of those to have a look around at sunrise/sunset, but I suspect you’ll want to be on a plane.
And again, the terminator won’t appear as a clean line underneath you. Rather, it’s a smooth gradient, with brightness in the direction of the sun and with darkness in the opposite direction. If you were in an airplane at cruising altitude I expect you would be able to resolve this gradient quite easily. Perhaps try looking out your window the next time you have a red-eye flight over an ocean. Those flights are usually east-west.
Even from space it’s still a gradient; check out this video taken from the ISS. While the terminator can be resolved from this height, it’s far from appearing as just a line. And the ISS only has an altitude of 250 miles, so if you want to take a picture of the terminator but that video still didn’t look crisp enough, you’ll have fly higher than any human has for decades.
As a final note, I recall a story that I’m having trouble finding. I believe the pilot was flying (maybe an SR-71?) at high altitude with unusually clear skies, and noticed that to one side he saw a starry sky and complete night, while in the other direction he saw day. Does anyone reading this know what I’m talking about? Anyone got a link?
image credit: NASA via Wikimedia Commons
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