Science Questions

Does a mountain make the day longer?

Sun, 7th Nov 2010

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Question

Alex asked:

How many more hours of light would you get if you were sitting at the top of Mount Everest compared to someone at the same latitude, sitting at sea level?

Answer

We put this to Dominic Ford from the department of physics in Cambridge:

Dominic - There are a couple of interesting differences in what you would see around sunrise and sunset on top of a tall mountain.  First of all, there would be difference in how long the sun would spend above the horizon.   You can think about that by imagining that the Earth is a ball and if you're standing on the surface of that ball, it appears like a flat plane.  It covers exactly half of everything you can see.  Whereas if you move away from that ball up a tall mountain, it starts to recede away from you and appear like a globe in the sky.

Mount Everest from Rombok Gompa, TibetNow, the Himalayas aren’t actually very tall in comparison to the radius of the Earth.  Everest is about 9 kilometres high and the earth is 6,000 kilometres in radius.  So that means that even at the top of Everest, this ball would only appear about 174 degrees across as compared to 180.  So that would make a difference of about 10 minutes in sunrise and sunset times, if you assume that the Earth is a perfect sphere and Everest is the only mountain on the surface of the Earth.

Now in fact, that’s not quite right because obviously, Everest is in the middle of the Himalayas, and you'll be familiar with the fact that if there’s a tall hill on the horizon, then the Sun will set behind the hill somewhat before published sunrise and sunset times.

 

Diana - So on the top of Everest, the Sun wouldn’t spend that much more time over the horizon because it would set behind the mountains, but what about the bit in between sunset and total darkness?

Dominic - Now, there’s a slightly different answer because when we talk about hours of daylight, we tend to be talking about when we perceive it gets light, and when we perceive it gets dark, rather than when the Sun is rising and setting.  That’s to do with twilight times and how long the sky appears bright after the Sun has set.  In the UK, we’re quite used to having a lot of twilight and that's to do with the fact that we’re at a high European latitude and when the Sun sets, it sets at an oblique angle, and it actually spends quite a long time sitting on the horizon as it’s setting.

Everest of course is close to the equator and at equatorial latitudes, the sun sets more or less vertically downwards.  So it sets very quickly, and you don't have much twilight time as the Sun is setting.

Moreover, twilight is caused by the scattering of sunlight off particles in the Earth’s atmosphere and at the top of Everest, you're above most of the Earth’s atmosphere.  So, you have a lot less light being scattered and twilight will appear a lot darker.  So once the sun has set, it will get dark relatively quickly compared to what we’re used to.  So you might find actually, there’s slightly less daylight time on top of Everest than you would see certainly here in the UK.

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We put this to Dominic Ford from the department of physics in Cambridge:

Dominic - There are a couple of interesting differences in what you would see around sunrise and sunset on top of a tall mountain.  First of all, there would be difference in how long the sun would spend above the horizon.   You can think about that by imagining that the Earth is a ball and if you're standing on the surface of that ball, it appears like a flat plane.  It covers exactly half of everything you can see.  Whereas if you move away from that ball up a tall mountain, it starts to recede away from you and appear like a globe in the sky.

Now, the Himalayas aren’t actually very tall in comparison to the radius of the Earth.  Everest is about 9 kilometres high and the earth is 6,000 kilometres in radius.  So that means that even at the top of Everest, this ball would only appear about 174 degrees across as compared to 180.  So that would make a difference of about 10 minutes in sunrise and sunset times, if you assume that the Earth is a perfect sphere and Everest is the only mountain on the surface of the Earth.

Now in fact, that’s not quite right because obviously, Everest is in the middle of the Himalayas, and you'll be familiar with the fact that if there’s a tall hill on the horizon, then the Sun will set behind the hill somewhat before published sunrise and sunset times.

Diana - So on the top of Everest, the Sun wouldn’t spend that much more time, over the horizon because it would set behind the mountains, but what about the bit in between sunset and total darkness?

Dominic - Now, there’s a slightly different answer because when we talk about hours of daylight, we tend to be talking about when we perceive it gets light, and when we perceive it gets dark, rather than when the Sun is rising and setting.  That’s to do with twilight times and how long the sky appears bright after the Sun has set.  In the UK, we’re quite used to having a lot of twilight and that's to do with the fact that we’re at a high European latitude and when the Sun sets, it sets at an oblique angle, and it actually spends quite a long time sitting on the horizon as it’s setting.

Everest of course is close to the equator and at equatorial latitudes, the sun sets more or less vertically downwards.  So it sets very quickly, and you don't have much twilight time as the Sun is setting.

Moreover, twilight is caused by the scattering of sunlight off particles in the Earth’s atmosphere and at the top of Everest, you're above most of the Earth’s atmosphere.  So, you have a lot less light being scattered and twilight will appear a lot darker.  So once the sun has set, it will get dark relatively quickly compared to what we’re used to.  So you might find actually, there’s slightly less daylight time on top of Everest than you would see certainly here in the UK. BRValsler, Tue, 2nd Nov 2010

Using Pythagoras's theory, the distance to the horizon can be calculated based on the Earth being a perfect sphere. But the Earth isn't a perfect sphere, so the horizon will differ depending on the curvature at the observers location and the terrain between the observer and the horizon, so calculations to establish the distance to the horizon will only be approximate and based on the horizon at sea level, unless the elevation of the surrounding terrain is known.

At sea level, for the average height individual, the horizon will be at 3 miles (4.8k) approx. At the peak of Mt Everest (29,029ft 8848m) the sea level horizon would be 208.8 miles (336.1k). Obviously, the actual horizon will be much closer than this and would be dependant on the direction of the observers view. Of course you need to add another 3 miles to this distance to account for the observers height.

It's worked summat like this:-



H = Horizon
O = Observer
R = Centre of Earth

H to R distance is 3963.2 miles (6378137m)
D to R distance is as above plus height above sea level.

Pythagoras = The area of a square on the hippopotamus is equal to the sunshine of the other two bits of stick (or summat to that effect).

Right, that's my 2 penny worth. Who's going to extrapolate that to hours of sunlight? I need to go lie down in a darkened room now. My brain hurts. Don_1, Wed, 3rd Nov 2010

I was going to say just that. I've worked and lived in Yosemite Valley in California and can tell you it gets quite dark long before local sunset outside the valley.

A while back the ISS passed directly overhead where I live. We watched it come over the western horizon and pass overhead then continued on to the East. It was very bright but quickly faded and disappeared about 45 degrees above the eastern horizon. mountaineirc1969, Sat, 6th Nov 2010

I think is more to do with angles.

From that diagram^

sin (theta) = HR / OR

where theta is the angle HO-OR

And if you think about it, if the sun is within that angle, either side of the observer, then it's night.

So if you were on the equator at midsummer, the sun moves 360 degrees in 24 hours (ignoring the slight orbital elliptical motion). So that's 360/24 degrees per hour = 15 degrees/hour

so you get 2*theta/15 hours of night which is 2*ASIN(HR/OR)/15 hours.

Now HR is the radius of the Earth, 6371km. The height of Everest is 8.840km, so OR is 6371+8.84 = 6379.84 =~ 6380km

Putting it all together I make it that, if Everest was on the equator, it would be about 11.60 hours of darkness per day at the very top. So the Sun is above the horizon about an extra 24 minutes.

Of course, it's not on the equator, but at Everest, midsummer, it should be pretty close. wolfekeeper, Sun, 7th Nov 2010

Hello, I am a student at Reykjavik University in Iceland, hoping to one day become a biomedical engineer. I enjoy listen to your show usually while take a long run. I had took a running break and recently started up again which usually means I must endure a couple of weeks of itching. While listen to one of your shows it dawn to me that I should ask you guys to demystify the "runners itch, I have had this condition before moving to Iceland from the Bahamas, so it doesn't have anything to do with the cold. I have tried using different washing detergent, staying hydrated , and using plenty of lotion to keep my skin moisturize. The best diagnosis I received said something like this "There are millions of tiny capillaries and arteries inside our muscles which expand rapidly due to the demand for more blood that is brought on by exercise. When fit, these capillaries remain open allowing maximum blood passage, but when unfit and inactive they tend to collapse, allowing only minimal blood passage (which is sufficient for a sedentary person however). The rapid expansion of these vessels causes adjacent nerves to send impulses back to the brain which are interpreted as an itch. That’s why after a few sessions the sensation tends to go away. Just another indication of increasing fitness levels." is this correct? And is there anyway to relieve runners itch besides having to run through it? I was told allergy pills and vitamin C may help. andrew, Sun, 7th Nov 2010

I find a can of does the job, andrew!!! Don_1, Sun, 7th Nov 2010

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