Globe Earth question: Percent of the Earth receiving sunlight at a given time

[Thomas456]

I recently stumbled on a problem I can't solve.

For background, there is a recent story from July 8 about 99% of people receiving sunlight at 11:15 am. Anyone can google it and it's explained fairly well at time and date. There is an illustration. Here: https://www.timeanddate.com/news/astronomy/99-percent-sunlight-july-8
is a region of daylight that accounts for 50% of the globe, with other bands indicating various types of twilight. This daylight region should align nicely with a 3D view of the Earth. Link here: https://www.echalk.co.uk/Science/physics/solarSystem/InteractiveEarth/interactiveEarth.html

Problem is it does not. Try as I might, I cannot get the 50% daylight region to align with the visible parts of 3D Earth. Why?

 

[PeroK]

I'm sure this question was asked some time ago.

 

[berkeman]

For background, there is a recent story from July 8 about 99% of people receiving sunlight at 11:15 am. Anyone can google it and it's explained fairly well at time and date. There is an illustration. Here: https://www.timeanddate.com/news/astronomy/99-percent-sunlight-july-8

I like the fact checking in the first link:

Claim Confirmed, But…

So, the claim is technically true if you count all twilight areas, no matter how dimly lit.

But the percentage of the population actually perceiving sunlight is a bit lower. Discounting all of the people in the astronomical twilight zone and half of the population experiencing nautical twilight, we get 7204.9 million people, or about 93% of the world’s population.

It’s still a very high number. But the wording of the more recent versions of the post, claiming that 99% of the population will “experience daylight,” is somewhat misleading.

 

[Thomas456]

Yes, I read it. Its not my question. My question is why the 50% of the daylight region does not align with what is visible on a 3D Globe. I have tried for hours, and it doesn't fit the parameters. If you can do it, all it takes is a screenshot to show it.

 

[Thomas456]

I like the fact checking in the first link:

Yes, its a good article. To be clear, Im not confused about the twilight region. I specified the daylight region. Try to line up the visible daylight region from the first link, with a global 3D map. It just doesn't align.

 

[Thomas456]

I like the fact checking in the first link:

Hopefully, this illustrates the problem. Here is a screengrab from 3D earth. This is one of my attempts to get alignment Notice how it does not align with the 50% daylight region? There are many discrepancies:

It should extend nearly to Antarctica.
It should include more of South America
It should include South East Asia
It should include most of North America.
It does not.

Move the 3Dglobal model about, and the problems multiply. Try it yourself. Why doesn't the visible region align with the Daylight region? Explanation requested. Or if you can get the 3D model to fit the very identifiable parameters of the Daylight regions as illustrated in the link, post a screenshot.

 

[phyzguy]

I think the viewpoint in your 3D global view is not at infinity, it is relatively close to the Earth. So it is not showing 50% of the Earth, but less than 50%. As you get closer and closer to the Earth, you see less and less of the area.

 

[Thomas456]

Hmmm, thats interesting. I have looked at several 3D models with the same result. Do you have one where it does show 50%? Seems to me that would be a pretty basic standard. And how would it need to be at infinity? The Sun is not at infinity. Thanks for your reply.

 

[Thomas456]

I think the viewpoint in your 3D global view is not at infinity, it is relatively close to the Earth. So it is not showing 50% of the Earth, but less than 50%. As you get closer and closer to the Earth, you see less and less of the area.

You do raise an good point though. Follow up question. What would be the distance that a 50% view of the Earth would be achieved? Math equation?

 

[Baluncore]

Problem is it does not. Try as I might, I cannot get the 50% daylight region to align with the visible parts of 3D Earth. Why?

1. When you look at the Earth from closer than the Sun, you do not see a full hemisphere because your horizon is closer. The area you see approaches zero, as your height approaches zero.
2. The 99% of population, comes I think from the definitions of the different twilights, when the upper limb of the Sun is 6°, 12°, or 18° below the horizon for astronomical twilight.

You can get to see it backwards from the antipodes, at night, when the two 18° effects of twilight and observer height can cancel. I have not calculated the exact observer height for an 18° encroachment of the horizons, but the cancellation effect is visible.
Use the link:
https://www.echalk.co.uk/Science/physics/solarSystem/InteractiveEarth/interactiveEarth.html
Select population density.
Then look at the Pacific Ocean, from above the Tropic of Capricorn, (23.5°S), and minimise the population visible. Make sure you cannot see the population of Japan.

At that time, those people you cannot see have sunlight or twilight.

 

[Thomas456]

1. Thats my question! So you are saying the 3D Globe is not going to show 50%. Any idea how much it does show? Isn't there a math formula for the distance needed to show 50% from the diameter? Btw, my Globe link is the same as yours only selected for terrain.
2. I have zero confusion over twilight vs daylight. I am going by the DAYLIGHT parameters of the link. I have zero questions about population density vs visible sunlight.
Thanks for your reply.

 

[DaveC426913]

So you are saying the 3D Globe is not going to show 50%.

Not unless the viewpoint is effectively at infinity, no.

Or a diagram (presumably) has no distortion, like this:

Any idea how much it does show?

Not without knowing the distance from the POV, no.

Isn't there a math formula for the distance needed to show 50% from the diameter?

Yes. 50% of the Earth will be visible when the rays from opposite limbs (i.e. diametrically opposed points) are parallel, which only happens at effectively infinity.

What you want is a compromise. Something far shorter than infinity will give you a view of Earth that is fractionally less than 50%.whats your comfort level? 49.9%? 49%? 45%?

 

[Thomas456]

Thanks someone else mentioned infinity. I don't understand this. The Sun is not at infinity, and illuminates 50% of the Earth. So how can we not see this?
Thanks for your reply.

 

[DaveC426913]

Thanks someone else mentioned infinity. I don't understand this. The Sun is not at infinity, and illuminates 50% of the Earth. So how can we not see this?
Thanks for your reply.

It is effectively at infinity..

The rays from the sun hit the north pole and south pole effectively in parallel.

Problem is, from the Sun,the Earth is too tiny to see. You can only see detail when close by.

 

[Baluncore]

Not unless the viewpoint is effectively at infinity, no.

The rays from the sun hit the north pole and south pole effectively in parallel.

Because the Sun has an angular diameter of about 0.5°, it has an angular radius of 0.25° which pulls the 180° of the illuminated sphere back to 179.5°, which does not require the Sun to be at infinity.

 

[DaveC426913]

Because the Sun has an angular diameter of about 0.5°, it has an angular radius of 0.25° which pulls the 180° of the illuminated sphere back to 179.5°, which does not require the Sun to be at infinity.

Yes, the OP doesnt really need infinity.

What they need is a orthographic projection of Earth, not one in 3D.

Plenty of static maps like like but not sure if renderers of that type are very common.

 

[Thomas456]

It is effectively at infinity..

The rays from the sun hit the north pole and south pole effectively in parallel.

Way over my head, but interesting! Thanks. It does answer my question on why I could not make the map align with the model. I was really perplexed.
And one more thing, could you give a rough estimate looking at the link of the 3D map, of how much % you think is showing? Just so I have an idea.
Thanks for your reply.

 

[russ_watters]

Maybe I missed something about how that 3d globe link works, but can you pick the day? The timeanddate link says it was July 8.

 

[Thomas456]

Thanks someone seems to have answered my question. The 3D globe is in the link. The other link is to an article, which is July 8. I cannot pick the day on the globe. I was trying to see if I could align it to roughly the solstice.

 

[russ_watters]

The 3D globe is in the link. The other link is to an article, which is July 8. I cannot pick the day on the globe. I was trying to see if I could align it to roughly the solstice.

I saw the link to the 3D globe model. What I'm asking is if you can set the date. I'm not seeing such controls on it. The 99% thing only happens at a specific time and date. Also...if you're using the projection as if you are the sun, that would mean you need to tilt earth's axis towards you.

 

[Thomas456]

I don't have any questions about the 99% claim. The article explained it really well.
I cannot set the date on the 3D model.

 

[DaveC426913]

What is left for you to accomplish?

In light of what you now know, can you restate your goal?

 

[Baluncore]

Also...if you're using the projection as if you are the sun, that would mean you need to tilt earth's axis towards you.

Direct observation cannot show all the people 18.25° over the horizon. But reversing the process, looking for less than 1% of the population, at the solstice, puts the observer over the Pacific Ocean, the southern tropic of Capricorn.

 

[Thomas456]

What is left for you to accomplish?

In light of what you now know, can you restate your goal?

I believe I said you answered my question. I was hoping for a rough estimate on how much the 3D model does show , but I can see physics guys don't deal in rough estimates.
Many thanks for everyone here.
Have a great night. My goal now is to enjoy the rest of the night.

 

[Thomas456]

I saw the link to the 3D globe model. What I'm asking is if you can set the date. I'm not seeing such controls on it. The 99% thing only happens at a specific time and date. Also...if you're using the projection as if you are the sun, that would mean you need to tilt earth's axis towards you.

Thanks for your input. Have a great night.

 

[russ_watters]

Direct observation cannot show all the people 18.25° over the horizon. But reversing the process, looking for less than 1% of the population, at the solstice, puts the observer over the Pacific Ocean, the southern tropic of Capricorn.

I'm aware and aware the OP's main question has been answered. I'm just saying I'm not even sure if OP was using his globe simulation correctly.

 

[Thomas456]

I'm aware and aware the OP's main question has been answered. I'm just saying I'm not even sure if OP was using his globe simulation correctly.

I did tilt the axis every which way, but It didn't make a difference. The answer seems to be that the 3D model doesn't show 50%, so it wouldn't matter. But it was still helpful to learn from you it should be pointed toward me to approximate solstise rather then may admittedly crude method of looking from the Northern Hemisphere. Thanks.
Have a great night.

 

[russ_watters]

I did tilt the axis every which way, but It didn't make a difference. The answer seems to be that the 3D model doesn't show 50%, so it wouldn't matter. But it was still helpful to learn from you it should be pointed toward me to approximate solstise rather then may admittedly crude method of looking from the Northern Hemisphere. Thanks.
Have a great night.

Ahh - you can click and drag it manually. Fair enough.

 

[Thomas456]

Ahh - you can click and drag it manually. Fair enough.

And I did alot of clicking and dragging!

 

[berkeman]

In light of what you now know, can you restate your goal?

I see what you did there...

 

[Baluncore]

This is my analysis and summary of the situation.

It is impossible to see on a 3D model of the Earth, where the 99% of the population, simultaneously illuminated by sunlight or twilight, will be.

That is because the Sun illuminates an extra 0.25° over the horizon due to its angular diameter. The 18° definition of astronomical twilight adds to that, giving 18.25° over the horizon. The part of the sphere that is then deemed to be illuminated is not 180°, but is 18.25° + 180° + 18.25° = 216.5°.

That leaves a dark circle with a diameter of only 360° - 216.5° = 143.5°. That circle, with radius = 71.75°, is centred over the Pacific Ocean above the tropic of Capricorn. The dark circle does not include the populous islands of Japan, Indonesia, or the Philippines, they will probably be in twilight.

What point is on the tropic of Capricorn, at an arc distance of 71.75° from the Japanese coast near Tokyo? Google Earth, Measure, intersects at latitude 23.5°S, longitude 175.464°W, as the approximate centre of the dark circle.

That view of the dark circle looks about right, with Indonesia, Philippines, Japan and California being over the horizon. Only Australia, New Zealand, Papua - New Guinea, Hawaii, many small Pacific islands, and Antarctica are then in the dark. The rest of the world, with 99% of the population, is enlightened.

 

[DaveC426913]

More than one way to skin a cat.

It is possible to see a 3D model of the Earth where a mere 1% of the population are in full darkness. And that's kind of the same thing.