#### edzieba

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« Reply #40 on: 01/28/2023 08:18 am »
You posted a graph that correctly showed that the sun blocking dropped as you got closer to the sun from L1. But you need to graph the other side as you get closer to earth.
No. The graph is distance from Earth, not L1.
Quote
A one meter diameter disk blocks more sunlight at 1000 meter than it does at one meter.
Still incorrect, for the reasons I've previously posted. The assumption that light intercepted by an object is proportional to light blocked on a target is invalid for extended sources like the Sun.

#### ppnl

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« Reply #41 on: 01/28/2023 09:41 pm »
You posted
A one meter diameter disk blocks more sunlight at 1000 meter than it does at one meter.
Still incorrect, for the reasons I've previously posted. The assumption that light intercepted by an object is proportional to light blocked on a target is invalid for extended sources like the Sun.

No, as long as the penumbra is smaller than the earth this is correct. Every photon that hits the disk would have hit the earth. If you don't believe me then draw the path where the photon would have hit the disk but missed the earth. There is no such path. Simple geometry.

Only when the penumbra is larger than the earth do you have such paths. It is the region of the penumbra that exceeds the radius of the earth that defines those paths. It is geometry, just draw it.

#### Bizgec

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« Reply #42 on: 01/28/2023 10:11 pm »
You posted
A one meter diameter disk blocks more sunlight at 1000 meter than it does at one meter.
Still incorrect, for the reasons I've previously posted. The assumption that light intercepted by an object is proportional to light blocked on a target is invalid for extended sources like the Sun.

No, as long as the penumbra is smaller than the earth this is correct. Every photon that hits the disk would have hit the earth. If you don't believe me then draw the path where the photon would have hit the disk but missed the earth. There is no such path. Simple geometry.

Only when the penumbra is larger than the earth do you have such paths. It is the region of the penumbra that exceeds the radius of the earth that defines those paths. It is geometry, just draw it.
Please just stop hand-waving and playing with words and do the maths. Or just read and understand the calculation already posted, which is correct. Your assumptions are wrong, period.

#### ppnl

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« Reply #43 on: 01/29/2023 01:18 pm »
You posted a graph that correctly showed that the sun blocking dropped as you got closer to the sun from L1. But you need to graph the other side as you get closer to earth.
No. The graph is distance from Earth, not L1.
Quote
A one meter diameter disk blocks more sunlight at 1000 meter than it does at one meter.
Still incorrect, for the reasons I've previously posted. The assumption that light intercepted by an object is proportional to light blocked on a target is invalid for extended sources like the Sun.

It is invalid for extended objects like the sun only at distances large enough  that the penumbra is larger than the earth. A one meter diameter disk blocks more sunlight when it is one meter in the air than it does when on the ground.

How many photons hit the disk on the ground in one second? Lets say a gazillion. How many of those would have hit the earth if not for the disk? All gazillion of them. It blocked a gazillion photons.

How many photons hit the disk one meter up in one seconds? Say a gazillion and three because it is ever so slightly closer to the sun. How many of those photons would have hit the earth if not for the disk? All gazillion and three. It blocked three more photons than the one on the ground.

Until the penumbra is larger than the earth all the photons that hit either disk is blocked from the earth. And one of those disks is hit by more photons because it is closer to the sun. It blocks more photons.

you need to visualize the geometry.

#### edzieba

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« Reply #44 on: 01/29/2023 11:13 pm »
you need to visualize the geometry.
See the geometry calculated above.

Calculating light hitting the occluder, penumbra sizes, etc, are all calculating the wrong thing: as the goal is to block light from hitting the Earth, then directly calculate light blocked from hitting the Earth. Only then will useful answers on the most effective method of blocking light from hitting the Earth be found.

#### ppnl

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« Reply #45 on: 01/30/2023 01:35 am »
you need to visualize the geometry.
See the geometry calculated above.

Calculating light hitting the occluder, penumbra sizes, etc, are all calculating the wrong thing: as the goal is to block light from hitting the Earth, then directly calculate light blocked from hitting the Earth. Only then will useful answers on the most effective method of blocking light from hitting the Earth be found.

Do you agree that for a one meter disk on the ground that every photon that hits the disk is a photon shaded from the earth? And if so calculating the number if photons hitting the disk is calculating the shading of the earth?

#### Proponent

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« Reply #46 on: 03/17/2023 08:03 pm »
Bow before the penumbra, master of us all.

Finally, I see the light, or, rather, the darkness.

It was when I tried to derive McInness's equation that I realized he implicitly assumes that the entirety of the shade is contained within the sun's apparent disk as seen from all points on the sunward side of the earth.  That's equivalent to the entire earth being within the penumbra.

Thank you, ppnl and eriblo, for persisting.  I repent and now too bow before the penumbra, master of us all.
« Last Edit: 03/18/2023 11:55 am by Proponent »