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.
A one meter diameter disk blocks more sunlight at 1000 meter than it does at one meter.
Quote from: ppnl on 01/28/2023 07:09 amYou 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.
You posted A one meter diameter disk blocks more sunlight at 1000 meter than it does at one meter.
Quote from: edzieba on 01/28/2023 08:18 amQuote from: ppnl on 01/28/2023 07:09 amYou 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.
Quote from: ppnl on 01/28/2023 07:09 amYou 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. QuoteA 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.
you need to visualize the geometry.
Quote from: ppnl on 01/29/2023 01:18 pmyou 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.
Bow before the penumbra, master of us all.
Quote from: edzieba on 01/19/2023 03:18 pmHowever, the point where the apparent diameters of the Sun and the Earth are the same is 1.36•106 km which is closer than L1 (1.5•106 km) so this will not be the case for passive sun shades.A complete non-sequitur. We do not care at what point in space the Earth and the Sun have the same apparent size, as we are not attempting to block light at an arbitrary point in space. We care about the total coverage of the solar disc from the point of view of the Earth's surface. And in that case, the further an object of fixed size is from the Earth the smaller the region of the solar disc it can cover.
However, the point where the apparent diameters of the Sun and the Earth are the same is 1.36•106 km which is closer than L1 (1.5•106 km) so this will not be the case for passive sun shades.