Unfortunately I can’t open the links on my phone so it’s hard to follow what you’re describing. I understand the rays aren’t perfectly parallel but they’re pretty close to parallel. Do you mind doing the math of where you are getting 3km from I’m not really following your logic. It doesn’t make sense to me that the light should suddenly spread out way more after bouncing off a mirror than if it has just continued traveling straight.
The links are actually only random images from an image search with the terms “solar eclipse through tree leaves” and “iss in front of sun”.
I think you have in mind, that the rays are not parallel because they have to arrive at different positions. As you say, this is negligible, and it can even be avoided by the tilting of the mirrors. However, the rays start from different parts of the sun, and as the sun is huge, this angle is not so small.
I’ll try to explain it in more detail, sorry for the wall of text, it got longer than expected. In this case, we can use simplified ray optics and ignore the wave nature of light. This means, the light of the different mirrors or even pieces of mirrors just adds to one another. An important point, even if obvious, is that each point on the mirror surface can only have one orientation. Now we “select” the orientation of this point, we orient it in a way, that it reflects the rays from the center of the sun1 directly on the sun.2 But until now, we have ignored the rays which come from the rim of the sun. These rays start at a different position, namely the sun radius (695700 km). Due to different starting position, the rays have a different angle to arrive at the power plant, arcsin(sun radius / sun-earth-distance), which is 0.27°. Now we already oriented the mirrors parts in a way, that the rays from the center of the sun are reflected onto the satellite, but the rays from the rim of the sun come at an 0.27° differing angle. If the incidence of the ray on a mirror is changed by an angle, the outbound ray is also changed by the same angle. This leads reflected rays leaving in a direction 0.27° offset from the direction to the satellite. Assuming the satellite is at a height of 300 km and directly above, it is 300 km away, the smallest realistic distance. With this angle, it leads to a miss of plant-satellite-distance * sin(angle) leading to 1.4 km. This thought is valid for all points on the rim. Similarly, the rays between the rim and the center land between the satellite and 1.4 km off target. Hence the plant projects an image of the sun onto the satellite with a radius of 1.4 km.
1 Well they actually do not come directly from the sun, they still come from very close to the surface, but they seem to come from the center of the sun and for rays it is not important how far they have already traveled. We can just assume the sun is a disc. 2 If we assume the mirror is optimally shaped, we can reflect every ray, which seems to come from the center of the sun, perfectly on the satellite. Such a mirror would be part of an ellipsoid, with focal points at the center of the sun and the center of the satellite. In practice, it would be practically indistinguishable from a paraboloid with the satellite (deviance of 1.5 µm with a guessed plant size of 1 km). This is possible as the rays through the center of the sun falling onto the plant are, as you say, almost parallel.
Unfortunately I can’t open the links on my phone so it’s hard to follow what you’re describing. I understand the rays aren’t perfectly parallel but they’re pretty close to parallel. Do you mind doing the math of where you are getting 3km from I’m not really following your logic. It doesn’t make sense to me that the light should suddenly spread out way more after bouncing off a mirror than if it has just continued traveling straight.
The links are actually only random images from an image search with the terms “solar eclipse through tree leaves” and “iss in front of sun”.
I think you have in mind, that the rays are not parallel because they have to arrive at different positions. As you say, this is negligible, and it can even be avoided by the tilting of the mirrors. However, the rays start from different parts of the sun, and as the sun is huge, this angle is not so small.
I’ll try to explain it in more detail, sorry for the wall of text, it got longer than expected. In this case, we can use simplified ray optics and ignore the wave nature of light. This means, the light of the different mirrors or even pieces of mirrors just adds to one another. An important point, even if obvious, is that each point on the mirror surface can only have one orientation. Now we “select” the orientation of this point, we orient it in a way, that it reflects the rays from the center of the sun1 directly on the sun.2 But until now, we have ignored the rays which come from the rim of the sun. These rays start at a different position, namely the sun radius (695700 km). Due to different starting position, the rays have a different angle to arrive at the power plant, arcsin(sun radius / sun-earth-distance), which is 0.27°. Now we already oriented the mirrors parts in a way, that the rays from the center of the sun are reflected onto the satellite, but the rays from the rim of the sun come at an 0.27° differing angle. If the incidence of the ray on a mirror is changed by an angle, the outbound ray is also changed by the same angle. This leads reflected rays leaving in a direction 0.27° offset from the direction to the satellite. Assuming the satellite is at a height of 300 km and directly above, it is 300 km away, the smallest realistic distance. With this angle, it leads to a miss of plant-satellite-distance * sin(angle) leading to 1.4 km. This thought is valid for all points on the rim. Similarly, the rays between the rim and the center land between the satellite and 1.4 km off target. Hence the plant projects an image of the sun onto the satellite with a radius of 1.4 km.
1 Well they actually do not come directly from the sun, they still come from very close to the surface, but they seem to come from the center of the sun and for rays it is not important how far they have already traveled. We can just assume the sun is a disc.
2 If we assume the mirror is optimally shaped, we can reflect every ray, which seems to come from the center of the sun, perfectly on the satellite. Such a mirror would be part of an ellipsoid, with focal points at the center of the sun and the center of the satellite. In practice, it would be practically indistinguishable from a paraboloid with the satellite (deviance of 1.5 µm with a guessed plant size of 1 km). This is possible as the rays through the center of the sun falling onto the plant are, as you say, almost parallel.