Yes. One place in space has different temperatures. I would assume even individual particles are not distributed by a Maxwell distribution, so the concept of temperature is hard to apply. The background radiation has one temperature. If you add the sun, however, you already have a problem as the sun radiation is not in thermal equilibrium. So depending on how you look at it, you get different temperatures. The particles have a high energy, so also a high temperature. But they are so rare, that radiation is the dominant mode of heat transfer and determines the temperature of a thermometer placed in space.

I think it is actually the other way around. You can consider the air inside the balloon to have internal energy from the heat. And additionally you have to make room for the balloon in the atmosphere, so you have removed the atmosphere from the volume the balloon takes, which also needs energy. If you consider both you arrive at the concept of enthalpy (H = U + pV), which is very useful for reactions in the atmosphere as pressure is constant. For this example it is not that useful as outside pressure changes when the balloon rises.

Another way to see it, the pressure has no “real” energy. In a ideal gas, the only energy comes from the kinetic or movement energy of the atoms. Each time a gas molecule is hits the balloon envelope it transfers some momentum. The cumulative effect of the constant collisions is the pressure of the gas. If the balloon is now expanding slowly, each collisions also tranfers some energy, in sum building the work the system has to do to the atmosphere. Leading to a decrease in internal, so “real” energy in the balloon. This corresponds to a decrease in temperature.

The stratosphere is heated not by the ground but directly from solar radiation leading to higher power input at the upper layers. So the top is hotter and now convection never starts and you get no cooling of the air when rising.

While I agree in general, one point is a bit to simplified in my opinion

In other words, there are fewer air molecules per cubic foot (volume of air). The molecules are farther apart and can hold less heat energy. Because “heat” is what we say when we mean molecules are moving around.

Less molecules mean less heat, it has nothing to do with the temperature, if you just decrease the density by removing half the molecules, you have the same temperature.

It cools down because it expands adiabatically. Consider a very thin balloon filled with air which is warmer than the surrounding. This now rises up, but as it does, the pressure decreases, causing the balloon to expand. During this expansion, the balloon transfers energy away from itself, because it has to push away air, to make room for expanding in the surrounding. This work cools the air inside the balloon. Assuming the air inside is dry, it would cool around 10 °C per km it rises. Now if you think about it, the balloon just stopped the inside from mixing with the outside. If you look at a large “piece” of air, it does not mix very fast, so you can remove the balloon and just consider what happens with warm air heated from the ground.

Now this does not mean, it has to be cooler when higher up. The same points hold, inside a house, but there it is often warmer when higher.

The best explaination is when looking where the heat comes from and goes too from the air. The atmosphere is mostly heated from the surface of earth, so the bottom and cooled from the upper layers. So naturally it gets hotter where it is heated. The question is now by how much? There are three modes of heat transfer in the atmosphere: radiation, conduction and convection. The first two are very slow. Connection is fast but has limits. Consider the piece of air, if it rises, it cools. So at some place it may be the same temperature as the surrounding air, so it stops rising. This means the convection works only when the air gets cooler by 10 °C/km going up (~6.5°C when the air is moist and precipation happens). So this temperature gradient is observable very often.

But also learn to feel your feelings by yourself.

I agree completely with this stance

If you need to talk a lot about your feelings, especially the deep stuff, talk to a therapist. That’s not brushing you off, it’s what therapy is for.

While I agree that therapy can help a lot in those situations, I don’t think these talks should be limited to a therapist. I try to be somebody you can come to and talk about deep stuff for my friends. With one friend of mine, I mostly talk about deep feelings. It is great to have somebody like her, it’s a different category than therapy. A therapist shouldn’t give you his opinion and rarely shares similar experiences. Sometimes it’s just nice to have someone to talk to in a more symmetric way. For me it’s almost never a burden to listen to the emotions of people I like. I want to hear the deep stuff.
Sure a friend is not a replacement for therapy, but therapy is also not a replacement for a friend with whom you talk about deep emotions.

This hits me hard. I am a cis male and currently trying to get rid of something like toxic masculinity, but as you say it is deeply rooted.

I acually never strived for the stereotypical man image, I wanted to have an emotional side. Now i know i always just considered “having am emotional side” just as another kind of requirement to be a good man. So i tried listening to others and beeing open myself, talking about emotional things. But only those, that i thougt were accepted. I never talked about my real worries. They always seemed to ridiculous to me. A good emotially healthy man shouldn’t have them or solve them himself. Now it feels pretty dumb in retrospect, but I am no longer letting this feeling stop me from talking about something. In some way I also have the feeling i betrayed other people with a fake personality.

I know this is not the mistake of feminism. I cannot really say what went wrong to land in this position. I do not even know why i tell this now. In some way, I just want to tell my story and hope someone can relate with it. Secondly i want to say, that the following is not obvious for everyone, at least it was not for me: Beeing emotional is not just some requirement for you, it’s also about having an opportunity to get support for your worries.

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.

Yes, you are right, considering the rays emerge from a point. And yes, each panel or all panels in unison can act like a magnifying glass. However, if they focus the light on a point at the height of the satellite, they work like a magnifying glass, or telescope with a focal length of the satellite – power plant distance, so at least 300 km. Considering the angular size of the sun, this telescope would lead to an image of the sun, the size of 3 km.

No sun rays are not parallel. If you looked at the sun (don’t, it will burn your eyes), would you see it as a point or a disc? As a disc. Why? Because even looking in slightly different directions, you see the sun. So the rays from the sun are not almost parallel, the rays from other stars are, they look point like.

Two interesting images for you: A solar eclipse viewed trough tree leaves: You can see the partial sun disc by using the small free points in the tree cover as pinhole cameras. Sure, the tree cover does not have lenses, but they only make the image sharper, not smaller. In this image the focal length is only the height of the trees and the image is already a few cm across. It also shows that the rays from the sun are not parallel. If they were, all rays going through the small free spots in the tree cover would end up at the same spot on the ground.

International Space Station, ISS, flying in front of the Sun: As the sun and the satellite are far away, we can assume that the angular size of the original sun and the virtual sun image are approximately the same when viewed from the power plant. Hence, this image shows how the mirrors would form an image of the sun, where only a small part of it hits the sun.
As the sun is much larger than the ISS, the angle of rays which come from the sun is much larger than the angle of rays which hit the ISS.

Yes i am, because it is unimportant if the light comes from the sun or the moon or a 3km large satellite (assuming they would have the same radiance). It would be important if the power plant were ten times larger, the satellite would be closer or larger. However in this case the limit to the power is is the etendue of the light at the satellite. The maximum power is the etendue at the satellite times radiant flux of the sun.
If you want a fun and interesting read which does explain a related “problem”, there is a relevant xkcd

I could explain it to you in at least five different ways in detail, three of them i have already done in short here in the comments. However, you never argued directly against my point. You don’t talk to me seriosly but laugh about it.
This is not what a serious disussion looks like like. If you want an explaination, i would be motiviated to take the time and explain it in detail.
Note that i listened to your point, considered it and argued why it plays no role. You have not considered my explainations.

No i am talking about all the mirrors as one surface, no matter they are really one or consist of small pieces

For the 65 W/m^2 i already used the size of the whole system, so all 10000 mirrors.

The sun has a angular diameter of 32 arcmin. (see here) Hence, the rays hitting one point of the one mirror, have come from different angles, namly filling a circle with this angular diameter. By reflection, the directions of the rays changes. But rays hitting the same spot on the mirror which were misaligned before by 32 arcmin are also misaglined by 32 arcmin after the mirror, independent of its shape. Therefore, the rays emerging from the power plant diverege by at least 32 arcmin. This is not a problem for operation, as this leads to a size of 4.6 m at an estimated maximum distance of 500 m between tower and mirrors. When the mirrors point at a satellite however, a distance of 300 km leads to a beam diameter of 2.8 km calculation

Even an ideal mirror can only project a point source onto a point. It is impossible to focus the rays of an extended source onto one point. See https://en.wikipedia.org/wiki/Etendue if you want to know details. With conservation of etendue you can also calculate this in a similar way.

The problem is the size of the sun. If you could look at the sun (don’t, try the moon its approximately the same size in the sky), you see it has a relatively large angular size. Its not just a point in the sky.

So the problem, the rays from one point of the sun are almost parallel. But the rays from the different points of the sun are not. So they also aren’t parallel after your mirror. They spread in an angle similar to the size of the sun on the sky. And this is much larger than a satellite. So you cannot focus all energy on a satellite.

It holds if the light spreads wider than the target. So also for directed light sources at large enough distances. Even a perfect mirror must spread the light in the same angle as it is incoming. Hence the beam would at least 3 km wide at the satellite. Therefore the satellite can only recieve a Illumination of ~65W/m^2 which is a few percent of the normal sun brightness of 1300 W/m^2 in space.

Another way to look at it, the mirrors cant make the sun seem brighter only larger. From the tower you see a large solid angle around you the mirror, therefore, it can seem like you are at the surface of the sun. However, fro. the position of a satellite, the power plant only takes a small solid angle, so it seems like a “smaller” sun. Assuming 400 MW and 1 kW/m^2 (at surface) solar power, it has an area of 400000 m^2, so a solid angle of 4.5e-6 sr from 300km while the sun has 70e-6 sr. So ten times smaller, therefore weaker. Note however here i did not account for attenuation in the atmosphere

It holds if the light spreads wider than the target. So also for directed light sources at large enough distances. Even a perfect mirror must spread the light in the same angle as it is incomming. Hence the beam would at least 3 km wide at the satellite. Therefore the satellite can only recieve a Illumination of ~65W/m^2 which is a few percent of the normal sun brightness of 1300 W/m^2.

Another way to look at it, the mirrors cant make the sun seem brighter only larger. From the tower you see a large solid angle around you the mirror, therefore, it can seem like you are at the surface of the sun. However, fro. the position of a satellite, the power plant only takes a small solid angle, so it seems like a “smaller” sun. Assuming 400 MW and 1 kW/m^2 (at surface) solar power, it has an area of 400000 m^2, so a solid angle of 4.5e-6 sr from 300km while the sun has 70e-6 sr. So ten times smaller, therefore weaker. Note however here i did not account for attenuation in the atmosphere

I cannot recommend mindfulness enough, as already suggested by many others in this thread.

I think, you said you are already in therapy? In this case, I would definitely talk with your therapist about this and things you want to adopt beforehand. If you want a simple concrete tip, you could try the “mindfulness coach” by the US department of veteran affairs. I liked it a lot and the apps from there get good privacy recommendations from mozilla.

I am a bit suprised by the many people recommending to just stop giving fucks. Is this what you really want? Or do you just want avoid the emotions of taking control?

You do not need to be that hard to yourself when your feeling “wrong”. Yes it is probably better for yourself if you don’t overreact. However you cannot really cotntrol your feelings. So it is still better to accept your anger. First, as you said, it drives up the frustration, because now you are also worried about your feelings. And second your original emotion wants to be “noticed”. I read and experienced a few times myself, the “wrong” emotion disappears often quickly when you accept it. It is an essential concept of mindfulness, to accept your emotions.

Edit: As far as i understand it and experienced it, saying to yourself “no i shouldn’t be angry about this” won’t change your thinking