Edit: In the maths section, it says d^2 z/d^2t, but it should be d^2 z/dt^2. Additionally, I have taken the time to actually make some nice captions/subtitles for this video. Apparently, about 8 to 10% of you use these. So to make my videos more accessible to other people I will do this from now on!
FALSE ADVERTIZING! I was FOOLED into thinking you'd be MAKING MYSTERY GOO in your kitchen but instead you're doing NERD MATH like a NERD! GREAT video though keep up the GOOD work!!!!!!!!!!!
Hmm in you derivation, you took 'g' to be a constant, while that is a good approximation for a planet the size of earth, it's really not for a smol planet like kerbin. Kerbin's radius is 600km and the atmospheric height is 70km which is pretty significant in comparison to 600. So the value of 'g' at the edge of the atmosphere is only about 80% of what it is on the surface. Maybe that's why we got a weird value of μ
That's true, but surface gravity on kerbin is 1g, despite it's much smaller size. I suspect you'd get accurate values if you scale up the size of the entire solar system by about 10 or so. Or at least more reasonable values
@ImieNazwiskoOK very good point, niw that I think about it it's probably to do with the fact kerbin is only about a tenth the size of earth, but the atmosphere isn't. The Karman line is at 100km, while on kerbin it's 70, where it would be 10 if it was to scale. I'd have to do the math to check if this is correct tho
Kerbin's atmosphere is actually the standard Earth reference atmosphere, scaled down to 80% height (your value is slightly lower still after accounting for that, likely because scale height varies as temperature does, and so the average is a bit lower due to the colder upper atmosphere). The remaining atmosphere don't really fit a realistic model, though, because their actual molecular weights are actually known: 43 g/mol for Eve and Duna, 28.96 g/mol for Kerbin and Laythe, and 2.2 g/mol for Jool and Kerbol. You can get these by using the other data available from the aero GUI (you can get things like density and speed of sound there, which are actually calculated accurately), openable through the alt-F12 menu. You can also simply get it from the Kittopia dumps - actual configuration files exported by a planet modding tool (note the values are in kg/mol there).
Kerbin is supposed to have the same atmospheric properties as Earth, but the scale height is purposefully decreased for the same reason the planets themselves are at 1:10 scale. A better approach would be to use the ratio of Kerbin and Earth scale height as the "atmosphere scale" and use this number to rescale the scale heights of other planets before doing further analysis.
But that would that would not conform to actual in game measurements. Measuring the pressures gives you the scale height. I see no reason to introduce a random ratio.
in the files for KSP 1 they are somewhat listed if you get them with Kopernicus, these being 0.0289644002914429 for Kerbin, 0.0430000014603138 for Duna, 0.0430000014603138 also for Eve, and 0.0289644002914429 for Laythe, im not exactly sure of what measurment is used here but it likely converts from a x/1000, x being mass in protons.
Probably what’s going on is that the developers just made up the values of the measurements you used to calculate the mean molecular mass, meaning your results are kinda meaningless. :(
Possible yes. The goal of the video is more about teaching about scale height, mean molecular mass and where they come from and such. Would be cool if it actually worked tho haha
Well, now i gotta finish my video using the presmat and thermometer to find the boundary layers of kerbins' atmosphere. Unless you've already done that.
@@AstroHopefulBenjaminGottsch Sure! you can find my e-mail address in the channel's bio if you want to send it over there. Are you still planning on making the video, or are you fine with me covering the material (and of course crediting you) if it is something I can fit into a video?
@curious_ksp_ If you want to make it, I don't mind. I might still make something similar, but idk rn. I've just had these notes and theories written down in my computer for a while, and I'd love it if someone would share them. If you need any help with the video, let me know. I can lend my voice or any other resources you need for it.
There is a sweet spot of course. In previous videos is was just for a couple of seconds and now I took it to the max with about 4 minutes of pure math. I think I should aim for 2 to 3 minutes or so. But glad you liked it!
Considering that the KSP system is a 10 times scaled down solar system, to make all the maths match, shouldn't you add some multiplication to the masses that the planets are made up to make things work? Kerbal is far too dense for its size to match the gravity shown. Can't you apply that same scaling of the mass being higher to the atmosphere?
Gravity in KSP still works the same way. We know the mass of Kerbin and the gravitational constant G, so there is no problem there. It is important to know that there is a difference in mass and density. Knowing that gravity works the same in the KSP universe, we can use the same general expressions
I think the simplest answer to the question of what the atmospheres of these planets are made of is, the developers just made things up as they went along and adjusted them until they felt right
If we assume Duna and Mars have the same atmospheric composition, we find that the game overestimates atmospheric weight by +91%. Adjusted atmospheric weights: Eve: 10.8 g/mol Kerbin: 21 g/mol Duna: 43.3 g/mol Laythe: 18 g/mol These numbers seem exceedingly sus since we know Kerbin and Laythe have significant quantities of O2 or O3, which would oxidize any reducing gases (H2, CH4, NH3). Monoatomic oxygen would give their atmospherics a red hue, not blue. Maybe they're predominately water vapor, some type of hycean planet. Eve could be the migrated core of a hot neptunian planet, a pseudo-chthonian world. It might explain its high concentration of exotic elements like iodine.
I think it would be cool if you needed to do certain science experiments before the game told you how high the atmosphere was, or how dense it was, or how hot it was, things like that. I also think it would be cool if you couldn't see any planets or moons until you visited them (Got within viewing range.) That would give new players more drive to send a probe or something FIRST, then send a probe that lands on the planet and its moons, and maybe keep a probe in orbit too. So that they know the latest information on the planet so they can do safer missions.
I think a lot of the issues from applying real-world models to KSP is thay the gravitational constant is quite different. Kerbin's surface gravity is still 1g even though its diameter is only 1/10th of Earth's.
The gravitational constant (G) should be the same I believe. So there is no problem there. The only thing is that the gravitational acceleration (g) is not really constant throughout the atmosphere as it is not as thin compared to Kerbin as Earth's atmosphere is compared to Earth. So, taking g as a constant was a mistake on my part, but I do believe G is still the same. Would be a nice video to make: determining G, as there are still people debating on what the value is apparently.
When solving the equation for P(z), I think you assumed H was a constant relative to z, but it's not because the temperature varies with altitude. If you used surface temperature, then your expression is valid only close to the surface and your results may be biaised (how much ? I don't know, maybe it's a good enough approximation). I think you could first use the thermometer to have an experimental model for T(z), then use that in your equation for P(z), and finally do what you did with the barometer. It was still a good video, I really like the concept!
Well, the thing is that we use this same model for planets in real life like Earth, even though Earth also has a changing temperature. Though it makes sense for it to be more accurate if we take T(z) into the equation, so I will add these ideas & corrections to a stream soon or maybe at the end of a video!
The devs probably didn't even thought about or just ignored the chemical composition of atmospheres, because KSP's universe is far from being realistic, the devs' main goal was to make flights as realistic as possible, so to do it they made unimportant things less rational, like they did with planets' density. If Kerbin atmospere was made from nitrogen and oxygen (Kerbin's and Earth's g is same) it would be 100% the same as Earth's, and as we all know in RSS it ends in 140 kms. Not that convinient for toy-sized Kerbin
I think maybe we should take Kerbin atmosphere composition as equal to Earth and instead recalculate molecular weights of oxygen, nitrogen and the rest of periodic table of KSP universe
~5:40 its possible that Kerbin has an elevated amount of O3 instead of O2 compared to Earth. By how much exactly, I don’t know. That's for people who are more capable at math than me to do. : P
Yeah, I am not too familiar with what kind of processes could form O3. Oxygen is quite reactive, so I cant imagine a large part or even majority of the atmospherr being O3, but if anyone else knows what could explain it, please do!
@@curious_ksp_ Could happen because Kerbin receives much more high-energy radiation from its star compared to Earth, which causes new ozone to form much faster. The rate at which gases react is proportional to their concentration, so to reach a steady state, the ozone concentration in the atmosphere must be higher. This kinda breaks down if you consider how much power solar panes produce on Kerbin, but that's a problem for the next generation of scientists
My (scientific) oppinion is: We never know, it could be made of an complete unusual stuff. This is because the Kerbol universe is not like our universe in many aspects. Some planets have too much density, so you have to assume degenerate matter to fit our understanding of quantum mechanics. Moreover, if you measure the gravity below the surface you discover, that all celestial bodies have singularities at their centers. Kerbol itself couldt never ever become a star with his mass (one order of magnitude above Jupiter), especially not a G-class star. And so on...
Very true, but this channel is, in my eyes, not réally about figuring out how the Kerbal universe works, but about learning scientific concepts and apply them in a fun way. Edit: so, there is indeed a point where things break down, but that does not matter, because by that time the audience learned about things like the Roche Limit, blackbodies, scale height, etc.
I'm so sorryy! I tried to make it as understandable as possible. I don't know much of math and physics you follow(ed) in school, because that can make a big difference. Do you have an idea how I could improve?
Edit:
In the maths section, it says d^2 z/d^2t, but it should be d^2 z/dt^2.
Additionally, I have taken the time to actually make some nice captions/subtitles for this video. Apparently, about 8 to 10% of you use these. So to make my videos more accessible to other people I will do this from now on!
Assuming the same oxygen percentage as modern day earth kerbin could have an atmosphere of 66% N2 21% O2 11%Xe and 1% trace gasses :)
@@kathyk3857-- No wonder the Ion thrusters are so powerful, xenon is cheap and the KSC needs to get rid of it!
FALSE ADVERTIZING! I was FOOLED into thinking you'd be MAKING MYSTERY GOO in your kitchen but instead you're doing NERD MATH like a NERD! GREAT video though keep up the GOOD work!!!!!!!!!!!
God dammit now I want a mystery goo tutorial too!!! 😢😢😢
Hmm in you derivation, you took 'g' to be a constant, while that is a good approximation for a planet the size of earth, it's really not for a smol planet like kerbin.
Kerbin's radius is 600km and the atmospheric height is 70km which is pretty significant in comparison to 600. So the value of 'g' at the edge of the atmosphere is only about 80% of what it is on the surface.
Maybe that's why we got a weird value of μ
It is very much true what you say, so I will take a look at it, very good point! My mistake!
That's true, but surface gravity on kerbin is 1g, despite it's much smaller size. I suspect you'd get accurate values if you scale up the size of the entire solar system by about 10 or so.
Or at least more reasonable values
@@stevbe1723 But the gradient should be higher shouldn't it? In which case I think it might be good to introduce value of gravity at a given altitude.
@ImieNazwiskoOK
very good point, niw that I think about it it's probably to do with the fact kerbin is only about a tenth the size of earth, but the atmosphere isn't. The Karman line is at 100km, while on kerbin it's 70, where it would be 10 if it was to scale. I'd have to do the math to check if this is correct tho
He has unlocked the fully potential of ksp science
This guy is alive? I thought he dropped off the face of kerbin
you need to check his posts lol
Great video to watch instead of doing my math homework
Kerbin's atmosphere is actually the standard Earth reference atmosphere, scaled down to 80% height (your value is slightly lower still after accounting for that, likely because scale height varies as temperature does, and so the average is a bit lower due to the colder upper atmosphere).
The remaining atmosphere don't really fit a realistic model, though, because their actual molecular weights are actually known: 43 g/mol for Eve and Duna, 28.96 g/mol for Kerbin and Laythe, and 2.2 g/mol for Jool and Kerbol. You can get these by using the other data available from the aero GUI (you can get things like density and speed of sound there, which are actually calculated accurately), openable through the alt-F12 menu. You can also simply get it from the Kittopia dumps - actual configuration files exported by a planet modding tool (note the values are in kg/mol there).
I love watching these as a student in science and pretending that i know what you're saying 90% of the time
🙃
Kerbin is supposed to have the same atmospheric properties as Earth, but the scale height is purposefully decreased for the same reason the planets themselves are at 1:10 scale. A better approach would be to use the ratio of Kerbin and Earth scale height as the "atmosphere scale" and use this number to rescale the scale heights of other planets before doing further analysis.
But that would that would not conform to actual in game measurements. Measuring the pressures gives you the scale height. I see no reason to introduce a random ratio.
in the files for KSP 1 they are somewhat listed if you get them with Kopernicus, these being 0.0289644002914429 for Kerbin, 0.0430000014603138 for Duna, 0.0430000014603138 also for Eve, and 0.0289644002914429 for Laythe, im not exactly sure of what measurment is used here but it likely converts from a x/1000, x being mass in protons.
Probably what’s going on is that the developers just made up the values of the measurements you used to calculate the mean molecular mass, meaning your results are kinda meaningless. :(
Possible yes. The goal of the video is more about teaching about scale height, mean molecular mass and where they come from and such. Would be cool if it actually worked tho haha
Well, now i gotta finish my video using the presmat and thermometer to find the boundary layers of kerbins' atmosphere. Unless you've already done that.
Have not done it yet, dang it!
@@curious_ksp_ I can show you my notes oknwhat I've found. I've been trying to make that video for a while and just never had the time to finish it.
@@AstroHopefulBenjaminGottsch Sure! you can find my e-mail address in the channel's bio if you want to send it over there. Are you still planning on making the video, or are you fine with me covering the material (and of course crediting you) if it is something I can fit into a video?
@curious_ksp_ If you want to make it, I don't mind. I might still make something similar, but idk rn. I've just had these notes and theories written down in my computer for a while, and I'd love it if someone would share them.
If you need any help with the video, let me know. I can lend my voice or any other resources you need for it.
What if kerbins atmosphere just has a bunch of xenon?
Eddit spelling
Assuming the same oxygen percentage as modern day earth kerbin could have an atmosphere of 66% N2 21% O2 11%Xe and 1% trace gasses :)
Oddly appropriate given that Xenon is used in ion engines. It seems very Kerbal that there would be an abundance of fuel in the atmosphere.
@@TheMoonRover Maybe if we got a Geiger counter it would also be very radioactive
Math poll: we now must survive the consequences of our actions
(In all seriousness enjoyed the additional explanations lol)
There is a sweet spot of course. In previous videos is was just for a couple of seconds and now I took it to the max with about 4 minutes of pure math. I think I should aim for 2 to 3 minutes or so. But glad you liked it!
Considering that the KSP system is a 10 times scaled down solar system, to make all the maths match, shouldn't you add some multiplication to the masses that the planets are made up to make things work?
Kerbal is far too dense for its size to match the gravity shown. Can't you apply that same scaling of the mass being higher to the atmosphere?
Gravity in KSP still works the same way. We know the mass of Kerbin and the gravitational constant G, so there is no problem there. It is important to know that there is a difference in mass and density. Knowing that gravity works the same in the KSP universe, we can use the same general expressions
@@curious_ksp_Couldn't the densities of the planets be realistic if the gravitational constant was 10x that of earth?
I think the simplest answer to the question of what the atmospheres of these planets are made of is, the developers just made things up as they went along and adjusted them until they felt right
Of course, but this is more fun, it is all what ifs
If we assume Duna and Mars have the same atmospheric composition, we find that the game overestimates atmospheric weight by +91%.
Adjusted atmospheric weights:
Eve: 10.8 g/mol
Kerbin: 21 g/mol
Duna: 43.3 g/mol
Laythe: 18 g/mol
These numbers seem exceedingly sus since we know Kerbin and Laythe have significant quantities of O2 or O3, which would oxidize any reducing gases (H2, CH4, NH3). Monoatomic oxygen would give their atmospherics a red hue, not blue. Maybe they're predominately water vapor, some type of hycean planet.
Eve could be the migrated core of a hot neptunian planet, a pseudo-chthonian world. It might explain its high concentration of exotic elements like iodine.
Worth the wait! 👨🚀
really good vid!
i was watching this video and i didnt know calcusus yet so i was like: yeah i undertsnad this, even tho i dont
I think it would be cool if you needed to do certain science experiments before the game told you how high the atmosphere was, or how dense it was, or how hot it was, things like that. I also think it would be cool if you couldn't see any planets or moons until you visited them (Got within viewing range.) That would give new players more drive to send a probe or something FIRST, then send a probe that lands on the planet and its moons, and maybe keep a probe in orbit too. So that they know the latest information on the planet so they can do safer missions.
I think Kerbol habitable zone closer in but the CO2 like on earth keeps it from freezing
I think a lot of the issues from applying real-world models to KSP is thay the gravitational constant is quite different. Kerbin's surface gravity is still 1g even though its diameter is only 1/10th of Earth's.
The gravitational constant (G) should be the same I believe. So there is no problem there. The only thing is that the gravitational acceleration (g) is not really constant throughout the atmosphere as it is not as thin compared to Kerbin as Earth's atmosphere is compared to Earth. So, taking g as a constant was a mistake on my part, but I do believe G is still the same. Would be a nice video to make: determining G, as there are still people debating on what the value is apparently.
Very great video! Cant wait for more
I am a bit busy at the moment with uni, but I hope to upload the next video this Sunday!
@@curious_ksp_ Sweet, cant wait!
When solving the equation for P(z), I think you assumed H was a constant relative to z, but it's not because the temperature varies with altitude.
If you used surface temperature, then your expression is valid only close to the surface and your results may be biaised (how much ? I don't know, maybe it's a good enough approximation).
I think you could first use the thermometer to have an experimental model for T(z), then use that in your equation for P(z), and finally do what you did with the barometer.
It was still a good video, I really like the concept!
Well, the thing is that we use this same model for planets in real life like Earth, even though Earth also has a changing temperature. Though it makes sense for it to be more accurate if we take T(z) into the equation, so I will add these ideas & corrections to a stream soon or maybe at the end of a video!
The devs probably didn't even thought about or just ignored the chemical composition of atmospheres, because KSP's universe is far from being realistic, the devs' main goal was to make flights as realistic as possible, so to do it they made unimportant things less rational, like they did with planets' density. If Kerbin atmospere was made from nitrogen and oxygen (Kerbin's and Earth's g is same) it would be 100% the same as Earth's, and as we all know in RSS it ends in 140 kms. Not that convinient for toy-sized Kerbin
but can you tell me what element the mystery goo is? :)
Future video!
@curios_ksp hell yeah can't wait
I love your videos, now I want to do math again
That's amazing! Math is so cool for understanding the world around you, so heck yeah!
Mystery goo... iz verry yummy
I have to try it then!
I think maybe we should take Kerbin atmosphere composition as equal to Earth and instead recalculate molecular weights of oxygen, nitrogen and the rest of periodic table of KSP universe
Would be an interesting calibration...
Would this deal with the density problems of planets and stars, too?
Kerbin might have lots of xenon in its atmosphere. Heavy and has anesthetic properties - i.e., makes the Kerbals stupid?
Lol I love that idea
How do you change the engine throttle?
You can click on the engine in flight, there's a slider you can adjust from 0,5 to 100%
Weren't the Kerbals a plant-type species? That would explain them breathing CO2
~5:40 its possible that Kerbin has an elevated amount of O3 instead of O2 compared to Earth. By how much exactly, I don’t know. That's for people who are more capable at math than me to do. : P
Yeah, I am not too familiar with what kind of processes could form O3. Oxygen is quite reactive, so I cant imagine a large part or even majority of the atmospherr being O3, but if anyone else knows what could explain it, please do!
@@curious_ksp_ Could happen because Kerbin receives much more high-energy radiation from its star compared to Earth, which causes new ozone to form much faster. The rate at which gases react is proportional to their concentration, so to reach a steady state, the ozone concentration in the atmosphere must be higher.
This kinda breaks down if you consider how much power solar panes produce on Kerbin, but that's a problem for the next generation of scientists
@@pocarski That does makes sense if Kerbin does receive more high energy radiation, but I am not sure if it does...
My (scientific) oppinion is: We never know, it could be made of an complete unusual stuff. This is because the Kerbol universe is not like our universe in many aspects. Some planets have too much density, so you have to assume degenerate matter to fit our understanding of quantum mechanics. Moreover, if you measure the gravity below the surface you discover, that all celestial bodies have singularities at their centers. Kerbol itself couldt never ever become a star with his mass (one order of magnitude above Jupiter), especially not a G-class star. And so on...
Very true, but this channel is, in my eyes, not réally about figuring out how the Kerbal universe works, but about learning scientific concepts and apply them in a fun way.
Edit: so, there is indeed a point where things break down, but that does not matter, because by that time the audience learned about things like the Roche Limit, blackbodies, scale height, etc.
Ozone?
Oops - the developers probably didn't consider this 😂
TOO MUCH MATH!!!!!! (nice vid tho)
Yeahh, there is a balance...
oh no mistakes have been made i voted yes for the math thingy but i dont understand it D=
I'm so sorryy! I tried to make it as understandable as possible. I don't know much of math and physics you follow(ed) in school, because that can make a big difference. Do you have an idea how I could improve?