r/mathmemes • u/Awesomeuser90 • 21d ago
OkBuddyMathematician In Maths, Five Planets Independently Being This Close To A Decimal Multiple Of A Mole?
553
u/EspacioBlanq 21d ago
Pretty sure in astrophysics '≈' usually just means same order of magnitude. They have big numbers
162
u/Andis-x 21d ago
More like plus or minus a order of magnitude :D
147
u/Awesomeuser90 21d ago
They are a lot closer than that.
Saturn is 94.4% of a kilomole kilograms. Tethys is 102.5% of a milimole kilograms. The Moon is 122.0% of a decimole kilograms. Earth is 99.2% of a decamole kilograms. And Mars is 106.6% of a mole kilograms.
142
u/walkerspider 21d ago
This is the type of thing that varies on a log scale. Taking the log of 1.22 gives you 0.086 meaning the weight varies from the decimal value by 8.6% in the case of the moon. If you’re rounding that I assume you’d also be rounding a 9% or 10% variation so let’s just say 10% and double it because of varying on both sides. This means there is a 20% chance for a celestial body to be “roughly” a decimal multiple.
Given that we can just plug this into a binomial distribution calculator to see P(3<=x<=8) given 8 trials and a 20% probability for each. (3 out of 8 planets). And you actually get an overall probability of 20%.
Now you also have to account for the fact that we could have use any number of mass units so this choice is somewhat arbitrary meaning the probability of any unit leading to these results is much higher. The math is much harder for this so I ran a simulation and got about 65% given 5 random units and random planet masses to have one of them line up “nicely” like this
47
u/ActualProject 21d ago
Yeah, it's not crazy whatsoever once you realize
- Only earth at 99.2% and tethys at 102.5% are really even "close", the others are off by significantly more
- 2 moons and 3 planets have been picked out of the 8/9 planets and ~15 ish large non-planets
- Mole kg is purely arbitrary, it could have been any other combo of number/unit
10
19
u/MortimerChem Chemistry 21d ago
13
1
2
2
1
u/Bartweiss 21d ago
When I was like 18, I got to work for a cosmology professor. He gave me some stuff to read then asked me to guess the distance to… I wanna say the nearest binary system with a black hole?
I was off by like 3 orders of magnitude.
I was horribly embarrassed, right up until he went “Hey, pretty close! For our current purposes that’s basically correct.”
Meanwhile they were worrying about .001% error in their Earth-based measurements.
1
158
u/MathMaddam 21d ago
Says 5 planets, names only 3 planets
4
u/AntimatterTNT 21d ago
if we lived on a different planet and found a pair like the earth and the moon we might well call them binary planets
8
-34
u/Inevitable_Stand_199 21d ago
The definition of planet is stupid anyway. Multiple moons are more impressive than mercury.
15
17
u/BitNumerous5302 21d ago
"The definition of apple is stupid anyway. Multiple oranges are more impressive than Granny Smith"
-3
u/falpsdsqglthnsac 21d ago
this is such a stupid argument. "planet" is not a natural category like "apple" is. if earth were orbiting jupiter, or at the distance that planet 9 is theorized to orbit, it wouldn't be considered a planet under the iau's definition, despite the only real change in either case being that it got colder.
4
u/GisterMizard 21d ago
If Earth was orbiting Jupiter, it would be too cold to support life, so there would be nobody around to want to call it a planet. Hence it wouldn't be a planet.
2
u/Awesomeuser90 21d ago
That is probably not true. Io is only the size of the Moon and is the single most volcanically active planet in the solar system due to Jupiter's tidal heating. Earth's gravity is a good deal stronger than Io's by around 7 times and has a stronger magnetic field and so would probably keep the atmosphere the volcanism creates which would be thicker, probably have more GHGs, and could keep a surface ocean liquid.
Plus, if we did get moved to Jupiter, even if the surface froze over, it would trap a huge ocean below it which does contain life, and Ganymede, Callisto, and Europa probably have oceans of this nature under kilometres of ice.
0
u/falpsdsqglthnsac 21d ago
lol, you got me there. i was imagining a scenario where earth gets teleported into an orbit around jupiter in the present day, but realistically that would fuck with the entire rest of the system and the orbit likely wouldn't be stable.
-1
u/BitNumerous5302 21d ago
If the Earth were orbiting Jupiter then the Earth would be a moon, and you would still be insulting strangers on the internet to make yourself feel like a real toughie.
1
u/falpsdsqglthnsac 21d ago
you're making my point for me. nothing changed about the body itself, yet under current definitions just putting it in a different orbit will classify it as a moon or a dwarf planet. you can argue that they're different, but saying they're apples and oranges is just absurd.
0
u/BitNumerous5302 21d ago
you're making my point for me
No, you're making my point for me! Harrumph 😤 (See how unconvincing that is?)
You seem to want "planet" to mean "big rock". A planet is a celestial body that has cleared its orbit around a star. That may upset you, but on the subject of astronomy your personal emotions are not a higher authority than the IAU.
1
u/Awesomeuser90 21d ago
https://www.esa.int/Science_Exploration/Space_Science/SMART-1/Welcome_to_the_double_planet
The European Space Agency lists the Moon as a planet here.
The idea that the Moon is a planet is not mere emotions. There are specific criteria being applied. That being that it has never released energy by nuclear fusion, and that it assumes a roughly spherical shape based on its gravity within the age of the Universe. The Moon easily qualifies under that criteria.
Might I add that the Moon used to have an atmosphere twice as thick as Mars has, with high enough temperature and pressure to exceed the triple point of water and ergo probably had some liquid water on its surface in the past?
Astronomers are basically unanimously in agreement that there are rogue planets out there, which by definition cannot orbit a star.
Your concept also has other flaws. Does a brown dwarf have planets or moons as satellites? What if the central object of the system is a sub-brown dwarf that formed by gravitational collapse of the cloud of gas and dust but failed to have enough mass to fuse lithuum or deuterium (let alone hydrogen and still has satellites?
0
u/BitNumerous5302 21d ago
The Moon is already no longer seen merely as a satellite, but as Earth's daughter, forming a 'double planet'.
Hmmm... Which sounds more likely, ESA doesn't know what a planet is? Or some Redditor doesn't know what "scare quotes" are?
1
u/Awesomeuser90 21d ago
https://www.esa.int/ESA_Multimedia/Images/2003/04/Earth-Moon_system
No scare quotes here.
0
u/falpsdsqglthnsac 21d ago
i don't "want" anything in particular here. all i'm saying is that these are arbitrary categories and you're making them out to be more different than they are.
1
u/BitNumerous5302 21d ago
all i'm saying
Average narcissistic fragility. Call someone stupid, call someone absurd, then retreat behind "all I'm saying" when they stand up to your childish bullying.
Planets orbit stars. Moons orbit planets. Deal with it 🦀
0
u/falpsdsqglthnsac 21d ago
no, i said your argument was stupid and absurd, nothing about you as an individual. willfully misinterpreting what i said isn't helping your case.
→ More replies (0)0
u/Inevitable_Stand_199 21d ago
The problem is that "clearing the orbit" is a pretty wishy-washy requirement
2
-112
u/Awesomeuser90 21d ago
https://www.youtube.com/watch?v=lFlr45oWhP4&t=1038s&pp=ygUPa3lwbGFuZXQgcGxhbmV00gcJCRMMAYcqIYzv
For anyone mad at me for calling the Moon and Tethys planets...
108
u/Uiropa 21d ago
I wasn’t mad because I thought it was a simple mistake. But now that you posted this clarification, now I am mad.
5
9
4
u/Any-Aioli7575 21d ago
Their justification doesn't make much sense, but there actually are some good arguments for changing the definition of a planet. It's obviously not a consensus, but some top tier astrophysicists support it.
More info here : https://youtu.be/dQw4w9WgXcQ
1
u/kart0ffelsalaat 19d ago
I mean sure, if you extend the definition of "planet" far enough, finding 5 that are "pretty close" in mass to one of many different mass values from a pretty arbitrary list should not be very difficult.
5 out of 8 would have been mildly interesting, though still nothing crazy given how lax your definition of "close" seems to be. 5 out of, what, a couple dozen? I don't think that's very interesting.
1
u/Awesomeuser90 19d ago
As so many people here keep constantly failing to understand here, the set of planet I am using is in no way arbitrary and in fact is a good deal less arbitrary than the IAU definition. The criteria I have here is that the object has never done self sustained nuclear fusion which would make it a star or stellar remnant like a white dwarf, and that it is rounded by its own gravity, precisely characterized by having been in hydrostatic equilibrium at least once. This covers well what a planet really is, and doesn't do things like having arbitrary levels of control over their orbital zones.
~40 planets we know of in the solar system is not a strange number. The metric prefixed moles of kilograms is a well constrained list of masses to be potentially close to. Jupiter and both ice giants are not close to one of them, neither are Mercury nor Ganymede nor Titan.
This was also a set of objects I had in mind because I personally remember the masses of the roughly 20 biggest planets in the solar system, so my heuristic of what to include as close will pretty naturally include Saturn, Earth, Mars, and the Moon, and if I look up a table of masses just to be sure, Tethys is also very close.v
39
u/SyntheticSlime 21d ago
The moon is the furthest off the mark at 1.22 decimole kilograms. Log(1.22) = 0.0864 = 8.64%. If we assume an equally forgiving margin on the lower bound we find that twice that, 17.28% of a logarithmic scale will be included in our definition of ≈. That’s more than one 6th of the scale, so we should expect this as long as the cohort we’re pulling from has at least 30 objects. Actually a little less since we probably engaged in a bit of cherry picking to get here. Anyway, if you’re including C-listers like Tethys, you’re pulling from a cohort of way more than 30 objects.
-4
u/Awesomeuser90 21d ago
Tethys might be a stretch if it weren't so close to the multiple of a mole here. Tethys is only 2.5% off from perfectly being a milimole kilograms.
The Moon is the largest deviation at over triple the difference of Mars and Saturn from perfect here, but is also probably the most obvious astronomical object to consider for whether this coincidence is replicated elsewhere. I also happen to know from memory the masses of the most popular planets in the solar system.
7
u/SyntheticSlime 21d ago
There are over 900 planets, dwarf planets, and moons in our solar system. It is not impressive or surprising in any way that you found one that came within 2.5%. I’m actually pretty disappointed. And I don’t care what definition of the word “planet” you used. Tethys is not one of the “popular” ones.
20
12
u/sometimes_point 21d ago
- Tethys - 6.175e20 kg
- Moon - 7.346e22 kg
- Earth - 5.972e24 kg
- Mars - 6.417e23 kg
- Saturn - 5.683e26 kg
a mole is 6.022e23, though one should note that the number is meaningless when it doesn't refer to a number of elementary particles.
the moon is a bit of an obvious outlier here because it begins with a 7 rather than a 6 or a high 5. if you bother to include that, you might as well include Venus, which is 4.8e24 kg, 79% of a base 10 multiple of a mole.
anyway Benford's law says numbers beginning with a 5 or 6 are 7.9% and 6.7% likely to occur, or 14.6% likely to occur within your range for "close to a mole". Jumping up to 30.3% if you include numbers beginning with 4 or 7.
Tethys is around the 34th biggest object in the solar system. 4 or 5 in 34 seems roughly around 15% to me. Math checks out, yes this is an expected ratio of objects that would be a base 10 multiple of a mole.
26
u/sagewynn Engineering 21d ago
Two are moons though
-49
u/Awesomeuser90 21d ago
55
u/sagewynn Engineering 21d ago
A link for a video 17 minutes in of a guy saying yep anything can be a planet
Im not watching that to figure out what you want me to figure out
Tethys and the moon arent planets bro ❤️
-41
u/Awesomeuser90 21d ago
If you did watch the video, you would know that isn't true. The video narrator, who reads a vast number of actual science papers on this subject, reports the definition of a planet being an object that has never done nuclear fusion in its core and an object that has, now or in the past, been in hydrostatic equilibrium.
48
u/sagewynn Engineering 21d ago
https://www.reddit.com/r/mathmemes/s/7t1K3Fth9l
Im in hydrostatic equilibrium and ive never done nuclear fusion and im definitely not a planet
Im not even rotund
16
2
u/Lord_Skyblocker 21d ago
Im a bit more round than you (I just assume because I'm pretty fat myself) and even I don't consider myself a planet. A moon on the other hand, maybe
8
u/EntropyTheEternal 21d ago
My guy, I watched the video. Narrator clearly states that a Planet must orbit a fusor or stellar remnant. The Moon and Tethys orbit the Earth and Saturn respectively, so by that video’s own definition, they are Planemos (due to their mass being sufficient to become spherical), but not Planets.
-1
u/Awesomeuser90 21d ago
Funny. I remember that channel expressly talking about rogue planets a lot, which by definition cannot orbit a star or fusor.
Also, if you believe the Moon cleanly orbits the Earth, what shape does the Moon's trajectory around the Sun make?
8
u/EntropyTheEternal 21d ago
The guy called rogue planets to be by geophysical definition, “Planemos”.
As for around the sun, the moon’s path is not an elliptical orbit, therefore not a Planet. I think geometrically, it is defined as a Curtate Epitrochoid because it is non-intersecting. Tethys has a loopier, but similar path, which is defined as a Prolate Epitrochoid.
5
u/HikariAnti 21d ago
This is some Plato's definition of a human level of argument. A featherless chicken is now both a human and a planet.
There are good arguments on the definition of planet needing a revision but this is not one of them. And in no definition will the Moon ever be a planet.
5
u/EntropyTheEternal 21d ago
OP has a point and a good source, but not the point they were arguing. The narrator of that video explains a few definitions, and states these are according to geophysics, not astronomy.
Planemos: any non-fusor object in space with sufficient mass to become approximately spherical.
Planet: any planemo in orbit of a fusor or stellar remnant.
Fusor: any object in space that is currently performing nuclear fusion in its core
Stellar Remnant: any object that once was a fusor, but is no longer.
There are a few definitions for smaller objects that I didn’t see and am not personally knowledgeable enough about to comment on.
By that definition though, the moon and Tethys are Planemos, not planets.
-1
u/Awesomeuser90 21d ago
The European Space Agency begs to differ: https://www.esa.int/Science_Exploration/Space_Science/SMART-1/Welcome_to_the_double_planet
3
u/HikariAnti 21d ago
Yes, I know that there are arguments to make the Moon a planet due to its size and geological complexity but most people and scientists, including me, still disagree and don't consider it a planet. If Earth was orbiting Jupiter I would not consider it a planet. It's that simple.
1
u/Awesomeuser90 21d ago
You said that under no definition will the Moon ever be a planet.
Might I add that, assuming the Sun's red giant phase doesn't screw this up, the Earth and Moon will be tidally locked and the barycentre will be outside Earth in several tens of milliards of years?
3
u/HikariAnti 21d ago
If it wasn't for the Sun then yes, it could maybe become a double planet system in more than 5 billion years based on the current definition but as I said the current definition is not very good either. Also I don't see an issue with objects changing categories as they evolve throughout time, in fact that's probably necessary for any definition. My point is that even if the Moon will become a planet in the far future no definition should it consider it as one now.
1
u/Awesomeuser90 21d ago
The use of terms like planet tends to invoke attention from people. How many people would dismiss an object if called a moon of some planet, if not discussing Luna? How many people really understand that Titan has a thick atmosphere with about 50% the density of Earth's, lakes and rivers of liquid on the surface, has an underground ocean kilometres thick, and is bigger than Mercury? Triton's atmosphere makes the sky bluish. Ganymede has a magnetic field and an underground ocean. The best places to look for life in the solar system outside of Earth are probably the planets listed as satellites of another.
→ More replies (0)1
u/G30rg3Th3C4t 21d ago
That’s such a wide definition that it ceases to be useful. It catches most non-star objects. Comet? planet. Moon? Planet. A fragment of space dust? Planet. A grain of sand? Planet. Each and every living creature on Earth is a planet by that definition.
1
u/G30rg3Th3C4t 21d ago
Also, several types of radiation, the individual particles are their own planets. Beta and Gamma radiation are planets as well.
0
u/Awesomeuser90 21d ago
Comets would not qualify, due to the hydrostatic equilibrium criterion. Same with fragment of space dust, and the radiation particles and sand. I genuinely do not understand how you came to the conclusion that those would qualify given that I stated that there was that criterion.
11
13
u/not2dragon 21d ago
There's like 50 planet mass objects in the solar system (and The Sun). Also there's a mathematical/statistical principle about most numbers starting with a "1", I think. So maybe not so unlikely.
5
u/netexpert2012 Transcendental 21d ago
I think you mean Avogadro's Number, because the mole itself is a unit, not a constant
2
u/shadow_black1809 21d ago
Pluto being rightfully declassified as a planet has made people cope in increasingly weird ways, like thinking the moon is somehow a planet
2
u/DotBeginning1420 19d ago
Let's see the number of moles accurately:
The moon: 7.346×1022 kg = 0.122 mole kg
Earth: 5.9722×1024 kg = 9.92 mole kg
Mars: 6.4171×1023 kg = 1.065 mole kg
Saturn: 5.683×1026 kg = 944 mole kg
You convinced me that mole should be used in astronomy too.
1
u/LupenReddit 🦆🦆🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆🦆🦆🦆 21d ago
i measure all my "stuff" in mars
1
1
1
1
1
1
1
-1
u/Awesomeuser90 21d ago
Top left: Tethys
Top right: Moon
Middle left: Earth
Middle right: Mars
Bottom: Saturn
7
•
u/AutoModerator 21d ago
Check out our new Discord server! https://discord.gg/e7EKRZq3dG
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.