Planet classification

Hi,
here it comes, here it goes. Today I will write about planet classification since I want to start to write about dwarf planets. This post will be little similar to Stellar classification but you will see that for planets there are not those classes for size differences. The most important thing is of course to know what is planet and what is not, which I will explain.

Ok in the year of 2006 International Astronomical Union anounced that Pluto is not a planet. It`s been almost ten years but I still know people that can not get over it. I know this picture is sad (and not to scale).

For now the definition go as follows:

Planet has to be orbiting Sun
Have to be generally spherical
Has to have enough strong gravity to clear its orbit.

So the thing is that Pluto can only check first two criteria but not the third so such a object is called a dwarf planet.
Also you can see that planet is only object that is orbiting Sun which as it seems is not any exoplanet. This means that those 2000 planets that we found are just a huge objects, but for the official definition they are not planets either. And.. because they are so far away, it can not be known yet if they are spherical or not.

You can see that those definitions are not very good but luckily one guy on some conference proposed new definition which is not yet agreed to be new one but anyway International Astronomical Union will have to make a better one which will be probably very similar to this:

Planet has to be orbiting at least one star or the remains of one. (So yeah, stuff that is orbiting white dwarf is still a planet if it meets the other criteria. Read about multiple star systems)
Planet has to have a clear path to itself. (Sorry Pluto.)
Planet has to have mass lower than the mass of Jupiter. (This is good so we dont accidentaly name brown dwarfs as planets.)

Now we know what are planets. Lets move what are dwarf planets. Those are the objects that are not able to satisfy the third rule, their orbit around Sun is not clean. Dwarf planets are: Ceres, Pluto, Haumea, Makemake, Eris and Sedna for example.There are some other candidates also.

There is type of objects that are called minor planets. Those can be at the same time dwarf planets, like Ceres. The number of minor planets is increasing by very large amount every month. Only few of them are named, large part is numbered and there is rest for which we dont even know exact orbit. Together there are almost 700,000 minor planets.

I did not find exact definition but minor planets should be those that are orbiting Sun, that is about it. They dont have to have any particular size, shape and their path can be trafic jam of asteroids. Actually yes, the asteroids are minor planets and also all the trojans and so on.
Above you can see all the types of objects that can appear in our Solar System except Sun.
Thats about it, I will definitely make post about or more about asteroids, comets and of course I will be continuing with moons.

Dragallur

Pictures are from wikipedia pages: IAU definition of planets, Minor planets and Dwarf planets and the first one is from this page:

Turn your brain into supermassive black hole

Hi,
here it comes here it goes! Today I am writing probably the last post from Brazil since I am leaving in Tuesday. Maybe tommorow after seeing Christ in Rio, I will be able to write another one.
Anyway, here comes the promised post about Ackermann function.

Ackermann function is a function with two inputs and it is growing extremely fast. To see the results it is best to make a table. Ackermann
function is written like this: A(m,n).
There are few types of Ackermann function because some people made their modifications of it to fit their plans. Here I will mention the most famous one.
$A(m, n) = \begin{cases} n+1 & \mbox{if } m = 0 \\ A(m-1, 1) & \mbox{if } m > 0 \mbox{ and } n = 0 \\ A(m-1, A(m, n-1)) & \mbox{if } m > 0 \mbox{ and } n > 0. \end{cases}$ So lets see what this function means:
A(m,n) is the input of this. If m=0 then you will make n+1 and find it in the table which is below.
If m is bigger than 0 and n=0 then you will call Ackermann function again with m-1 and n=1.
Last one, when you have m>0 and n>0 then you call the function again with m lowered by one and n will be defined by another A function which obeys

m\n	0	1	2	3	4	n
0	1	2	3	4	5	$n + 1$

the rules again. Lets see the table. This is the first row which is extremely simple. M is the vertical axis. So when the arguments are A(0,0) then you go as follows: m=0 which means that you higher n by one which is 1 and that is the result.

If A(3,2) it gets very messy: here you go.
A(3,2)
A(2,A(3,1) — because n and m are higher than 0 you lower m by one and then you call another function with n lowed by one.
A(2,A(2,A(3,0) — both are still higher, so you do the same thing again..
A(2,A(2,A(2,1) — change the function from A(3,0) to A(2,1) because n is 0 according to rule above
A(2,A(2,A(1,A(2,0)
A(2,A(2,A(1,A(1,1)
A(2,A(2,A(1,A(0,A(1,0)
A(2,A(2,A(1,A(0,A(0,1)
A(2,A(2,A(1,A(0,2)
A(2,A(2,A(1,3)
A(2,A(2,A(0,A(1,2)
A(2,A(2,A(0,A(0,A(1,1)
A(2,A(2,A(0,A(0,A(0,A(1,0)
A(2,A(2,A(0,A(0,A(0,A(0,1)
A(2,A(2,A(0,A(0,A(0,2)
A(2,A(2,A(0,A(0,3)
A(2,A(2,A(0,4)
A(2,13) — I skipped lot of the steps because it is such a mess when you have to do it whole again but it equals 29.
=29

Values of A(m, n)
m\n	0	1	2	3	4	n
0	1	2	3	4	5	$n + 1$
1	2	3	4	5	6	$n + 2 = 2 + (n + 3) - 3$
2	3	5	7	9	11	$2n + 3 = 2\cdot(n + 3) - 3$
3	5	13	29	61	125	$2^{(n + 3)} - 3$
4	13 = ${2^{2^{2}}}-3$	65533 = ${2^{2^{2^{2}}}}-3$	2⁶⁵⁵³⁶ − 3 = ${2^{2^{2^{2^{2}}}}}-3$	${2^{2^{65536}}} - 3$ = ${2^{2^{2^{2^{2^{2}}}}}}-3$	${2^{2^{2^{65536}}}} - 3$ = ${2^{2^{2^{2^{2^{2^{2}}}}}}}-3$	$\begin{matrix}\underbrace{{2^2}^{{\cdot}^{{\cdot}^{{\cdot}^2}}}} - 3\\n+3\end{matrix}$
5	65533 = $2\uparrow\uparrow\uparrow 3 - 3$	$2\uparrow\uparrow\uparrow 4 - 3$	$2\uparrow\uparrow\uparrow 5 - 3$	$2\uparrow\uparrow\uparrow 6 - 3$	$2\uparrow\uparrow\uparrow 7 - 3$	$2\uparrow\uparrow\uparrow (n+3) - 3$
6	$2\uparrow\uparrow\uparrow\uparrow 3 - 3$	$2\uparrow\uparrow\uparrow\uparrow 4 - 3$	$2\uparrow\uparrow\uparrow\uparrow 5 - 3$	$2\uparrow\uparrow\uparrow\uparrow 6 - 3$	$2\uparrow\uparrow\uparrow\uparrow 7 - 3$	$2\uparrow\uparrow\uparrow\uparrow (n+3) - 3$

Here is the rest of the start of the table. It increases rapidly since it repeats over and over again (this is called recursion). You see that you have to use Knuth`s up-arrow notation.
Now you see why A(G64,G64) is such spawn of hell.
The reason for Ackermann function to exist and to be so famous is that it is one of the first functions that are used in computability theory. It is the theory which asks what means that the function is not computable and how much not computable it is. Computable functions are those for which we can find some algorithms, and algorithms are very important. For example in computations.
It seems for example that there is no computable function for finding prime numbers or at least no efficient one.

Dragallur

Turn your brain into black hole

Hi,
here it goes, here it comes! Today I want to write about Graham’s number which is very interesting number and highest number which has some usage in mathematics.

Ok first of all, what is its purpose?
Imagine square where all vertices are connected. You can connect them by two colors, blue and red. You are trying to avoid one special pattern which you can see behing the mathematician Ron Graham who invented this number about which I will talk in a while. So those points can not be connected by single color the thing is that when you increase the dimension it is little harder (you already now everything about dimensions if you read my last post).
When you have 3rd dimension as you can see on the right there are 8 vertices.
This means that there are 28 lines between those dots.
Yes it is possible to avoid the special configuration. When you continue to fourth dimension you can still do it but here comes the problem. In fourth dimension there are 2^120 possible ways to color this cube. This is such a large number that no computer can solve it, in decent amount of time. Now you need to make some better way to solve it. Through some better way which I dont know mathematicians got up to 13th dimension, now they dont know maybe it is possible maybe not but the number when we are COMPLETELY sure that it is not possible is Graham’s number.

To show you how large is Graham’s number I first of all have to explain Knuth’s up-arrow notation.
3+3+3=3*3
3*3*3=3^3
3^3=3↑3=27
That’s about it when you have one arrow. It gets better when you have two:
3↑↑2=3^3=27 , easy.
3↑↑3=3^3^3=3^27=over 7 trillions $\begin{matrix} a\uparrow\uparrow b & = {\ ^{b}a} = & \underbrace{a^{a^{{}^{.\,^{.\,^{.\,^a}}}}}} & = & \underbrace{a\uparrow (a\uparrow(\dots\uparrow a))} \\ & & b\mbox{ copies of }a & & b\mbox{ copies of }a \end{matrix}$
Lets see three of them:
2↑↑↑2=2↑↑(2↑↑2)=2↑↑4=2^2^2^2=2^2^4=2^16=65536
2↑↑↑3=2↑↑(2↑↑(2↑↑2)=2↑↑65536 $\begin{matrix} a\uparrow\uparrow\uparrow b= & \underbrace{a_{}\uparrow\uparrow (a\uparrow\uparrow(\dots\uparrow\uparrow a))}\\ & b\mbox{ copies of }a \end{matrix}$
Easy it continues and it gets hella huge.
So when I found out that Graham’s number needs arrow notation to be written I was like: “Easy, there will be few arrows, arrow notation is such extreme tool.”
Then after I found out how big is Graham’s number I was just like: “Oops!” You will se why.
So lets define the number g1
g1=3↑↑↑↑3
=3↑↑↑(3↑↑↑3)
=3↑↑↑(3↑↑(3↑↑3)
=3↑↑↑(3↑↑(3↑(3↑3)
=3↑↑↑(3↑↑(3↑27) i think that this is enough for ilustration.
now lets define g2=3↑↑↑↑↑↑↑…3 number of arrows equals to g1

Surprised? We are not even in beginning.
g3=3↑↑↑↑…3 number of arrows equals to g2 … so you know the process, this continues up to g64 which is Graham’s number.

Ok this is extremely large number and to remind you it is number of dimensions, which means that the combinations are even much higher, not kidding.
The Graham’s number has real meaning but I am not really able to understand so if you want to check it, somewhere in the video Ron Graham explains it. Also Numberphile has some other videos about it so check them out.
Next time I will write about Ackermann function. After that you will get this XKCD joke:
Thanks for reading,
Dragallur

PS: I found lot of people trying to liken stuff to Graham’s number. Dont even try that, you wont get very close.

Dimensions

Hi,
Here it goes, here it comes! Really long time (means few years) I was wondering about dimensions. It started when I was watching videos like: how to imagine higher dimensions, what are dimensions and so on. At the beginning I did not understand any of it.

As time went on I accidentally bumped into black holes and later on into wormholes (actually this post has some mistakes as for example it is saying that time is fourth dimension.) which should connect space through higher dimensions and make a shortcut through Universe (picture is from here).

Ok first of all lets clear out some things. This post can have some mistakes, but I hope that there wont be any.
Second, fourth dimension is not really a time. The thing is that time does not work like space dimensions. Space dimensions also known as spatial dimensions, are the dimensions in which we can move forward, backwards, horizontaly, verticaly.. like in our world. Time is not so free, it runs just one direction and it is special type of dimension called the temporal dimension.
We live in 3+1 dimensional world.

Ok so what are those normal spatial dimensions? Well I will start with the most simple dimension, 0th dimension.
On the picture you can see 0th dimension, pretty fun huh? It is point, and point has no volume by the way, this one is just enlarged. In 0th dimension you can not do anything, I am serious.

The problem is that if you lived in 0th dimension you would not be able to imagine 1th dimension because it would be like imagining new color which you never saw.
When it comes to creating higher dimensions ALWAYS you have to copy the lower dimension infinite amount of times. This means that if you want to have 1st dimension which is line you have to line up infinite amount of points from 0th dimension. As you probably know from math there is infinite possible places to place point on line.

So here comes the 1st dimension which is line made up of infinite amount of dots. On line you can place all of the real numbers.
In the movie Flatland, which is fun movie you watch the line creatures to move back and forth because they live in 1st dimension.

I dont need to put any picture of second dimension, since you see it every day, on your computer, book on board in school.
To create 2nd dimension, again you need infinite amount of lines next to each other to create plane. Now 2nd dimension is pretty useful, for lot of stuff from: graphs, photos, any text, movies… you know I could continue for long time.
So the standard object of 3rd dimension is cube. Again when you want to create it you need infinite amount of planes because they dont have any thickness.
Well now we are in our world but of course I can continue for the fourth dimension.

Ok the problem is with imagining 4th and higher dimensions on their dimension. By this I mean that I can easily draw on plane any dimension but it is just impossible to imagine 4th dimension since in our world we dont have space to expand it into. Over time I found some things that can help you anyway.

In one episode of Futurama Doctor says: if you looked from fourth dimension to third you would see inside of this egg as when you look from third dimension to second and you can see egg’s inside. I would say that this is little mind bending. In fourth dimension there is direction in which you can move but from here we can not imagine the direction since it seems that we can already move anywhere.
Finally here comes the drawing of dimensions: Always the angle between new dimensions is 90 degrees. In

third already you have to imagine it because if you would measure the angle on the plane you would have about 60 degrees. But it continues and the angle is still 90 even if it seems impossible. 5th dimensions is just expansion of all of those dots to another direction and so on and so on (the picture is from here).

Actually from plane you can see 3rd dimension with pretty neat trick that I found some time ago. On the next picture there is 3D object in 3D, 2D and 1D. To see the first one in 3D you have to look as you would look behind it so there are fourth of those objects on row. At one point those objects would be only three because two would be over each other. If you are precise enough you can match them well enough to see the picture in 3D.

Well this is about it. (The last picture is from here.)
If you want to read about more time dimensions, check this page.
The person there assumes that with 2 time dimensions you would be able to turn around in time as you can turn around here.

Dragallur

WTF? A conspiracy? 5) Not parallel shadows

Hi,
here it comes, here it goes! Another debunking of the Moon hoax. As for now I already covered 4 “arguments” and you can check them on my other posts, just to see how silly they are.
Flag flapping in the breeze. Deadly radiation of Van Allen belts. Copied backgrounds of NASA images and Erased stars on the pictures + the prologue of those series.

So today I continue and this time I chose the argument of non-parallel shadows on the pictures by NASA.

As you can see on the picture which was taken on Moon the shadows seem very strange. The yellow lines clearly show that the light is much closer to the objects and the Sun would not cast such shadows. This clearly means that those photos are faked and we never went to the Moon.

Ok here comes the fun part again. The hoaxers forgot on thing named: perspective.
The thing is that the Moon is 3D while the photo is just two dimensional. This makes some strange things such as those shadows. Actually I found one debunker to have on his page this photo so, thanks to him. If you viewed this from birds view you would clearly see that those shadows are parallel but from ground and on picture it seems as the shadows head into different directions, so if you dont believe that the Earth is hoaxed you should be convinced. If not you can try it for yourself. Plus if there is some downhill it can be distorted even more.

Thats about it. Thanks for reading.
Dragallur

SpaceX

Hi,
today I will write about Space X which is a first privately founded company which launched and recovered rocket from low Earth orbit. Also SpaceX was the first private company to launch rocket for ISS, the Interational Space Station.

It is company which was created in the year of 2002 by Elon Musk who is a billionaire and also the man behind PayPal and Tesla motors. Elon Musk Net Worth
The company goals are:
Make a much more cheaper space launching and traveling. Already competition had to lower all kinds of things that need to be done for launching because SpaceX is creating everything on one and only site in California which makes it lot cheaper. Musk thinks that he can make the launch of one kilogram for 1,100 dollars.
Another goal was stated by Musk in the year of 2011 that he wants to take people to Mars in 10-20 years. And later on to create self-sustaining colony.
In June 2015 SpaceX asked goverment for permission of project which would access internet to rest of planet.
For now the company has signed contract with NASA so that they will send rockets to ISS with supply and they will have there safe vehicle if something went wrong. Also this would enable 7 people to be present at the same time on ISS.
Now SpaceX is developing Dragon V2 which is manned version of Dragon spacecraft. It should be the safest spacecraft built.

Dragallur

Space NEWS #4

Hi,
last time in Space NEWS I was writing about SLS, the Space Launch System. Today I will add some more stuff because NASA finished simulations of booster separation.

So first, those boosters are those things you can see on the right. They are the first part of rocket to be used up when its launched. The problem is that something can happen when they are separeted from the rest of rocket (the separation must be precise so it wont move with the rest of the rocket).

There had to be about 22,000 different simulations to see if everything is ok. Those simulations were made by the supercomputer Pleiadas (like the constellation). Each simulation took about 200 hours and together with some other simulations it took 12.7 million hours Simulating SLS Booster Separation to complete it (there were also overflow more precise simulations. Each of them took 20,000 hours and there was almost 400 of them). Omg really? On the left is one of those simulations. The violet, red and orange thing is the shockwave. On the end you can see the separation of boosters.

Dragallur
EDIT: Those 12.7 million hours were divided between 400 Intel Xeon Nodes, otherwise it would take over half a million days to complete it.

Pictures from: https://www.nasa.gov/ames/image-feature/simulation-sls-booster-separation AND “Two Space Shuttle SRBs on the Crawler transporter” by Photo credit: NASA/Ben Cooper – http://mediaarchive.ksc.nasa.gov/detail.cfm?mediaid=49261. Licensed under Public Domain via Commons – https://commons.wikimedia.org/wiki/File:Two_Space_Shuttle_SRBs_on_the_Crawler_transporter.jpg#/media/File:Two_Space_Shuttle_SRBs_on_the_Crawler_transporter.jpg

Planets of our Solar System: Neptune

Hi,
here it goes, here it comes the last post for the series: Planets of our Solar System, maybe if you discover new one I will mention it.
Ok so today I am going to write about Neptune, the eight planet of Solar System, you will see how much we now about thing which is so far away, lets go!

As I said, Neptune is eight planet and the last once since Pluto is no longer considered to be planet (I will make sure to write epitaph about him).

It was discovered not by accident but by math. When Uranus was discovered and its motion across sky was calculated astronomers saw that it is not on the place where it should be. This was because of Neptune which is influencing Uranus. This happened in the year of 1846 and was discovered by Johann Gall and astronomy student Louis d`Arrest.
Neptune was named after Neptune, the roman god of sea. Greek equivalent is Poseidon of course.
Neptune orbits at the distance of 4.5 billions kilometers. Its radius is 25,000 km and he is little smaller than Uranus but much denser.
He gets 1\800 of the Suns energy as we do and as other gas giants in our Solar System he is radiating more energy than recieving, 2.7 times more.
Interior of Neptune is similar to Uranus`s.
The core makes up two thirds of the planets radius and is made up of rock, ice and some iron and nickel silicates.

Mantle is similar to Uranus`s and there are also probably small diamonds created from methane molecules.

Atmosphere is made up of hydrogen and helium but because Neptune is ice giant there is only 80% of hydrogen and 19% of helium. There is also methane which creates the same effect as on Uranus, it absorbs red light which makes the planet blue. Atmosphere also makes 5 to 10 % of planets weight.
The atmosphere is much more violent than Uranus`s. There are frequent storms and as far as I know they (not counting solar winds :D) are fastest in Solar System.. 2000 kmh. When Voyager 2 flyed around Neptune it saw a giantic storm in its atmosphere. It was similar to Red Giant Spot which is on Jupiter. It was called Dark Giant Spot and it soon dissapeared but some other stormy features appear often (You can see it on the picture).
On the surface is temperature higher than on Uran, about -213°C.

Neptune has magnetosphere and it is as strange as the one on Uranus. It is moved by about half of planet`s radius which astronomers think can be feature of all ice giants. Neptune also has aurora.

There are 5 known rings of Neptune and 14 moons about which I will talk in future episodes of Moons of our Solar System, so stay tuned.

Dragallur

Pictures taken from wikipedia and http://astronomy.wikia.com/wiki/Neptune_Project and http://spaceplace.nasa.gov/review/solar-system-scramble/scramble-text.html

WTF? A conspiracy? 4) Identical backgrounds

Hi,
with one day pause I am coming with post about conspiracy theory of Moon landing. Yes again there is another “argument” by those hoaxers which I am going to crush to pieces thanks to awesome Phil Plait and his Bad Astronomy webpage.
This time lets focus on identical backgrounds on two images which were surely taken from very different distances and they must be faked because NASA was too lazy and they used same background twice.

Ok so here are the pictures from Apollo 15. On the first one where you can see more of those mountains there is no moonlanding apparatus and there is this rocky ground. While on the other there is the opposite but on both pictures there are same “backgrounds” used.
Fine here comes the debunktion. On Moon things stuff does not behave as one would execpt. On Earth we can judge distances by things around because we already know their size from experience, like house, shrub or car. But we dont have these things on Moon.
Once I was looking into the heart of Black Canyon in USA. It was one of the best things I have seen in my entire life and the same thing happened, I was not able to judge the distance.. it looked like that the bottom is 200 meters below me, but bottom of Black Canyon can be almost 700 meters (on the picture you can see the tallest cliff in Colorado, it was taken from wikipedia, thanks).

So there are no things by which you could judge the size of stuff which means that you dont really know how far it is + we also judge by the blur of the air. When there is stuff far away it is much less visible but on the Moon there is everything perfectly clear and you dont know if the rock is meter, 2, 200 or 10000 far away. Here is nice video which will blow your mind and show that you simply can not trust your eyes.

This means that the first picture is probably much closer to the mountains but still very very far away since they are on both pictures of identical size.

Dragallur
Check out the debunking of: Flag, Stars. And the prologue.

Space NEWS #3

Hi,
today I am bringing third space news. This time I will talk about journey to mars and especially SLS the Space Launch System.

Ok it is planned. What? The journey to Mars. But sorry guys I can not tell you exactly when, actually noone know but it is planned by NASA to about 2030. Damn so far away, anyway I am looking forward to see faces of those none believers of moon landing when we will land on Mars.

So there is lot of stuff scientists have to do. There are many issues that need to be solved, and yes right we dont know how fast we can solve them.
But today I want to mention the SLS. Because Saturn V which was the rocket that took us to the Moon is not strong enough and not modern enough we need something better which will be lighter, faster, with more space for stuff to carry and still not too large.
The main problem with older rockets was that more than 90% of the weight was fuel which is not something that NASA wants to repeat, rather they are working on some new technologies.
For example almost one year ago in December NASA tested Orion spacecraft which will on top of SLS carry astronauts to Mars some day. Orion orbited succesfully Earth two times.
Lot of stuff is happening around journey to mars so I will try to update on this topic.

Dragallur
Picture thanks to NASA.
PS: hope those guys in wordpress will return the function “link to existing content” because right now it is pretty anoying to find every post I want to link to on my blog

Science and rationality

Universe and everything

Month: November 2015

Planet classification

Turn your brain into supermassive black hole

Turn your brain into black hole

Dimensions

WTF? A conspiracy? 5) Not parallel shadows

SpaceX

Space NEWS #4

Planets of our Solar System: Neptune

WTF? A conspiracy? 4) Identical backgrounds

Space NEWS #3

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