How do we know that Sun is a star?

Hi,
today I will shortly explain how is it that we know that Sun is a star and why it is not so trivial.


When you look up on the clear sky in night you see dots and they are said to be basically the same thing as our close Sun. They definitely shine, but not so much, they are not very warm, light up in different time than Sun, for some reason twinkle and are way smaller, even with binoculars they are still dots.

Hell yeah, they are quite small dots! Even if you take our best telescopes you will always have them so tiny! They are “point source of light”, which means that they are simply so small that from our view and practical purposes they are dimensionless.

They are huge though, most a bit smaller then Sun but still big, but so far away that they seem only as points. If even now we can not see the star’s surface as anything else than a dot, how do we know that it is the same thing as Sun?


The thought of Sun being star was there for some time. I found that already guys in ancient Greece thought that, the same idea came to the famous row of astronomers like Copernicus, Galileo, Kepler, Newton and others but they still did not have an access knowledge that would prove it.

In 1838 Friedrich Bessel measured the distance to star for a first time without considering anything about it (I guess he might have used stellar paralax but I am not sure). He found that the distance is huge, as we know today and soon we calculated that these dots are actually about as bright as Sun, also with astronomical spectroscopy scientists found out that what is happening there is also happening here. To make it clear, we do not have a “close up” image of any star, nor do we have image of any exoplanet.. for now that is simply impossible, still we can admire the cool Jupiter that Juno is taking pics of! (it is literally porn for eyes 😉 )

Dragallur

Precession

Hi,
in the last post about Polaris I mentioned precession as the effect that causes change of North and South stars. I did not really explain what is happening there so I decided to make a short post only on that topic.


There are two other good examples of objects that precess alongside Earth. Take gyroscope for example:

On the left you can see gyroscope. It consists of spinning wheel (orange/yellow) and a pin on which it stands. When you speed the gyroscope up it will be able to stand as you can see on the animation. This is basically what Earth looks like and what it does in matter of 26,000 years.

There is a thing called torque in physics. If you hold a pole on one side and something is hanging on the other side it will be very hard to lift it up. You will have to use both of your hands and one will push down and the other up to counter the torque that the objects has, that is a force causing it to rotate around one of your hands.

If you spin the thing though it will suddenly be easy to lift the thing, why? Because of angular momentum and conservation of angular momentum. If you spin on your chair and stretch your arms and legs you will slow down but if you do the opposite you will speed up. No force is acting on you only conservation of angular momentum takes place. Angular momentum is calculated as the amount of mass spread in distance from axis of rotation. If it is further away it does not need to be so fast as then the mass is closer to the axis.

When you speed the object up the angular momentum will stay conserved so you do not need to provide the torque anymore, in other words it is going to be easy to lift the thing up. If you try to change the angle in which it spins it will feel weird and it wont like it.

Even than gravity is still pushing down. If you add the vectors of the forces together, you will find out that the object will rotate –> precess. The slower it is the bigger the angle in which it precesses. If the force would be applied only on one spot all the time then it would not precess. Take a round sheet of cardboard and rotate it on tip of pencil. If you blow on the spot close to you the thing will tilt left from your point of view. Gravity though will try to tip the thing over always on the side that is lower and thus it will continously change and rotate – precess. If Earth had no tilt there would be no precession.

Dragallur

Polaris won’t be North Star forever

Hi,
today I will write about precession and what effect it has on our sky.


Polaris is the North Star or Pole Star. This means that it is close to the celestial pole. Celestial pole is a point created by expanding the Earth’s axis of rotation and piercing through the celestial sphere which is imaginary “area” where stars sit. (For Earth based observations you do not really need to take into account that the stars are in completely different distances from us)

Precession is shown by the circle on the top.

But Polaris was not always the North star. For example when the Great Pyramid of Giza was build aobut 4600 years ago, there were two shafts from the tomb added. One points towards some random stop in the sky and the other one to Polaris.. oh wait but 2600 BC it pointed to Orion’s Belt and the star Thuban in the constallation of Draco. Orion was in Egyptian mythology connected to the god of dead Osiris and Thuban used to be the star closest to celestial pole. WHY?

Orange circle shows how the celestial pole’s position will change during the next years

 

Because of precession. That is an effect on Earth by Moon and Sun. The same way as gyroscope creates a kind of cone shape with it top, Earth also rotates like this but very slowly, it takes about 26000 years to rotate once. This type of precession is also called axial precession.

On the southern hemisphere the South Star is Sigma Octantis. It has very high magnitude so it is barely visible and not very good for naked eye observation. This will of course also change in the next hundreds of years.

Because of precession astronomers have to update every 50 years the positions of stars and objects, right now we are in what is called J2000 epoch and the next one will be J2050.

Dragallur

1st picture: By NASA, Mysid – Vectorized by Mysid in Inkscape after a NASA Earth Observatory image in Milutin Milankovitch Precession., Public Domain, https://commons.wikimedia.org/w/index.php?curid=3993432
2nd picture: By Tauʻolunga – self, 4 bit GIF, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=891838

 

Isolation for long space missions

Hi,
so I was watching Michael Stevens’s first and only free episode of Mind Field where he was talking about isolation. He mentioned that there were experiments of people in closed systems to test how body and mind reacts to long term isolation.


In 1989 Stefania Follini was for 130 days in a cave without any visitors, she could only communicate via “internet”. She also had books to read and some small animals like mice. Her menstruation stopped at some point, she slept for about 10 hours and was awake for 20-25! Also during the visit she lost 7.7 kilograms. This is not the longest isolation at all.

NASA also did in the last few years isolation of 6 people for 8 and later 12 months. This was to test the team work of the people since they were closed together cabin fever showed up, but they did not have to cancel the mission. In 2007 Russians did experiment called Mars 500 where six males stayed together for even longet rime, 520 days, only artificial light as before, they brought with them books and games or dvds but they had limited connection with outside world.

https://www.nasa.gov/sites/default/files/thumbnails/image/hiseasgroup-uhi.jpg

Eight months in “cabin” (project HI-SEAS)

Michael Stevens on the other hand spent “only” 3 days in isolation, but it was a bit different. He was in soundproof small room with white walls, white and black bottles with food and water, sink and toilet. This had dramatically different effects. He had halucinations and could not really tell apart dream from reality, also at one point he was counting bottles and counted 6 instead of 9 😀

What are such experiments for? You want to know what happens to body if it is thrown out of its rhytm and mind too. When we are finally able to get to Mars we need people that are capable of staying in small spaceship for months and months.

Dragallur

Numeral systems

Hi,
today I will write a post about numeral systems and how they generally work. I already wrote about binary and decimal system, but in the last week I did some research on generally numeral systems.


So, just to recap. We normally use decimal system, this means that we use ten symbols to represent numbers, from 0 to 9. First place of number is the number itself, second position represents the number times 10 because we are in decimal system and 3rd represents number times 100 and so on. The general formula to transfer numbers to decimal system goes like this:

anbn + an − 1bn − 1 + an − 2bn − 2 + … + a0b0

a stands for the number that we see written, b stands for the system it is written in, n is the digit where a is –> 0 is the first place.

For example 1334 in the numeral system “7” would be:

4*1+3*7+3*49+1*343=515 in decimal system.

Note how you can represent easily any number in any system because of how the exponents rise in every single digit by one. If the numbers before the next digit are all full, like x9999 in decimal system or x4444 in base 5 system you always need to add only one to reach the next digit, this way there are no numbers left out.


What I really like is that if you had a machine that could change from any numeral system to other you could multiply numbers extremely easily. In decimal system if you multiply by 10 it is very easy because you just add one zero, why? Because all the numbers are “multiplied” by 10 with some exponent already and you just add one which moves all of the numbers to left. In binary system if you multiply by two you just move all the numbers by one digit:

101010111*10=1010101110      (10 is 2 in decimal) Or in 6 base system:
420351234*10=4203512340   (10 is 6 in decimal)

You are basically multiplying by “10” though you need to remember that the number is still in that system.


What about rational numbers? The stuff behind point?

I was really wondering about this and Wikipedia helped out! The exponents are simply negative as in the example below (binary number 10.11 to decimal system):

1×21 + 0×20 + 1×2−1 + 1×2−2 = 2.75

First place –> exponent 0
Second place –> exponent 1
First place behind point –> exponent -1Second place behind point –> exponent -2

Thats it for today.

Dragallur

Book review 13) Dangerous women

Dangerous Women 2013-1st ed. cover.jpg

Hi,
when I was on winter vacation I finished another book. This one as you can see higher is called Dangerous women.

Book: Dangerous women

Author(editors): George R. R. Martin and Gardner Dozois

Genre: Science fiction/Fantasy

Pages: 784


This is book that was edited by the two people above. Otherwise it is written by 20 people who contributed with their short stories. While all stories revolve around different time and different people they have one thing in common, they are about how women are dangerous.

The book was great. I can pick about 1 or 2 stories that were kind of weird and I did not really understand them but otherwise, good job.

For example 1st story is about young woman who is trying to escape because there is lot of money promised for her head. 3 men catch up with her in streets of empty village, the poor guys end up horribly.

Other story is about women that has Alzheimer and her son wants to put her in old folks home, that one was quite impressive. One speaks about queen in exile or post-apocalyptic world where most women can not have children due to some virus.

My most favorite one was by George R. R. Martin.. he also wrote Song of Ice and Fire which is my favorite series and this short story was about Dance with Dragons, war that happened way before SoIaF did (130 years or so). The one that I will share with you is different one though, it is called Shadows for Silence in Forest of Hell (translated by me).

It tells story of a widow that takes care of her children and owns inn that is very important place for anybody moving around that area. She lives in Forest of Hell which is a place that is full of shadows, everybody seems to become shadow when they die. These shadows are scary but harmless if you do not break one of three rules:

Do not run
Do not make a fire
Do not spill blood

If you provoke them you will probably die. Once they touch you, your flesh dries and dies. Only thing that works against them is silver and silver has HUGE value. If it is not late you can even cure the wounds using silver dust.

This inn is of course protected by silver because the shadows are everywhere. At the same time Silence (the widow) does not have much money and she is in debt to one guy from outside of this creepy place. To feed her children and keep guests save she catches thiefs and criminals and then through the person that she is in debt with she brings them to justice earning part of the money for their head.

Once such a group of well-known criminals comes into her inn. She lets them eat there but mixes potion that will make them weaker into their meal. (The Forest is a good place for such people to live in since there are not many authorities) In the night she tracks them down and with the help of one of her older daughters she takes them all down without catching attention of any shadow, though it is quite close. When they move the bodies, mostly suffocated people, they clash with a group that steals these bodies which is basically fatal for Silence as she knows that she is basically out of money. With trick she gets them back but one of the enemies scratches softly the neck of her daughter which makes the shadows crazy. In the end the daughter almost dies and she needs amputation of arm and leg.. Silence is also able to get rid of the person that was blackmailing her.

Amazing, I loved the plot.

The only thing that I found a bit annoying was that there were two stories with basically the same setting, the one with Alzheimer and one with old women taking care of their mum who has dementia.. but hey, you can not have all stories bringing completely new stuff!

Dragallur

The picture source: By Uploaded by TAnthony, from Amazon.com. Digital scan of book cover; copyright maintained by publisher or artist, as applicable., Fair use, https://en.wikipedia.org/w/index.php?curid=41143558

 

 

 

Orbital period

Hi,

in today’s short post I will write about orbital period of planets, more accurately synodic and sidereal period.


In the post about year and how difficult it is to determine how long it is, I mentioned that there are some ways you can measure the time it takes for planet to orbit star.

Sidereal period is the time it takes for Earth or other object, orbit once with respect to distant stars.

Now distant stars are great because they tend to be on the same spot most of the time. For example on the Voyager plague there is a map to show the position of distant pulsars, why? Because such things are stable, easy to see and far away. For year we use stars in Milky Way which is still fine, most move by fractions of arcseconds every year which is something you can not notice with eye and has some effects in thousands of years.

Sidereal period of Earth around the Sun is 365.25636 days. (I wonder if you could talk about something like sidereal period of Sun around the center of Galaxy, probably yes)


Synodic period is about two bodies orbiting Sun for example. It is the time that it takes for the two objects to get to same position. So if Mars and Earth are right behind each other (which is called opposition), synodic period is the time it takes for it to happen again. Now of course both planets orbit and the faster one (the one closer to Sun) always has to make at least one revolution. When that happens it just needs to catch up with the slower planet. With this simple thought you can come up with equation that lets you calculate the synodic period:

1/S=1/P-1/p

(lower case p is the sidereal period of the object with longer period)

Thats about it for know, enjoy your winter holiday while/if you still have it!

Dragallur

Book review 12) Thing Explainer

Hi,

Cover of the book Thing Explainer

Randall Munroe is a great guy. Creator of XKCD (totally free nerd comics) and the author of What If which you can also read on the internet maybe only some parts… Now one day about two weeks ago I noticed in our school library that they bought his “new” book Thing Explainer. I wanted to buy it earlier but I found out that it costs like almost two new books and was quite discouraged (and I did not have the money anyway). So for some reason the people in the library bought it and I have read it in few days.


Book: Thing Explainer

Author: Randall Munroe

Genre: Science

Pages: dunno

Rating: 10/10


Thing Explainer is a book that explaines complicated stuff in simple words, simple means ten hundred most used words. Great idea I admit. Randall says that when he was younger he purposefully used complicated words so that nobody thought about him, that he did not know them, but in this book he does not need to care about it.

Inside you can find explanations of: Saturn V (Up Goer Five), Keyhole (Shape Checker), Periodic table, Sun, Washing maschine, Car and many many more. There are I think two or three double pages which extend the books already giantic size to double and the page about Skyscraper (Sky toucher) is of the format A2

1000 words is not much. Most technical terms do not exist and even if you know them IRL (in real life) you may find yourself wondering what some things mean. “Fire water” took me some time indeed. Or helium is “kind of air that makes your voice funny”.

Basically there is no objection from me, hopefully the author will write 2nd part since there is lot of stuff outhere that still needs to be covered!


Here is in the same style Einstein and Theory of Relativit explained.
Here is Up Goer Five.

This video is from Minute Physics about getting to space:

Dragallur

Do we see in 3 dimensions?

Hi,
its been quite long time since I wrote about dimensions. Just a quick recap since people do not click on links much: 0th dimension is point, 1st dimensions is line, 2nd dimension is plane and 3rd dimension is space. We are talking about spatial dimensions, another thing is atime dimension, but that is not important here.


So I got into this argument if humans see in 3 dimensions or not, I got no clear conclusion though so I am just going to discuss it here. We live in 3 spatial dimensions, proof, cubes exist. How do we see though? We can see cubes but I would argue that we see in 3rd dimension.

  1. Retina does not capture depth, it is 2 dimensional detector so we simply can not have a 3 dimensional vision.
  2. We have two eyes though, lot of people seem to like to point this out. With second eye you have what is called a stereoscopic vision.. the second eye has little bit different point of view and when brain combines it stuff gets depth. This does not mean that we see in 3D though. Still it is just two 2 dimensional pictures put together. Brain interprets this picture as 3 dimensional and based on experience judges distance. Also colors and shades can help us with that.

    File:3D stereoscopic projection icositetrachoron.PNG

    This is stereoscopic picture, disalign your eyes and match the pictures so you see 3 of them.

  3. You can draw anything you see on piece of paper and it will be exact representation of what you see, all angles same and so on. This I think would be impossible if you actually wanted to transfer 3D image to 2D plane because by definition 3D space is made up of infinite 2D planes put on top of each other. Same as you can not take infinite picture and store it in 1D line.
  4. If we could see in 3D we would see all angles as they actually are. If you look into corner you do not see 90° angles though because you remember the way that walls work you know that they are there.

Thats about the arguments I have, hope you enjoyed reading,

Dragallur

Sunset elevator

Hi,
today I will write about one particular physics problem that I was solving during weekend. It was pretty hard, but quite interesting set-up. (It is originally from Czech physics seminar called Fykos)


You and your boyfriend/girlfriend are sitting on a beach watching sunset. Luckily you are prepared to extend the romantic moment with elevator that will drive upwards. How fast does it need to drive for you two to be able to watch sunset continously?

Normally sunset related problems are about plane or car driving and how fast does it need to be for you to watch sunset all the time. That is freakin’ easy because you just need to drive at the speed that the Earth turns in your place. For Prague this is roughly 300m/s which is about the speed of sound.

This problem is way more unique. I do not know if my solution is correct since the people from seminar did not release solutions yet.

Basically you are standing on top of circle that is rotating at 300 m/s or also 0.00417°/s. You are soon leaving place from which you could see the sunset so you need to go up. The problem is that you are not actually going directly upwards to this place but as Earth turns your elevator rises in a line perpendicular to tangent of Earth at your paricular location, check out this desmos graph which helped me a lot to understand it (my creation): https://www.desmos.com/calculator/oftnm48s3b

Here is a picture though it is better to go on the original link which is very interactive:

(Check out complete end of post for explanation of picture) What does it mean for you in practice? In one hour you will be going almost 100 m/s. After 6 hours you will certainly be dead because the acceleration will kill you. At this point Earth would still be bigger on the sky though you would already be 500,000 kilometers away. After another three minutes from what I have considered last time you would be almost 3 million kilometers away and Sun and Earth would be the same size, at this point you would also ride in 1/3 of speed of light. But this journey still continues. After another 13 seconds you would go faster than the speed of light with acceleration of 14 km/s. There is not much time left but lets see.. 10 million kilometers would be reached by next 9 seconds. 5 seconds later you would go in freakin 10 million kilometers per second if it would be possible. One second before the journey would end you would reach 0.5 of AU. Soon after you would divide by zero which is dangerous[1]. After exactly 21600 seconds which is 1 quarter of day your elevator is perpendicular to this horizon, which sucks.

I bet your girlfriend/boyfriend would not be so happy about this trip though the first few hours would be amazing.

Dragallur

Explanation: black circle is Earth. Green line is elevator that with you turns left, after 21600 it will go 90 degrees. Red dot is the spot where you need to be in order to see sunset. Blue line is the original horizon.

[1]Do not be discouraged by only 0.5 AU. In the next mili and microseconds you would whizz through whole Milky Way and Observable universe as you would reach infinite speed.