How long is a year actually?

today I will write about a year. The thing is that as in many other subjects when you look down into the simplest things you might find that they are not as simple as they seem. So how long is year? 365 days? 366 days?

You very well know that every 4 years we have 1 extra day in February. You might also know that this is because year is not 365 days long exactly but roughly 365.25 .. its important to say roughly because it is not perfectly true and it matters how you define one year.

First lets see how we define one day. One would say that it is the time that it takes for Earth to rotate once. Problem is that we need to define some object to compare it to, some ground, some reference point. It might be the Sun, but Sun is too close and since we go around it, this would change the length of the day.

Sidereal day is the day that is defined as a rotation of Earth around its axis compared to very distant stars that are relatively stable. 23.9344699 hours… that is pretty close to 24 that we use, but it is not what we use.

The thing is that we decided to use what is called solar day, which is in fact compared to Sun. As Earth rotates around its axis, it also rotates around Sun, which makes the solar day different length.

This is how the effect looks like. You need to turn Earth n.2 by little bit more since it moved around the Sun too.

Problem is that the length of solar day changes since our orbit is sligthly elliptical and when we are closer to Sun we are faster which means that the solar day is shorter and there is more time needed for the same spot to face Sun again. This effect adds up to almost 365.25 solar days in a year. If it was so simple we could just add one leap day every 4 years to make up this 0.25 difference but it is actually 0.242181 which makes difference over time.


Julian calender ran with 0.25 for a long time but after about 1500 years it was already 10 days behind of the real date and Christians wanted to predict Easter exactly so they changed on Gregorian calendar. This calendar is the same, except that if the year is divisible by 100 it wont be a leap year, though if it is also divisible by 400 it will be a leap year. This almost fixes the problem, though every 3216 years one day is still off from the real time. Yup. Check out this video to see how we can improve this slight mistake:

So thats it. But you can not really capture the length of year or day since it changes all the time (effect of other planets and what happens on Earth). Check out this video which I used mostly as a source, it has got cool animations that will help you understand it:


Is this a proper perpetuum mobile?

today I want to investigate one particular perpetuum mobile machine. First when I wanted to write this post I wanted to let it open ended since I did not know the solution for why it does not work but I have found it so here you go:

Physics is basically based on the fact that energy and mass are conserved. If you were able to put enough strong evidence against it, modern physics would basically collapse, this is the foundation.

Now perpetuum mobile is a machine that is trying to break this law, but not very succesfully since none was ever built. Perpetuum mobile is a machine that gives out more energy than it needs for running.

Performance is larger than power and effciency is larger than 100%. This is not possible though you can check your basic physics skills by debunking these machines.

One of the most common “perpetuum mobiles“. As it turns it is supposed to create torgue and rotate forever.

It has been while since I saw what is called “Brownian ratchet” and I was simply stucked. It is kind of different from other “perpetuum mobiles” since it uses what is called brownian motion to work.

Feynmann was one of the guys who popularised this machine and also showed it flaw.

In the box 1 you have small paddle wheel. Particles bump into it because of brownian motion, that is a motion of small particles that goes indifinetely (this is type of thermal fluctuation).

This paddle wheel can only turn in one direction because in the other box you have ratchet as you can see above. The paddle wheel turns one way lifting up something or simply doing work. Where is the problem?

I remember asking my teacher about this. She said that it would really be perpetuum mobile. I knew she is not a good one. Now I did not know but I was sure that there is some flaw in this and I found that there is but I did not find explanation.

Today I found wiki page about this “Brownian ratchet” and they basically say that if the pawl is the same temperature as the paddle it will also undergo the same brownian motion sometimes jumping up and down. The thing is that we can not forget that the thing is also extremely small. If it would be different temperature it would work but based on thermal difference which over time disappears.


Solution to 12 coins balance problem

in the last post I described this cool balance problem with 12 coins where one of them is false one (heavier or lighter than others). You are allowed to weight them 3 times to find out which one of them it is and if it lighter or heavier.

The hint that I gave you is to separate them on 3 groups of 4 coins. Otherwise it is not possible to solve it. For the first one there are two options as you weight 4 coins against 4 coins.

If the outcom is even it goes as follow:

  1. If nothing happens the 4 coins that you have not used must have the false one. Now this is quite tricky. You have probably come out to this part but you have to use all the facts that one weighting will get you as you will see. If something goes down, it is good to know it and vica versa.
    1. a) Now you know that the rest of the coins (4) have to have the false one since it was even. You take one away and put the three against 3 that you are sure about (you have 8 of those). If it is even you know that it is the last coin and you just weight it against one of those normal ones to see if it is lighet or heavier. If you find out that one of the three has to be false you will remember if they were heavier or ligher. Then you take two of them and weight them against each other. The one that did the same thing like in the last weighting is the false one. (If in the 3 vs 3 it was heavier you are searching for the heavier side again.) If they are even you know that it is the last one.
  2. Now it can also happen that one side from the first weighting is heavier than the other. All of the 8 coins are unknown but you can use the fact that one went down and the other up so you need to remember that fact. You also need the 4 coins that you know must be all ok. Put three of those on the “lighter” part. From the lighter part move three original to “heavier” part and from there away three.
    1. b) The easiest thing is when the heavier part is again heavier. Then it has to be one of the original coins from both side which are only 2. You weight one of them against any other coin to get the result.
    2. b) If the part that was heavy is lighter this time, one of the three coins that you moved from lighter to heavier last time must be the wrong one. It is also lighter as you know. Weight two of them against each other. If they balance it is the third one if they do not it is the lighter part.
    3. b) If they balance it must be one of the three coins that we removed completely. We use the procedure described in the last post to find the solution, it is heavy coin then.

Now that is for solution. It is not easy to come up with it and there are some even more difficult versions. Thanks for reading and thanks to Wikipedia for the solution.


12 coins balance problem

today, in this short post I want to show you this cool puzzle that I first encountered on my summer camp. The problem goes like this:

You have got 12 coins. One of them may be false one. You can not know by looking but you have a balance weights. You are allowed to use it 3 times and find out which one of the coins is heavier or lighter (you do not know and it might happen that none is).

I really recommend you to try it out. I almost had a solution though when I checked it I saw that I had mistake in one of the scenarios. Try it out for yourself and in next post I will reveal the solution.




Try to take first step of weighting 4 coins against 4 coins, it will help you 😉


Private companies take the space industry by attack

today I want to talk about how private companies like SpaceX ,which I already talked about few times and Blue Origin for example, influence the space industry.

For many years there was NASA and only NASA. Now these days you could have noticed that SpaceX appeared, self-funded company with priority of making space cheap. Same interest has also Blue Origin, space company founded by Jeff Bezos, the owner and CEO of Amazon. (billionare as well as Elon Musk of SpaceX)

These two guys and others are aiming for cheap space which is something that NASA was never able to do. After Apollo 11 they wanted to start to use reusable rockets but it never went to perfection. The primary goal of 25 dollars per pound on the orbit of Earth, changed more into something like 25,000 dollars per one pound.

Now NASA wants to make Space Launch System and Orion capsule to get us to Mars. Noble goal it is. There is one “minor” problem. Look at NASA budget over years:

The peak is when we were trying to get to Moon

Right now NASA has about 0.5% of federal budget compared to 4.5 that got us to Moon. Estimates are that the whole Space Launch System (SLS), which is basically huge rocket, will cost in the matters of tens of billions of dollars (this is just development, see later for launch price)! (0.5% is something like 19 billions of dollars).

The thing is that there are other players, like SpaceX who can do this much easily. SLS will be using boosters RS-25 that are from 70s and throw them away after every launch while we have New Shepard of the company Blue Origin that has already been used 5 times over!

From what I have read from Phil Plait and others, SLS will probably be one huge fail. Already now it is behind schedule for its first unmanned launch, not talking about the approximation of mission to Mars (something like 2030-40) where as SpaceX is investing huge amount of money to Falcon Heavy that should be able to carry over time enough stuff to build a base on Mars. Falcon H. payload capacity is over one third of SLS though it should be able to fly several times for the same price as SLS. (I found that it would be able to make more than 5 flights for the same price on the Low Earth Orbit, thats some difference!)

The thing is that NASA is underfunded and right now it even spends money on something that may not ever be working while there are smaller players but with clear and cheaper mission.

Mind you that SpaceX is planning to design Interplanetary Transport System and Blue Origin’s New Armstrong (they are working on New Glenn right now which is one of these huge rockets anyway).

From what I have understood, the key in the future of space exploration is reusability.


Check out these pages for more info: 1) 2) 3) 4) 5) 6)

Btw. NASA does not plan to use SLS more than 3 time per year because otherwise they would have to build up huge facilities. Also the first version of SLS will have payload capacity of almost half the one that I counted in this post. They will have to change it a bit and add some things over time to get to the final capacity.

Binary system explained (part 2)

in the last post I wrote about converting from binary to decimal number. Today I will continue, if you want to read the basics about binary just check out the post. This is also linked to my post about counting to 1,023 on your fingers.

So lets say that we have number 137 and we want to convert it into binary.

You have seen in the previous post that there is some highest digit that has the value of 1 instead of 0 which means that it stores the information[1]. We need to find out this value.

Its easy, its the highest 2ª number smaller or equal to our original value (137).

Such a number is 128 which is 2^7 so it is going to be the 8th number since we use 2º too (and 2º is on the 1st place).
Now we subtract it having 137-128=9 (1xxxxxxx)

Now we repeat with 9. The number that is smaller or equal is 2³=8
9-8=1 and the next 1 that stores information is on the fourth position. (10001xxx)

1 is easy because 2º also equals to 1 and it is on the first place. So 137 looks like this in binary: 10001001.

Lets try 759:

759-512=247 (10th number is the first 1) =1xxxxxxxxx
247-128=119 (8th number is 1, stores the information) =101xxxxxxx119-64=55 (7th number is 1) =1011xxxxxx
55-32=23 (6th number is 1) =10111xxxxx
23-16=7 (5th number is 1) =101111xxxx
7-4=3 (3rd number is 1) =10111101xx
3-2 … 1-1 === 1011110111 (quite lucky with so many ones ;))

Hope this all makes sense, if it does not just write in the comments below.

Btw. thought you have infinitely many systems that you can use, binary is the simplest of them all. You can not store information in less symbols because with one symbol you would not be able to distinquish where one information ends and another begins. You need to use “space” or some number or something.