How long is a year actually?

Hi,
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:

https://www.youtube.com/watch?v=qkt_wmRKYNQ

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:

Dragallur

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Leap seconds

Hi,
I was just reading post by Science Geek and then I realized that I was learning some stuff for school on similar topic so I decided to make a short post about it.
Today I will write about leap seconds.


Look at the picture on the left. Now look at it again if you did not find the strange thing there. Unless you have some kind of strange clock you should not see 60 seconds normally but you should see instead one more minute and 00 seconds.

So lets take a look on what exactly happened here.

So this picture is picture of time when leap second was added to our time because our day was shifting with actual solar day which corresponds to our position with Sun (this gets messier when you see that on this also our orbit and axis have effect).

The problem here is that the rotation of Earth for longer term is unpredictable, of course we are talking about very small amount of time. The thing is that lot of stuff can change the Earth`s rotation: earthquakes, crust moving relatively to core, slowing of the rotation because of friction from tides (about 2ms per century) and many others, actually anything that happens here is slowing Earth rotation down.

There are of course two types of leap seconds but only positive ones were added for now, actually 26 of them and last one on June 30, 2015. This makes some problems in computing because of course all-time running programs with lot of data are not very well prepared to just add one second. This is also why those seconds are always allowed to be inserted two times per year.

On the graph you can see how the time changes (y-axis) through years (x-axis). Those fastest vertical changes are leap seconds. As you can find on Wikipedia on the table with leap seconds, around the year 2006 there were none needed.

Dragallur

Both pictures are from wiki article about leap seconds

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.
https://i2.wp.com/www.askamathematician.com/wp-content/uploads/2011/05/projectout.jpg
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