What does the 3rd Kepler’s law say?

today I want to do a short post about the 3rd Kepler’s law. I kind of really like it because it has very simple explanation but lot of uses at the same time.

The law goes as follow:{\frac  {T_{1}^{2}}{T_{2}^{2}}}={\frac  {a_{1}^{3}}{a_{2}^{3}}}

T stands for time and for semi-major axis of ellipse, that is basicly radius for planets since

What is semi-latus rectum?

their orbit is highly circular. The index and 2 stands for first and second object, basicly you are comparing two objects with each other though they must orbit the same body. This is very useful since you can compare anything in Solar System orbiting Sun with Earth. Why is it useful? Because Earth’s semi-major axis is 1AU and orbit lasts for 1 year which means that this fraction will disappear and you are left only with the object you want to calculate with.

Where did this even came from? The prove for this equation is very simple and basicly stands on the fact that centripetal force equals gravitational force for our orbiting object.


We can find the equations for both of these forces and from them finally get to the Kepler’s law:KeplerLaw3

Ok, before you start to freak out, this is completely easy. First line is clear, I have accidentaly indexed Fd instead of Fc because in Czech the force is called “dostředivá”.

Second line shows the forces and their equations, third canceles the mass of the orbiting body and the radius of orbit. Since v=s/t we can write it down as is shown. Also watch out because s is whole orbit so s^2=4π^2

The equation that you have in fifth and six line is also usable equation! It is more general and does not need the second orbiting body but it needs the mass of object. From this equation you can also figure out the mass of Sun which is completely amazing! (You have to watch out for the right units!)

After the small space I have divided the equation by the same one except that it works with some other object orbiting the same star (or planet..), with this step I will get easily rid of all the π, gravitational constant and mass of the center object.

Now we have the original 3rd Kepler’s law!


PS: in the prove we also assumed that r=a which means that planets orbit on circles not ellipses but it is accurate enough

Right ascension and declination

in the last post I explained what is celestial equator and what is ecliptic, check it out if you did not read it.

Today I want to look upon right ascension and declination which is the system that lets you describe where stuff is on the sky and it does not matter where you are on Earth.

Basicly the gif on the left explains it: you have Earth inside your celestial sphere. Through the middle comes the equator, that makes sense but since Earth is tilted by 23° degrees to its ecliptic, in our picture it must be ecliptic that is tilted (it is always just a reference frame).

Of course there are two points where equator and ecliptic meet, as I said in the last post, those are autumn and spring equinox.

As you go around the circle your “value” gets higher, it is called right ascension (or RA). Full circle has 24 hours and when you take some place there it tells you in how much time the equinox that has “0 hours, 0 minutes” will get there.

The value of right ascension increases from west to east (’cause rotation).

Of course since we are in 2nd dimension we have to use another coordinate that will tell you how above you are from the equator (or below). This is called declination and is normally measured in degrees. Since furthest you can be from the equator are poles the angle wont be bigger than 90°.


Where do equinox come from?

today I was trying hard to understand basics behind the coordinates that are used for stars and other celestial objects, once you grasp some basics you will get it, important part is the equinox and the “mechanics” that are behind it.

The celestial sphere with all stars at one distance

Basicly what you see on the left gif is the celestial sphere around the Earth (most of these things are geocentric since it is easier). Red line is the ecliptic. This is basicly the line that Sun follows over year, of course such motion is purely apparent but it is important to remember this one.

The white-green lines are the lines of equatorial coordinate system. The middle should be Earth’s equator though it does not match it much.

There are two points in which ecliptic and equator intersect. These points are called spring

How ecliptic is made (not to scale)

equinox and autumn equinox. When Sun passes through them the day is everywhere on whole Earth the same as the night. You already know that this happens happens twice a year, once for each equinox.

I will get to the coordinates in another post, hope you enjoyed this one 😉


Moons of our Solar System: Thebe

continuing in the promised series about moons I will today cover the satellite Thebe, this time I even have some “high resolution” pictures so keep on reading!

There are few huge craters on Thebe. (largest is Zethus with diameter of 40 km)

Thebe is another Jupiter‘s moon. It is quite smaller than Amalthea, with 100 kilometers as mean diameter. It was named for Greek nymph, in both stories I found, she was lover of Zeus (yet again) but in one she was also the daughter of Egyptian king.

It is quite similar to Amalthea, again it is tidally locked, which means that one side always turns toward Jupiter (this is also true for Moon). The surface is probably red what you can not see on black and white pictures of course. We can estimate its mass only based on the similarity with Amalthea, the value you will get is roughly 4*10^17 kilograms.

For the first time its image was taken back in 1979 by Voyager. Later, Stephen  P. Synnott found it on one picture. Four years later the name we use was first used.[1]

The fact that it is blurry wont help you much.

The above picture is the first sign of another moon, but watch out, this one is only shadow.

In background you can see some huge storms on Jupiter.

Another picture of Jupiter but this time Thebe is really visible! (Yeah it is not just filth on you monitor).

Finally, Jupiter has faint rings. These rings have to made up of something. Usually rings are created when some rocks are ripped apart by tidal forces. Also they can be fed over long periods of time be debris that leaves some moons.

Thebe has one very faint ring which is created by the second method. It is three times fainter than the ring of Amalthea which is very faint too. It has diameter of 65k-113k kilometers and it is not so thin (8400 km) as the Saturn’s rings which are even only several meters tall.


References: 1) 2) 3) 4) 5) 6) 7)

PS: the second and third pictures were taken from the same site and official permission should be needed only for commercial purposes, which is not me.

[1]S/1979 J 2 was the original name, though I did not decode it it probably means S=satellte 1979=the year it was found J=Jupiter 2=probably second in row with this designation.

Levers are amazing!

today I want to shine light upon one of the simplest machines that there ever were. Those are levers, so intuitive that you will see even small kids use them.

SPOILER alert:

They are amazing in crushing your fingers.

I kind of connect this word with the game Neverwinter Nights where it was used for the handles on walls that opened doors and so on, I had to use translator to make sure it was right because it did not feel so.

With this “door thing” it could come up to your mind that levers are kind of long rods of wood or iron. It is quite useful to have them like that.

Take for example something very close, door handle is an amazing illustration of how levers should look like! It is long quite enough for you to open the door.. now try to take

Epic door handle

just the closest part to your door, the one perpendicular to the plane of door. Sure it is much harder, probably even impossible for you to open them. This is because the further away you are applying force from axis of rotation the easier it is to rotate the whole thing.

Lets assume you have one Czech locomotive of class 363.

V čele orient expresu.

This is old Czech locomotive… there is ENGLISH wiki page about it!

Lets say that you are able to stabilise it and you have unlimitely strong rod of something that is also weightless. Also you have something that works as axis of rotation and it is also undestructible.Levers are amazing!

Everything is put like above. Lets say that you weight 70 kilograms (if less than you have sack of sand with you, if more than you touch the ground with your feet).

How far away do you need to be if you were able to put the locomotive 1 centimeter from the axis?

Well, we have to calculate it precisely because if you sit too close you are going to be thrown across a long distance!

What you want for balance is that the final moment of force is equal to 0. Both you and the locomotive has this moment which means that:


You calculate the moment here pretty easily, there have to be to things in the equation and those are very intuitive. If you push on door handle very hard (force) it is easier. If the door handle is longer it is also easier (r for distance).


This type of locomotive weights 87 tons. Now we can calculate the moment (F=m*g):

M=87 000*10*0.01=8 700 N*m

You moment of force must be the same and you know your weight (times gravity acceleration) so there is last thing the distance.

r=8 700/700
r=12.4285714286 meters

Wow, only if you are 12.5 meters from the train you can easily rest down! The problem here is that usually in this type of physics we consider that all of mass of one object is compressed on one place called center of mass. This is the problem because in reality whole locomotive simply wont be 1 centimeter away from the center. Cool anyway 😉

I mentioned at the start that levers are good in crushing fingers.. and they are. Take for example door that is 0.8 meter long and somebody pushes it with the force of 5 Newtons which is like lifting 500 grams. If your finger is 2 centimeters from the door it is literary going to be crushed with the force of 200 N which is like putting 20 kilogram thing on your pinkie.



Moons of our Solar System: Himalia

it has been about 4 months since I last posted about moons. The last post was about Amalthea (pretty cool name huh?). I thought that maybe I should resume some of the series so lets see how it will go. (its mostly astronomy blog so no wonder that these things are here.)

If I count right, Himalia has 29 pixels!

Last time I was talking about Jupiter’s moons so I will continue with those. Today the topic is Himalia.

As you could guess, this name is connected to Jupiter (Zeus in Greek mythology). Most of the time all the people (moons) are lovers of Zeus and Himalia is no exception, she was the nymph that brought 3 sons to Zeus, those were Spartaios, Kronios and Kytos.

Though I found that she is good for watching I highly doubt this since the apparent magnitude (how bright it is) is only 14.6 which makes it almost as visible as Charon, the moon of Pluto (15.55).

Himalia is the largest irregular satellite of Jupiter. To be irregular satellite means to be formed somewhere else and be captured later on by the planet. Such moon has highly eccentric orbit which is also inclined and even retrograde. She orbits much further from Jupiter than the other moons I talked about. The distance ranges from 11-13 million kilometers! This is one 15th of the distance of Earth to Sun which is quite a lot for a moon!

Since there are many other objects around Jupiter like Galilean moons that are easier to study (also more interesting) not many missions studied this piece of rock. It was discovered on 3rd December of 1904 by Charles Dillon Perrine. We know some things from spectroscopy, it is similar to C-type asteroid which means that it contains minerals with

Not so good either

water though otherwise such an asteroid is pretty dark. While Himalia is small compared to planets, it has masss of 4.19*10^18 [1]. It’s diameter is not very clear because the closest pictures were taken millions of kilometers away. There are basicly two pictures of this moon, one which you can see above is by Cassini-Huygens and second is by New Horizons (on the right).

It was thought that Himalia has something to do with the disappearance of other even smaller moon Dia when it disappeared in 2000. Dia was luckily found in 2010 so Himalia is innocent.


[1] This does not mean that Himalia is heavy in Solar System, Earth has roughly 6*10^24.

Why does the VIIIB group have 12 elements?

so I got this question that you can read above (it is about the periodic table and its groups). When I was trying to find the answer I basicaly bumped only on one page that explains it. It is important to note that this system is old one and nowdays you only number these groups from 1-18. If you want to read the answer from first hand go here: 1)

So in the new system they are not in the same group, but why were they there before?

The groups are made by comparing the physical and chemical characteristics of the top electron shells. This special VIIIB group are the collumns under Fe, Co and Ni which makes it quite unusual.

Basicly as you move across the periodic table, different oxidation states are more and more stable (in chemistry most things just want to get as stable as possible).

Those elements that have similar stable oxidation states are then put together. Take for example halogens. Those are the very very reactive elements next to noble gases.

Halogens in periodic table.

All of them will have oxidation number -I (most of the time). This puts them together. Transition metals are much more difficult to grasp with their d-orbitals. As you have seen in my other post they make some problems. The oxidation numbers for them are not very clear. Iron can be in II as well as III but generally these twelve/nine elements are occuring in the similar ones. Oxidation for these elements is actually almost always 2 or 3, this is especially true for nickel.


YFU meeting

if you read my blog frequently you may remember that I said HERE that I am going to Germany for one year! It is with the organisation YFU and this weekend I was on the meeting before the flight (train in my case).

As you may have guessed, this was the reason why I was not answering comments or reading any posts. I will try to catch up though I can not promise that I will read all of your stuff.

There were people from all around Czech Republic and also kids (some older than me) who were just before leaving for home.

It was for three days and after some games we were generally discussing some expectations from the year, fears, how we should behave in the host family, what we should watch out for (culture shock was very discussed issue). In free time we were playing voleyball since it was kind of nice weather except Sunday.

Though I did not meet anyone interested in astronomy particularly I found people listening to similar kind of music. It was quite cool to get to know so many new people.

From all the students I am planning to visit one of the closest countries. Of course there are some other kids who want to go to Austria and one girl for Germany but than as one would guess there is huge interest in USA, Latin America and more west generally. I will be leaving Czech in 21st August or something like that. This does not mean that I will stop writing blog, not at all, it may some time happened that I just leave some posts simply because I will be overhelmed. Also I will be going for summer camp which I am very much looking forward but since it is roughly 2 weeks there wont be many posts. (The number depends on how much I will work now.)


PS: there was question about VIIIB group in periodic table, I will answer it as soon as I can.

There is just an empty space

here is the second season of facts I created, enjoy:

1) The highest ionization energy for copper is over 1,000,000 kJ/mole, one mole of copper is approximately 63.5 grams and the energy taken by this process is equivalent to the chemical energy of 160 L barrel of oil. This equals also to 250 kg of TNT.
2) The longest protein known is Titin: C169 723H270 464N45 688O52 243S912
3) The thickness of soap bubble ranges from 10-1000 nanometers.
4) One Japanese engineer memorized 100,000 digits of pi.
5) Marie Curie was the first woman to get Nobel prize in 1903. She is also the only woman that got 2 Nobel prizes and this happened to only three other people and two organisations. Also her daughter Irène got Nobel prize with her husband.
6) Einstein was asked to be the first president of Israel, he refused.
7) Four new elements have their names, the most massive (proton num. 118) is called Oganesson.
8) Carbon has the highest melting point and that is 3823 K. The highest boiling point is for Rhenium and it is stunning 5869 K!
9) Yes I am serious, if you fold regular piece of paper 42 times you will get it on a Moon. (42? This is no coincidence!)
10) Everything is just a space.


PS: This was automatic post, I will not be able to respond to comments until Monday.