# What does the 3rd Kepler’s law say?

Hi,
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:

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.

Fg=Fc

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

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!

Dragallur

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

Hi,
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°.

Dragallur

# Where do equinox come from?

Hi,
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 😉

Dragallur

# Moons of our Solar System: Thebe

Hi,
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 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.

Dragallur

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.

# Moons of our Solar System: Himalia

Hi,
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.

Dragallur

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

# Where is the edge of Solar System?

Hi,
today I want to look on the problem of edge of Solar System. The problem is that such a border is not very clear. It is similar problem as the classification of what is planet and what is not, simply because there is no clear distinction in size or so for something to be planet. Biologists also had/have this problem with defining what is life since they discovered that there are lot of small things that are lying on the edge of dead (it was never alive) and alive.

So whole post I will be working with this picture, so take time to acknowledge what is there:

Sun is in the center.

So the short answer is that heliosphere is the edge of Solar System. It is defined as region with the border where Sun’s solar wind is stopped by the pressure of interestellar medium.

Solar wind is the flow of plasma from the Sun. It is pretty fast, up to 400 km/s or even more. This plasma is then hitting the interstellar medium which is stuff from other stars and simply dust and so on.

Since this solar wind pushes the stuff out we have smaller pressure inside our bubble. This creates the border called heliopause where solar wind is slowed to 0 velocity.

It is best to define the region like this because otherwise Sun is technically visible anywhere in the space and its gravity also just decreases a little bit by the distance but solar wind just stops.

You may have noticed that I did not mention the termination shock which is another border in Solar System (btw. heliosheath is just the region between heliopause and termination shock).

It is the border where the velocity of the solar wind decreases below the speed of sound in space [1]. This creates a termination shock which I will explain in other post when I will talk about the speed of sound!

Dragallur

PS: also I promised something about orbitals so I should do that too..
PPS: Bow shock probably does not exist and it should be shock wave of interstellar medium.

[1] Oh yes, there is speed of sound space too. It varies from region to region but since there is dust and other stuff lying around the speed of sound is roughly 100 km/s.

# Green trail, golden leaf!

Hi,
this is very abstract title I guess but it summarizes why I did not post last Saturday when I planned, yes I am sorry. Anyway I was on this contest called Green trail, golden leaf which is contest of mostly biology though there is also astronomy, meteorology (not this year) and geology. I was not contestant for the first time, but organizator and I helped with astronomy site.

There are two categories which are basicly for older (10-15) and younger (0-10) kids (numbers are rough). The contest happens in groups of 6 people. They are then walking the trail three at a time, getting points on various sites on various topics and finally their points add up.

In Friday I had actually presentation first. I was pretty happy how I did it except that it was a little bit too long. The problem was that even that the presentation was for roughly 50-60 minutes the kids were discussing and asking questions a lot (which made me happy of course) but finally the presentation was roughly 100 minutes.

I was talking about the view on Earth, geocentrism, heliocentrism, no centrism at all and why the Universe is so big and why people usually think it is not. I followed up with aliens and Fermi paradox, of course wow signal and KIC xx… were also mentioned. In the end I mentioned SpaceX, terraformation of Mars, New Horizons and Voyager.

As I said the presentation was going pretty good as well as the contest itself. For younger kids we had questions like:

1. Name 3 astronauts
2. What is astronomical unit and what is light year
3. Name 3 missions (Apollo and other count as 1)
4. Name 4 constellations that are visible in Czech Republic
5. Highest mountain in Solar System and where it is
6. Where do comets come from?
7. Difference between meteorite, meteor, meteoroid and asteroid.
8. … (and other)

For older it was bit more difficult:

1. What is afelium and perihelium
2. Name all Galilean moons and give a small info for one of them
3. What is HR diagram
4. (Lot of pictures about life time of star)
5. Draw the orbit of typicall comet and draw both tails and name one place where they come from.
6. … (and other)

From 12 sites astronomy was the 2nd toughest 😀

Lets see how would you do, I will return to it some other post.

Dragallur

# Receding planets

Hi,
today I will continue with short post because I have a lot of work to do for my 15 page essay.

When you are watching planets they travel along some predictable paths which from the view of whole Solar System are ellipses. If you measure where they are on the sky you must do it relative to something. Usually you will use stars that is because ground is too far away and it would be inaccurate (too far away in degrees).

So you measure the planet’s position every day and then strange thing happens, the planet goes back and weeks later it returns back to its original pathway, what happened?

This movement is called retrograde – backwards motion. Of course nothing like that happens simply because there is nothing to cause it.

T is Earth, P is planet which we observe, A is the projection on celestial sphere.

The picture above should explain you what happened here. The thing is that we orbit faster than Mars. The picture that we see A1-A5 is the projection on the background, also called celestial sphere.

The same thing happens when you are driving on highway and there is truck ahead of you. As you catch up, the truck moves relatively to objects that are very far away. At one point as you drive around the truck you may not even see them and then suddenly the truck seems to be behind the far away stuff that you watched but the truck was moving the same way all the time.

This was a huge problem for astronomers. First they made various epicycles on epicycles to explain this strange movement and it took Copernicus to show that it is just an optical illusion.

Dragallur

# Moons of our Solar System: Amalthea

Hi,
today I will write about another moon of Jupiter. This is surely not known to larger community because it is much smaller than the Galilean moons. I would like to say that it is beautiful as her name which I really love but the images of its surface are kind of blurry.

Totally beautiful:

Amalthea was discovered in 1892 by E.E.Barnard (that guy after whom Barnard’s star is named after [1]). What this tells about it? Well it has to be quite big because back then the observations were not so good yet.

It was named after Amalthea, the Greek nymph who nurse Zeus, so once again it has to do with the planet it orbits.

### Orbit

Amalthea if part of one ring of Jupiter, this one is called Gossamer ring. It is orbiting as 3rd satellite from Jupiter as far as we know, at the distance of roughly 181,365.84 kilometers, there is practicly no eccentricity in its movements and it take almost 12 hours to complete one spin. Some of those strange features can be explained by the moon Io.

### Surface

When I said that it is not small I really meant it: 250 x 146 x 128 kilometers does some stuff. It does not have any geological activity as Io so its surface is heavily covered with craters.

There are some huge ones on its surface which were surely made by violent impact probably changing the orbit of the moon a lot, you can see them on the picture.

Otherwise there is not something too special observed about the surface of the moon, it is cold place but we still have a lot to search there.

The ring in which she orbits is made from her because Jupiter is reaping dust from its surface.

When person would stand on its surface it would see enormous Jupiter over 40° of sky. The gravity there is not so strong compared to our Moon but still great: 58m/s. Jupiter would also be very very bright, 900x brighter than Moon when it is full.

Dragallur

[1] Check out my page about Daedalus mission!

# Moons of our Solar System: Io

Hi,
it has been couple of posts since I last wrote about moons ofour solar system. Today I will write about the last Galilean moon: Io.

Io is kind of hellish world. With extreme temperatures and extremely poisonous chemicals, everywhere. Still it has suprisingly beautiful colors and this piece of strange rock is very important component in Jupiter‘s system, lets see why.

Io was with the rest of Galilean moons found out first by Galileo and Simon Marius who gave her the name: Io which was pristess of Hera. She was also Zeus’s lover as it happens frequently.

### Surface

The picture which is above is taken in true colors and there is yellow red and brown because of certain element. You probably remember this one: sulfur.

There are also various kinds of silicates, this is stuff that contains silicon. Otherwise sulfur dioxide and all other various compounds.

What really suprised scientist when they saw the surface for the first time was that there were and are not many craters. They wanted to date how old the moon is but it surpised them what they found. The surface is in this feature similar to Earth. There are almost no craters because of its geologic activity (othewise rare) which transforms the top layers all the time.

There are more than 400 active volcanoes. Io, is the most geologicly active thing in whole
known Solar System.

There are roughly 150 mountains on the surface ranging to even higher heights than Mount Everest. There are not very steep because there is a huge erosion causing stuff to smooth out. Those mountains were created by the push of the litosphere going down while some parts went up. There are also special features called paterae. They are similar to what on Earth we call caldera which forms as you can see on the right.

This particular picture shows the formation of Crater Lake in state of Oregon, I have been there and I must say that it is something extremely beatiful!

Otherwise the surface is cold, about -143°C but there are some areas around volcanoes which are heated up to even 17°C.

### Observation

For a long time humans just saw Io as a point in the sky with magnitude of 5. It took the first probes to actually observe something about it except roughly the color.

Pioneer 10 and 11 launched in 1972 and 1973 respectively were the first probes to collect some data.

After that famous Voyager 1 and 2 did another flyby collecting even more data followed up by Galileo and New Horizons.

### Orbit, size and atmosphere

The orbit of Io is in resonance with Ganymede and Europa as I already mentioned before. This creates tidal heating through friction causing all this geological activity. Io orbits as fifth moon from Jupiter but it is the closest one of the Galilean moons. This means roughly 421,700 kilometers and one orbit takes 42.5 hours, the moon itself does not rotate because it is tidaly locked to Jupiter.

Io is just a little bigger than Moon, by about 5% which means diameter 3642,6 kilometers but far greater mass (+20%). Io is very dense moon.

There is even atmosphere but it has the pressure of about one billionth of our atmosphere. It is mostly composed of oxide disulfide. If some probe would land there it would not be able to use parachute and it would not need heat shield to prevent from burning. To slow down, it would have to use its rocket nozzles.

What is really interesting is that it interacts with Jupiters magnetosphere which takes out about one ton of material from Io. Io also works as giant generator creating electric field which would kill human in matter of minutes with the power of 400,000 volts and 3,000,000 ampers.

Dragallur