Pioneer Anomaly

today I will write about strange phenomena that occurd to Pioneer 10 and 11 spacecrafts.


Pionner – artist’s concept

Both of these missions are quite old in the space exploration sense. One launched in the year 1972 and the other 1973. They were made to explore outer part of Solar System (meaning still quite close) and after that they of course just went on.. there is no way to retrieve object so far and it would not make much sense.

We lost contact with both but before that we knew how far they were because of their signal. There was something wrong about it anyway, every year when we predicted where they would be they would lack behind about 400 kilometers. Thats almost the length of Czech Republic though Pioneer 10 is able to cover the distance in 33 seconds so that is not much of a difference. But… there is a lot known about the forces acting on the spacecrafts and those could not be it. For example gravity from Sun is slowing them down but it is a thing that one can account for quite easily.

It took few decades to solve this problem (paper finally explaining it was published in 2012). Now we know that it was because of radiation from the spacecrafts as it was losing heat. Pioneers were spin stabilised so that their antennas always pointed towards Earth. The way it was build scientists found out that the radiation causes acceleration towards Sun. But it is kind of weak only: (8.74±1.33)×10−10 m/s2

Thats now much but in Viking program if radiation pressure from Sun (which is a different thing of course) would be ignored it would miss Mars by 15000 kilometers which is quite important.


Pionner picture: By NASA –, Public Domain,

Europa Multiple-Flyby Mission

today I am going to write about proposed mission to investigate Europa.

Europa Multiple-Flyby Mission is a plan consisting of orbiter and a lander directed towards Jupiter‘s moon.

The reason why to choose Europa is quite clear. There is probably liquid water under its surface and if one launches such a thing, it might get public’s attention.[1] (Which might be now more important than ever considering how Trump wants to cut down NASA’s budget especially on the most important thing that they do: Earth’s climate monitoring.)

First of all the orbiter, which would be launched in the next decade, would learn as much as it could about the surface of the moon, Jupiter’s magnetosphere (see later), weird water

Composite image of Europa superimposed on Hubble data

This is two images of course. The original does not have the Europa in middle but only black spot. You can see the plumes on roughly 7 o’clock.

plumes and so on. There are 9 instruments together planned.

Instruments on those orbiters are able to collect data faster than we can receive it. This is because there are more mission that need attention of our receivers. Those are not some small receivers but specialized ones and all missions have some time to send information. For example New Horizons, just from its flyby of Pluto kept sending data for some 6 months.

In case of Jupiter oriented mission this might be a problem because Jupiter has extremely strong magnetosphere which will probably damage the instruments in matter of few weeks. This way it is best to get close to Europa and then get away as soon as possible and send the data later. This can not be done for the lander so it really lasts in matter of days. (Yes, it is still a problem even if you cover your equipment under 150 kilograms of titanium as is planned!)

The lander is thing planned even further into future, around 20 years or so. Much can change and we will see what the priorities are at that point.


[1]People will probably get quite excited by mission promising founding signs of extraterrestrial life.

Polaris won’t be North Star forever

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.


1st picture: By NASA, Mysid – Vectorized by Mysid in Inkscape after a NASA Earth Observatory image in Milutin Milankovitch Precession., Public Domain,
2nd picture: By Tauʻolunga – self, 4 bit GIF, CC BY-SA 2.5,


Orbital period


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:


(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!


Sunset elevator

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):

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.


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.

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:


Juno is right at the party!

wondering what to write about today I decided that best would be to catch up with the mission Juno which is going to explore Jupiter.

Juno Reaches Jupiter

This is doodle by Google which shows the excitement of the scientists as they watch the signal from Juno coming back after it started to orbit Jupiter.

So it has been basically 5 years since NASA launched Juno (2011 August). This satellite is the second one after Galileo that is going to orbit around Jupiter. Most of others were just on flyby to other places and Galileo kind of broke.

Artist’s impression of Juno.

Juno mission is going to last for about 1 and ½ of a year. This seems kind of short time when you consider that it took alone 5 years to get there. SciShow Space said that it is because NASA does not want to risk getting Europa spoiled with ANY organisms from Earth though I think that this is nonsense and that NASA just does not have enough money which is something I will get to in another post.

What will we get? Well hopefully we will learn more about formation of Jupiter and whole Solar System, this is basically the main purpose but priority is also the gas of Jupiter and its magnetic field. We wont get probably any pictures of the moons because they are not part of the mission and they would be very small. At one point the JunoCam instrument will have a great resolution of Jupiter, about 15 kilometers per pixel. This is something amazing since Jupiter has about 140,000 km in diameter.

Right now Juno is on what is called “capture orbit”. Those are two 53.5 days long orbits which will then lead to 14 day science orbits where the real data is going to be harvested.

Everything about the mission is quite planned.

Juno is also the furthest man-made satellite that is powered only on solar panels. At the distance where it is, there is only 4% of sunlight compared to Earth.

Next time I will cover what tools Juno carries.


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 😉