Precession

Hi,
in the last post about Polaris I mentioned precession as the effect that causes change of North and South stars. I did not really explain what is happening there so I decided to make a short post only on that topic.

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There are two other good examples of objects that precess alongside Earth. Take gyroscope for example:

On the left you can see gyroscope. It consists of spinning wheel (orange/yellow) and a pin on which it stands. When you speed the gyroscope up it will be able to stand as you can see on the animation. This is basically what Earth looks like and what it does in matter of 26,000 years.

There is a thing called torque in physics. If you hold a pole on one side and something is hanging on the other side it will be very hard to lift it up. You will have to use both of your hands and one will push down and the other up to counter the torque that the objects has, that is a force causing it to rotate around one of your hands.

If you spin the thing though it will suddenly be easy to lift the thing, why? Because of angular momentum and conservation of angular momentum. If you spin on your chair and stretch your arms and legs you will slow down but if you do the opposite you will speed up. No force is acting on you only conservation of angular momentum takes place. Angular momentum is calculated as the amount of mass spread in distance from axis of rotation. If it is further away it does not need to be so fast as then the mass is closer to the axis.

When you speed the object up the angular momentum will stay conserved so you do not need to provide the torque anymore, in other words it is going to be easy to lift the thing up. If you try to change the angle in which it spins it will feel weird and it wont like it.

Even than gravity is still pushing down. If you add the vectors of the forces together, you will find out that the object will rotate –> precess. The slower it is the bigger the angle in which it precesses. If the force would be applied only on one spot all the time then it would not precess. Take a round sheet of cardboard and rotate it on tip of pencil. If you blow on the spot close to you the thing will tilt left from your point of view. Gravity though will try to tip the thing over always on the side that is lower and thus it will continously change and rotate – precess. If Earth had no tilt there would be no precession.

Dragallur

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Polaris won’t be North Star forever

Hi,
today I will write about precession and what effect it has on our sky.

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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.

Dragallur

1st picture: By NASA, Mysid – Vectorized by Mysid in Inkscape after a NASA Earth Observatory image in Milutin Milankovitch Precession., Public Domain, https://commons.wikimedia.org/w/index.php?curid=3993432
2nd picture: By Tauʻolunga – self, 4 bit GIF, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=891838

 

Orbital period

Hi,

in today’s short post I will write about orbital period of planets, more accurately synodic and sidereal period.

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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)

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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:

1/S=1/P-1/p

(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!

Dragallur

Sunset elevator

Hi,
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)

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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): https://www.desmos.com/calculator/oftnm48s3b

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.

Dragallur

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.

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

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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

How do orbits work?

Hi,
I “came up” with this problem already some time ago but it is today that I am going to solve it here.

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When you draw satellite above Earth and draw the forces that act on it you will see that there is only one force there (only one really important). It is the gravitational force of Earth. Why does not this satellite fall back you ask?

Well this is actually very interesting. The thing here is called orbital velocity. This is the velocity you need to orbit around Earth at particular distance.

So such a satellite orbits around Earth and you need the speed to be so big that gravity wont just pull it back but not too big so it does not fly away. I read somewhere great analogy: orbiting is just a falling without the crash. Take ISS for example. Why are there astronauts in “zero G” when they still receive 96% of Earths gravity? This is because the ISS is actually falling, kind of. It is falling around the Earth.. AROUND so it actually misses all the time. With extremely small drag and friction the  satellites slow down just a little bit so they orbit for tens of years. For example ISS has to use its motors to get back on her height from Earth because otherwise it would fall down in some time. 

The closer you are to Earth, than the drag from atmosphere is greater so you must orbit at faster pace (+ the small amount of bigger gravity). Most satellites orbit in the low Earth orbit which is from 150-2000 kilometers or so.

Sometimes satellites need to be put away so they are moved on what is called satellite graveyard and they will orbit there for a long time. Or their path can be changed so they burn up in the atmosphere. The problem on Earths orbit is huge mess because of those years that we were just launching new and new satellites. This is a huge problem for the ones that are actually working and also for ISS because just a small piece of debris can do tremendous damage.

Dragallur

The picture

 

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.

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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

Planets of our Solar System: Jupiter

Hi,
lets see what we got here, the biggest planet of our Solar System into which all other planets would fit with space to spare. It is Jupiter, named after Roman god of gods or Zeus in Greece mythology.

It is nine times wider than Earth but its mass is 1300 times larger. It is the fastest spinning planet, one day on Jupiter is 10 hours long which makes him 6% less like a circle. Mean distance from Sun is 800,000,000 km or 5.2 AU.

Jupiter is the closest gas giant, which means that he has no surface only thicker and thicker poisonous clouds with various gases. Darker parts are called zones and lighter belts, both of them are rotating in opposite directions. This process is powered by the internal heat of planet (Jupiter loses heat more than he receives) and by fast rotation.
On the picture you can see The Great Red Spot, it is on left of southern hemisphere. That is storm which lasts for decades but now we know that it is shrinking and eventually it will disappear. But for now it is stronger than any storms we ever hope to have on Earth with winds of over 500 km.

When we would dive beneath its deadly atmosphere we would appear in ocean of metallic hydrogen (hydrogen atoms that are sharing their electrons which makes them act as metal). Underneath we are not really sure but there can be solid core of metals and/or rocks.

While Jupiter is really large it is not even close to becoming star, it would have to be 12 times more massive. There exists a theory that Jupiter helps Earth by changing the pathway of comets and other stuff in space but on the other hand it could work in the same opposite way, but still we are not dead yet.

Juno (Hera) spacecraft is right now heading towards Jupiter. In the half of 2016 it will arrive and for 15 months it will collect the most accurate data that we ever had because of its close orbit.

For now there is 65 known moons orbiting Jupiter and I will definitely mention some of them in the future.

Dragallur

PS: be sure to check out Mercury, Venus and Mars!

Moons of our Solar System: The Moon

Hi,
since I have done first two planets of Solar System I would go to the Earth but I find it not so important for me 😀 so I will do the Earth´s partner, the Moon.

Our Moon is largest compared to other moons with their planets.
It has radius of 3470 km compared to Earth which has 6378 km. Moon is orbiting about 380 000 km far away while Earth orbits Sun in 150 000 000 km.

First of all. It is assumed that the Moon was created by extremely huge impact of some planet about the size of Mars which collided with Earth. From this collision Moon was born having both material from Earth and from second planet (Theia is it´s unofficial name).
This event made Earth very very hot so when Moon was cooling its closer side to us was
cooling more slowly and when material evaporated it felt on the dark side. This made Moon much thinner on the side turned to us. (Moon is locked by tidal force)

Over eons and eons stuff fell on our brother. When something collided on the thinner side it was much more common to break through thin layer of the surface so lava could bubble up. When this happened couple of times places called mares (marines) were created, this could not happen on the other side because of its thick crust.

There are lot of different structures on the surface. Dark one are marines, there are also craters and lines from old lava flow or even small canyons and places where it is thought that can be milliards of liters of water in the form of ice. Moon is not geologically active but there is still some liquid lava inside, even after 4.5 mld years.

Dragallur

PS: I saw the blood moon and it was amazing!