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)


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.

Traveling faster than sound: shockwaves

Hi,
today I want to shortly explain phenomena called “shockwave”.


You may have heard this word already used in the context of supersonic traveling. That is exactly it. Shockwave is the event, whether it is visible or not, that comes when you reach and/or cross the local speed of sound.

I say local because speed of sound changes with temperature, air density and humidity but for normal purposes it is roughly 343.2 meters per second.

When you are slower than the speed of sound the waves made by your movement do not

Circles to illustrate shockwave.

ever hit each other (without obstacle). This you can see on the left first picture. As you move through fluid [1] you create those “circles/ripples” around you and they are closer to each other in the direction you travel.

 

When you speed up to the speed of sound you will create this shockwave because suddenly all of those circles are hitting

everything at the same time which means that the hit is pretty hard. What you see usually is something similar to the picture on the right. This is just the condensed water in the squashed air.

I have read that it is quite dangerous to fly exactly at the speed of sound. It is not very efficient at least because the drag increases 2-3 times compared to supersonic speeds.

With sonic speed you can calculate two numbers. The first one is Mach number which is calculated as your speed divided by speed of sound. This means that Mach 1 is exactly the speed of sound. There is also something called the Mach angle which exists only in supersonic speeds. You can see it labeled as theta in the picture above. The smaller the angle is the faster you travel and the equation goes like this:

sin θ = c/v

Shockwave can also be created in space, though here that speed of sound is way higher (9,000 m/s), I already mentioned this in another post.

For more illustration you can check the video below that I made in GeoGebra:

Dragallur

Read more: 1) 2)

[1]Watch out, fluid means both liquid and gas!

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:

Voyager 1 entering heliosheath region.jpg

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.

What is going up on Mars?

Hi,
while thinking about today’s topic I find some random stuff and decided to share it with you. So here you go, new exoplanets, tsunami on Mars, good view on Mars and SpaceX announcement.

Artist’s impression of exoplanet.


Thanks to new statistical method there were 1,284 exoplanets confirmed[1].
This is biggest number ever in one shot. There is of course lot of data form Kepler which observes stars for those exoplanets. You can not be sure always if what you saw was really exoplanet so you need more data. When uncertainity is below 1%, it is officially agreed that the planet is there. With this new method, lot of those uncertainities went below 1% so yes they were “discovered”. Other data was “thrown away” because the percentage went lower and generally this was nice breakthrough.[2]

For long time it was thought that Mars’s terrain was shaped by its ocean that later on evaporated. But the shoreline would be graduall which is not what we observe, rather exact opposite with many geological features along it. These features could rather be explained by huge tsunamis that were formed by asteroid impacts.

Also Mars is going to be these weeks in oposition to Sun and basically really close to Earth, on about 1/2 of AU. The closest it could be would be about 1/3 of AU because its orbit is kind of excentric. If you want to see it well, just take a telescope and with good one you should be able to see even some of its geological features. If you get to see (if it is possible for normal people) Olympus Mons, say hello from me 😉

After SpaceX landed second time on the barge, Elon Musk stated that they want to land on Mars in the year of 2018, which is in two years! They have really lot of work to do so lets see where they will be in that time! (Read more here on the blog of Phil Plait)

Dragallur

[1]Exoplanets are planets that orbit around other stars.
[2]From the data we also know that 550 are probably rocky and 21 are in habitable zone.

How to! 4) Go stargazing for the first time

Hi,
since I went out stargazing couple of times already, I would like to mention few things here for you, when you decide to go alone or maybe with your boyfriend/girlfriend stargazing. While I live on northern hemisphere all of these tips will be useful to south people.


Preparation

Check out the time when the sun sets where you live. This page is quite useful for that, you just need to insert your location.

It is quite useful to know what these terms mean, astronomical dusk is what you are looking for.

So you need to watch out for the time when first stars/planets appear which will be some time after the dusk, of course there must be clear sky which you need to check on Google forecast [1] or in TV.

Then while it depends on the time of year, it is good to take some extra clothes, because most probably you will be standing still for some time, so you might get cold.


How to stargaze

First option: take some sky map on paper with you. You can print some from internet but check if you are printing the right hemisphere. For this, you will need also some light, but not white, since you would never build night vision, take red, eyes are not so sensitive to it.

Second option: take your smartphone and download application with stars, I use Star Walk 2 Free and it is pretty good, especially because there is option for night vision so it is red, this is very useful though you must never lock your phone, because when you want to use it again the light from you display would pretty much destroy the night vision you build up.

What is night vision anyway? It is the activation of all your non color sensors in eyes and the adjusting of your vision in darkness by enlarging the part that collects light, it take about 30 minutes though you may see the effect even after 4 or 5.


Pick a good location

Be sure to pick a good location. If you are in big city, than make sure to drive to countryside because the light pollution would just waste your time.

Best is hill though it is good to be on some field or place where there are no trees.

Keep away from any buildings and streets. It is important for you to keep the night vision, one single mistake when you look in street light could destroy the whole process.


Enjoy 😉

Dragallur

PS: it is better to go stargazing when there is new moon, otherwise, full moon spoils the view of huge part of sky.

[1] To get in Google forecast just type “weather” and “your location”.

Why are radio telescopes so large?

Hi,
take a Hubble telescope, it has primary mirror 2.4 meters tall. Now take this:

Arecibo Observatory Aerial View.jpg

The giant Arecibo radio telescope

I mean the thing above which is Arecibo radio telescope has diameter of 305 meters. Both things are for the same thing, to observe the Universe.


So the answer lies in the name. Arecibo is a RADIO telescope which means that it works on quite different wavelengths, actually magnitudes bigger wavelengths since the wavelength of for example visible light for Hubble is 550 nanometers which is quite small while radio waves can have wavelength of hundreds of meters.

This is essentially the key. If you want to see clear image in light (that we can see) you need just a small telescope. Both work the same way though from what I understand you need larger area to collect all of those waves and reflect them on the focus which is above. The equation shows it clear:

θ=1.22*λ/D

Where θ shows how close two points can be to each other without you being able to distinquish them. λ is the wavelength of the light and D is the diameter of your telescope. So you will see best when wavelength is small and diameter is huge since this will lower the angle that you are not able to distinquish. Of course that there is huge difference when you insert meters instead of nanometers so you must compensate it with the diameter of the telescope.[1]

If you want to have a clear image in radio waves, well you have to build Arecibo.. really? Isn’t there another option?

Yes there is! You can build a lot of small radio telescope that would alone be very weak but if you take lot of them you can have a Diameter of kilometers. Such a device is called interferometer which means that is “operates by myltiplying the data from each pair of telescopes together to form interference patterns”.

There is more of them and this one is ALMA observatory.

So those are huge fields or rows of smaller (even 60 meter) discs that collect data. They have to be extremely accurate what is time concerned (atomic clocks).

Dragallur

[1]1.22 is just an empirical value.

Can you see a coin from 400 kilometers?

Hi,
no, probably not with naked eye, I think, though if it would be some special coin, maybe? The point is that you can use some cool things to see such a coin, for example Hubble Space Telescope!


Ok, I found some page with physics problems and one of the first was to calculate what is the smallest angle that Hubble Telescope can distinquish. I calculated that it is roughly:

0.0127”

This means 0.0127 arcsecond!!!

How far away football has to be to have the angular diameter of one arcsecond

What about a human eye how good is it? Well eye can distinquish only things that are 1′ away from each other [1], which means one arcminutes, one degree has 60 of those so it is pretty good but not so much as Hubble. But anyway, back to the title, how small is a coin?

I measured the second largest Czech crown to have 2.55 centimeters.

Now how far away do you need to be to not be able to see it with naked eye? We will use this formula to get the diameter:

θ=D/r

Where the diameter (D) is 0.0255 meters. The distance (r) is what we are trying to find and the angle eye can distinquish is θ (in radians). [2]

r=D/θ

If all the calculations went right it should be:

r=87.6625 meters

But beware this is not counting air, humidness and so on so you will most certainly not be able to see coin on this distance.

What about the Hubble telescope? We can use the same equation but for θ we will insert much smaller value!

And yes, you can see the coin from 414,153.744827 meters! Which means that you can see one freaking coin from London 50 kilometers behind Paris! One coin![3]

This is so cool.

Dragallur

[1]You can try this by drawing two dots on paper and then moving away from it, at one point when you are far enough you should be able to see only one.

[2]This equation is simplified but it should work for small angles.

[3]Again, this works only in space because there is nothing that would block your sight.

 

Easy way to get excentricity

Hi,
it has been few days since I looked on some problems from astronomy contest. One of the problem was about excentricity of Pluto.


This has to do with ellipses since according to Kepler’s laws, planets are orbiting on ellipses, shapes just a little different from circles, at least when you consider their equation.

For circle equation is x2+y2=1

For ellipse equation is x2/a+y2/b=1

Sun is always the focus of the elipse, above those two points are -c,0 and c,0. For planets those ellipses are much less excentric which means that in the equation above, “a” and “b” are fairly similar.

In the problem I knew only perihelium and afelium of Pluto.

e = \frac{\varepsilon}{a}=\frac{\sqrt{a^2-b^2}}{a}

“e” is excentricity. “a” is semi-major axis. “b” is semi-minor axis. “ε” is linear excentricity (not really important).

Since the equation goes as the one above you need both semi-major and semi-minor axis to get the result. From knowing afelium and perihelium I easily got semi-major axis. To get semi-minor you must know that the distance from focal point to the top or bottom of ellipse is equal to semi-major axis, from this you can use pythagorean theorem and then all this information insert into the equation. All went right and with perihelium of 29.66 AU and afelium of 49.32 AU the excentricity is 0.246 which is just right, if excentricity is equal to 1 than it is parabola and if greater it is hyperbola.

Dragallur

Chelyabinsk meteor is whole new level of destruction

Hi,
I decided to make a short post of ten facts which I found over time, this is the first in series, enjoy:


1) Even that the surface of Mercury has 400 degrees Celsius, there is water ice at the poles inside craters where temperature may be low as -170°C.

2) Jupiter is the oldest of planets in our Solar System.

3) Most distant cluster of galaxies was found to be 3.8 billions of years old and at the distance of about 16 billion lightyears. It is 1000 times as massive as Milkyway.

4) Satellite SOHO found more than 3000 comets.

5) The longest time spent in space is 437 days by Valeri Polyakov.

6) Tardigrades are organisms that are able to withstand even vacuum of space and reproduce after high doses of radiation.

7) As of March 24, 2015 the longest distance traveled on other world was by Opportunity on Mars, 42.2 kilometers.

8) Today Scott Kelly and Mikhail Kornienko return to Earth after one year in space.

9) Person passes out when unprotected in vacuum after about 15 seconds.

10) Chelyabinsk meteor damaged more than 7,200 building and hurt 1,491, mainly because of shattered glass.

Dragallur

Telescope of new generation

Hi,
today I would like to mention new kind of telescope which is right now being build. It is quite amazing piece of human technology, The James Webb Sp Telescope.


Named after James E. Webb who was leading NASA about 50 years back. First they wanted this telescope to name Next Generation Space Telescope but then they decided to give James Webb the honor.

Labeled Spacecraft

Above you can see how it should look like when we will launch it. It is telescope which should work instead of Hubble’s Space Telescope which even that it did great work, is not good enough right now. James Webb Space Telescope should have even better view in the vastness of Universe. Also more details which means that for example, we could get much more information about exoplanets, we could even start to analyze more of their atmosphere and learn more about stars and so on.

Still Hubble’s telescope has some time since James will be launched in 2018 in French Guiana. Here you can browse some pictures for sun shield testing, this is the part that is turned towards Sun and protects all the fragile tools that are on the telescope because in space, radiation could easily destroy transistors and other equipment.

https://i1.wp.com/jwst.nasa.gov/images/JWST-HST-primary-mirrors.jpg

The most kind of shocking part, which you can see above is the primary mirror. You can see that James Webb has upgraded a lot from Hubble. This mirror is actually too big so it had to be made from separate pieces, hexagons. It was quite fun to watch as they for months placed those plates on the structure. The mirror is made from beryllium because it is strong and light element and the top is covered in gold for protection from radiation. This kind of mirror is used on optical telescope and the bigger the mirror is the better the image which is formed. This is why they must be so polished, it is also important to have the working area clean so this is how the engineers usually look like:

JWST Team Photo with Completed Flight Instrument moduleThere are few more instruments that collect the light in various spectrums. For now we must wait before they finish whole work, and there is nothing more to do than admire the work that Hubble has done for us (and is still doing (actually the work of engineers and scientists)).

Dragallur

Pictures from here here and here.