PHY 101: Vector Integration

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What is Integration? Integration can be thought of as a continuous analogue of sum (\(\sum_{ }^{ }\)). We integrate or simply add infinitesimal small quantities together to form a continuous chain. Integration can be of 3 kinds rather I would call it 3 ways of integration. Linear, Area and Volume way. To show what each of them looks like here is a visual representation: $$\begin{aligned}& Linear \hspace{1mm}integration:\int_{ }^{ }f(x)dx\\ \\ &Area\hspace{1mm}or\hspace{1mm} surface\hspace{1mm} integration: \iint_S f(x,y)dxdy \\ \\ & Volume \hspace{1mm} integration: \iiint_V f(x,y,z)dxdydz \end{aligned}$$ You might have already noticed that the number of integration symbols (\(\int_{ }^{ }\)) increases with the increase in the number of variables. Hence, most books adopt the notation of calling these single, double and triple integrations. We at physics are creatures of simplicity and thus have kept it easy to remember. Let us talk about each in some detail! Single or Linear...
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Exoplanets: World beyond Our Horizon

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 Do you know what Exoplanets are?

Exo-planet means, external planet by the literal meaning of the word. One can say a planet outside our solar system is an exoplanet and they would be correct. However, what makes these "exoplanets" so special? they're just planets like our Venus or Neptune or Saturn. they are just planets, right? nothing we already do not know about. Kinda!!

Our planets are special no doubt and we have learned a lot about them, there are still many things we do not know about them regardless exoplanets become an interesting observation for astronomers because these planets are in a different solar system. It could be a binary one or something else. They have different chemical compositions as opposed to what we find in our solar system.

TrES-2b: A World of Eternal Darkness
credits: https://twitter.com/NASAExoplanets/status/1402010819525693471 


You would be amazed to know what kind of planets are actually out there, for a start TrES-2b is a very dark planet, cause it reflects >1% of the light it gets. Do you remember our ringed planet? Saturn? it has beautiful rings really but J1407b has approximately 640 times the extent of the rings found on Saturn, which effectively means HUGE rings.

J1470b-Super Saturn
credits: https://exoplanets.nasa.gov/resources/242/j1407b-super-saturn/


What's with the crazy names?

At this point, you might say wait our planets have pretty sane names, Earth, Mercury, Jupiter, etc. What's with the weird lingo for exoplanets, who names a planet TrES-2b or J1407b it doesn't make much sense now, does it?

Remember the saying "There’s a grain of sand for every star in the sky", imagine so many galaxies, so many solar systems in them, and imagine the number of planets out there, it is difficult to name all the planets so scientists have a way to catalogue these planets[1]. The world of eternal darkness, our darkest planet is named because of the star it revolves around, and the star is named TrES-2 while the b tells us that it is a planet and that is how the exoplanets are named. After the star system where they were found in.

What is the Habitable Zone?

In a star system, there is a region of space where the starlight and the heat is just right for Life to be there. The chances of finding life on some planet increase if the planet is in the habitable zone. The age-old question of whether there is life in the Universe other than that on Earth motivated us to build large telescopes and seek the answers we are looking for in the stars. While we haven't found beings of higher intelligence yet we do know microbial life is out there in space[2].

Habitable Zone
credits: https://exoplanets.nasa.gov/search-for-life/habitable-zone/


Conclusion: Exoplanets expand our perspective in space allowing us to see a world full of possibilities and mystery, they force us to expand our imagination and seek answers about our place in the universe.

Reference:

[1] To know more about exoplanets and the catalogue visit:- https://exoplanets.nasa.gov/eyes-on-exoplanets/#/

[2] To know more about the discovery of microbial fossils visit:- https://www.amnh.org/learn-teach/curriculum-collections/cosmic-horizons-book/fossil-microbes-mars

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