PHY 101: Vector Integration

By -
Image
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...
1 comment

Demystifying Planet Formation: The Definitive Guide

By -

How are planets formed?

Well, you all know by now how the stars are formed, planets are no different. When our sun was in its beginning stage, becoming the star it is now…the dust around the star was in constant motion. Some of these lucky dust crash into each other and form a larger pebble-like structure, more of these collide to become larger and larger clumps of rocks. These are what we call planets now.

Formation of planets
credits: https://k-poster.kuoni-congress.info/eas2021/poster/8d42d420-c000-412d-9a75-2a7ce80be1fe


What about moons though?

The moons are formed similarly….take our moon for example. It is believed the contents(minerals) of the moon’s surface match the range of the Earth’s surface and maybe it was due to some asteroid that hit Earth carved the moon out. The moon then became our only natural satellite.

We can from this say that is how the moons of Jupiter and Saturn also formed, although not from them but undoubtedly due to the dust around these massive objects i.e. due to gravity.


What about the core then?


This theory is all fine but what about the molten/solid core inside our planet, or the core of other planets, how in the world they came to be?


What you need to understand is that the core is solid, at least the innermost region is, and we believe it to be made from Iron, as it is the only abundant material in the universe that agrees with the seismic data, while it is also liquid in the outermost part. The rotation of our planet depends on the motion of the core, the fluid due to centrifugal force moves and causes the motion of the planet, while this rotation is slowing down, but by a very small fraction every year. This is due to the opposite force of the moon’s tidal effects. Usually, the Earth’s rotation is slowing down so that the length of the day increases by about 1.8 milliseconds per century, on average. This means that 600 million years ago a day lasted only 21 hours. But did you know Mars has a solid core and Jupiter might have a solid core might not? We don’t know for sure.


Conclusion:

While the planets are rocky they have so much of a deeper mystery inside of them that we don’t about. The core is yet to be understood by scientists and right now we have no technology capable of reaching the core and performing experiments to find out more about it. Also to leave you a bit confused, in 2020 scientists found the speed of Earth’s rotation has actually sped up in the last 50 years and the shortest 28 days all recorded were in 2020. Why did it increase? What could be the cause? Is it going to increase further in the years to come? That’s for you to find out!


References:

  1. https://www.sciencedirect.com/topics/earth-and-planetary-sciences/planetary-core

  2. https://www.sciencefocus.com/planet-earth/earth-rotation-speed

Comments

Post a Comment

Popular posts from this blog

Floating Rocks: A Quick read on space Rocks!

By -
Image
  Asteroid V Meteoroid credit:  https://science.nasa.gov/gallery/asteroid-comets-and-meteors/ What is the difference? Asteroids: "Rocks" floating in space is the best description one can provide to define either of these objects. A layman's way of knowing which is which is based on the size of the rocks. credit:  https://www.jpl.nasa.gov/asteroid-watch If the chunk of rock is significantly larger or in the range of 500-1000 kilometers in diameter it is given the tag of an Asteroid. We have one such belt of asteroids in our Solar system between Mars and Jupiter called as Asteroid Belt (No Joke!). While these may seem extremely big boulders floating in space compared to the massive size of the planets, they seem quite small. But these are not just rocks wandering in the dark space, these are composed of minerals and silicates and based on the amount of the chemicals present in them they are classified as C, S and M type of Asteroid. According to the International Astronomi...
Read more

PHY 101: Vector Integration

By -
Image
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...
Read more

PHY-101: Introduction to Vector Calculus

By -
 Beginning of a New series Welcome back to my blog. Over the months I have posted many blogs on different things in space be it the infamous space race between the US and USSR, the difference between an asteroid or meteor, or be it what are stars and what they are made of etc. But I think it is time for us to dive a bit deeper and understand how it all came through together. Why do we study physics? Why ask questions about the observable universe, and in extension why ask these questions at all? I will take you from the start of physics which is through mathematics to the world of vector calculus, from then on we will discuss Classical mechanics, Electricity and Magnetism extending to Electromagnetic Theory, Thermodynamics, Solid State Physics, Quantum mechanics and a bit of Astrophysics. (Not necessarily in that order) So hold tight for we will first start with arguably the most important and boring part of the series(for some do not like the math). Let us begin with Vector Calcul...
Read more