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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...

Space Junk: Graveyard of Debris in Low Earth Orbit

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credit: https://www.timetoast.com/timelines/space-race-99225b5b-6daa-4e7a-9c81-5945e1de0bc4 Since the dawn of the 1950s, the world has stated a race in the view of not who can conquer the Earth but who can dominate space. During World War 2, the Soviets and States were in a race to launch their own space program. The US spent a massive 257 billion dollars(Adjusted with inflation till 2020) while the Soviets spent around 255 billion dollars(adjusted with inflation till 2020), while the actual figures for the Soviets are not available this is an estimate taken from the assessment of various agencies available online. The race did help us in the form of putting the first satellite in space, humans in space, animals in space, etc. It also allowed us to upgrade to better technology. The Technology from the space race has also been applied to directly improve public safety and reduce the risk of accidents and injury. It acted as a boost for the world economies. While the race between the...

Did You Know about this?

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  Various events in space, you might have no clue about: 1. Kilonova: It is a beautiful astronomical event that happens in a binary neutron star system when the two neutron stars merge into one. To explain this imagine a scenario of two stars often referred to as a binary system, where both the stars rotate about a common Centre of mass, similar to what our Sun and Jupiter have going on, whenever the stars while completing their revolution around that point would come close to each other, the gravitational pull will pull them closer with every turn, after some time they would rotate so close to each other that they would end up merging into one. This would lead to a huge explosion, called a Kilonova. The amount of energy released during this event is approximately 10^40 Joules. While they are generally weaker compared to supernovas, which have a general energy output of 10^44Joules, they also tend to be brighter than a kilonova. Kilonovas are very rare as there are not many stars ...

The Birth of Stars: Igniting the Cosmic Flame

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What is a star? Stars can be regarded simply as; A big Ball of Fire. It is quite simple to define it but the way most books will do it is to call it a luminous gas giant/astronomical object. What we can understand from these definitions is; that stars are not just balls of fire, they are hot no doubt, but they are also filled with a large quantity of gas like Hydrogen(H) and Helium(He). These basic elements act as fuel sources. What you can imagine to understand this better is to consider the Sun as a thermal factory of plasma and heat, and to run this factory some source of energy is needed. These elements are the sources of that energy In the early universe, different gasses were coming together some of them came too close to each other and brushed against themselves, this friction along with their own gravity of the gasses compressed them together to form a spherical-shaped object. We now call it Stars. Credits: https://www.nationalgeographic.com/science/article/stars   Stages...