Per Aspera Ad Astra (Part 1)

This is a series of articles intended to educate aspiring astronomers about observational and theoretical Astronomy. Our discussion will range from the basic unaided techniques to the frontiers of ongoing Astronomical research which will include fun Mathematics and Physics involved in Astronomy. Advanced technologies, and engineering methods prevalent in modern Astronomy will also be covered in the forthcoming articles of this series. A dedicated post shall also look into the various career options related to Astronomy.
Have you ever wondered what the sky really is? Have you ever asked why the sky acts like the largest canvas you have ever seen, a canvas that stretches from the horizon to the zenith (the point directly overhead) which consistently carries varying pictures at various times? If you have evolved to have become a human being, you must have. We humans have always wondered at the enormity of the sky. Not just wondered, we have shed our sheer animal instincts and have evolved as humans by relentlessly trying to look at the sky and understand it. No other animal than Humans have acquired the physiological vantage point of the human head that is the best suited to watch the sky. Or should we say, the heavens, as commonly perceived.

So, what is the Sky and where does it those colours that it flaunts?

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Charged Particle in Coexisting Electric and Magnetic Fields

This is a key problem for students preparing for JEE Advanced, JEE Main, and NEET (undergraduate). Many questions of varying standards and toughness can be formed on its basis, some of which have been put here in the question statement. For example, the magnetic field working perpendicular to the velocity vector all the time is not going to produce any work. Thus the question can be a little modified to be easily solved by using the Work-Energy principle so that the work done by the electric field can be equated to the kinetic energy of the particle. However, in this particular problem, that technique is useless. That’s why we must understand the Physics and Mathematics involved in this question. A short tutorial post explaining how a sample variant of this question can be asked is going to be published next.

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Bead embedded to a rotating wire

This problem can be solved in at least 3 meaningful ways, (a) from the ground frame, (b) from the rotating frame and (c) with Lagrangian. Let us do it in all of them. But even before we begin to decide whether to use Lagrangian mechanics or not, we need to understand the motion from the ground frame. It is not always advisable to use the ground frame to solve problems in rotational motion. More often than not, the ground frame calls for more variables and thus more equations than the rotational frame. However, using the rotational frame calls for fictitious or pseudo forces and without a firm understanding of the motion through the real forces, there is a big possibility of making mistakes. Hence, ThePhysicist suggests that the students, while practicing, should always try to solve problems of rotational motion from the ground frame first and then from the rotational frame.

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