# Engineering Mathematics

## Linear Algebra

• Matrix algebra,
• Systems of linear equation,
• eigen values and eigen vectors.

## Calculus

• Functions of single variable, limit, continuity and differentiability,
• Mean value theorems,
• Evaluation of definite and improper integral,
• Partial derivatives,
• Total derivatives,
• Maxima and minima,
• Vector identities,
• Directional derivatives, line, surface and volume integrals,
• Theorems of Stokes, Gauss and Green.

## Differential calculus

• Frist order linear and nonlinear equations,
• Higher order linear ODEs with constant coefficients,
• Cauchy and Euler equations,
• Initial and boundary value problems,
• Laplace transforms.
• Partial differential equations and separation of variables methods.

## Numerical Methods

• Numerical solution of linear and nonlinear algebraic equations,
• Integration by trapezoidal and Simpson rule,
• Single and Multi-step methods for differential equations.

# Comet ISON ( C/2012 S1 )

C/2012 S1 AKA Comet ISON or Comet Nevski-Novichonok, is a latest comet discovered and confirmed on Sep 21 2012 by two Russian astronomers Vitali Nevski and Artyom Novichonok.  The discovery made using the 0.4 reflector of the International Scientific Optical Network near Kislovodsk, Russia and the Automated asteroid program CoLiTec.

It was actually on 28 Dec 2011 by Mount Lemmon Survey and by Pan-STARRS from 28 Jan 2012 were quickly located. Later on after the discovery some observations are made by SWFIT and suggests that the comet’s nucleus is around 5 kilometers (3.1 miles) in diameter.

Now let’s talk about it’s orbit. This comet is coming from the Oort cloud which is beyond the Kuiper belt surrounding our solar system outside Pluto’s orbit. It will come to the perihelion ( which is the closest point to the sun in it’s orbit ) on 28 Nov 2013 at a distance of 0.0124 AU (18, 60,000 km) from the centre point of the sun, which makes it 11,65,000 km from the surface of the sun. The trajectory is found to be hyperbolic, which means this comet never came before and will never come again. It has passed the Mars at a distance of 0.07248 AU on Oct 1 2013 and it also been captured by the Mars Reconnaissance orbiter (MRO). It has been given below. It will pass near Earth on Dec 26 2013 at a distance of 0.4292 AU (6,42,10,000 km).

Are you asking will it visible on earth….???

The answer is yes. Initially it is predicted to reach an apparent magnitude greater then full moon, but later observations predicted that it only will reach a magnitude just greater than Venus. However it will be only visible to the naked eye from the first week of the Nov 2013. It will get brighter and brighter when it closes on Sun and it will be visible even after it survives the perihelion until the first week of Jan 2014.

There is debate going on on whether the comet will survive it’s closest approach to the Sun or it will disintegrated by our Sun’s immense gravitational field. Because there is something called “Roche limit”, it will determine the comet’s survival. We will see about Roche limit about later

The above image is the prediction of the trajectory of the comet ISON. Hubble’s capture of ISON near Jupiter orbit, it is given below

Our site will post further updates and images captured us using our telescope………

# Radial Velocity method of finding an exo-planet

You might want to recollect some of the topics you have studied before going into this, if you haven’t don’t worry I will explain it all in this summary. Let us begin the journey………..

You might have studied about Doppler Effect in physics. Of course it deals with the sound from a moving object while listening from a stationary point. The same applies in the light spectrum too. If a light source is drawn away from an observer the most of the blue light in that spectrum will get scattered and the red light is all that remains in that spectrum. This is because the low wavelength of the blue light makes it to scatter when travelling through air molecules and the red light has a larger wavelength which mays it to travel longer distance without getting scattered.

We all know that stars and planets are bound together by a weak and a long range force called gravitational force of attraction. Each and every mass in space possess gravity. Depending upon its mass and density the gravitational magnitude will vary. If an object is lot denser it’s force of gravity will be huge, if its density is low the force of gravity will be low. That’s why extremely dense black holes possess inescapable gravitational force and it can even rip the space and time. We’ll talk about the black holes later.

So, you might ask what this has to do with the spotting of an exo-planet, here’s the reason why.

When a planet revolves around its host star its gravitational force affects the star’s axis of rotation, i.e. the star wobbles due to the gravitational force of the planet.

When the planet comes between the earth and the host star the host star is pulled towards earth for a fractional amount, this makes the light spectrum from the star to possess some blue light wavelength too and when the planet goes behind the star, the star gets pulled away from the earth and the starlight spectrum goes red. By detecting these variations in a starlight spectrum we can easily confirm that a planet definitely revolves around it. By using this method we can also find the mass and density of the planet revolving around it. Although this method can only be used for detecting large planets because only large planets have enough gravity to make the host star wobble along its rotational axis. Remaining ways to find an exo-planet will follow later.

# Want to discover an exoplanet..? Then Hop on

Exo-plants or extraterrestrial planets are really exciting to find and hard to find. Do you really want to know how to detect and find an exo-planet, then tag along on the amazing journey of ways to find one.

The different ways are given below

• Transit method
• Orbital light variations
• Light variations due to relativistic beaming and ellipsoidal variations
• Timing variations
• Gravitational micro lensing
• Direct imaging
• Polarimetry
• Astrometry