Booster Class Topic: Constrained Motion Page 1 Section: Mechanics For IIT- JEE M Booster Class/3 C O. Class Notes X Y L A A S G I C YS P H Class. Booster Class Topic: System of Particles & Dynamics (Tran & Rot) Page 1 Section: Mechanics For IIT-JEE M Booster Class/4 C O. Class Notes X Y L A A. Physics Galaxy, world's largest website for free online physics lectures, physics courses, class 12th physics and JEE physics video lectures.

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In , Hendrik van de Hulst predicted that microwave radiation with wavelength of 21 cm would be detectable from interstellar atomic hydrogen gas; [49] and in it was observed. This radiation is not affected by dust absorption, and so its Doppler shift can be used to map the motion of the gas in our galaxy.

These observations led to the hypothesis of a rotating bar structure in the center of our galaxy. In the s, Vera Rubin uncovered a discrepancy between observed galactic rotation speed and that predicted by the visible mass of stars and gas.

Today, the galaxy rotation problem is thought to be explained by the presence of large quantities of unseen dark matter. Among other things, Hubble data helped establish that the missing dark matter in our galaxy cannot solely consist of inherently faint and small stars. Particularly, galaxy surveys in the Zone of Avoidance the region of the sky blocked at visible-light wavelengths by the Milky Way have revealed a number of new galaxies.

A slightly more extensive description of galaxy types based on their appearance is given by the Hubble sequence. Since the Hubble sequence is entirely based upon visual morphological type shape , it may miss certain important characteristics of galaxies such as star formation rate in starburst galaxies and activity in the cores of active galaxies.

These galaxies have an ellipsoidal profile, giving them an elliptical appearance regardless of the viewing angle.

Their appearance shows little structure and they typically have relatively little interstellar matter. Consequently, these galaxies also have a low portion of open clusters and a reduced rate of new star formation.

Instead they are dominated by generally older, more evolved stars that are orbiting the common center of gravity in random directions. The stars contain low abundances of heavy elements because star formation ceases after the initial burst.

In this sense they have some similarity to the much smaller globular clusters. Many elliptical galaxies are believed to form due to the interaction of galaxies , resulting in a collision and merger.

They can grow to enormous sizes compared to spiral galaxies, for example , and giant elliptical galaxies are often found near the core of large galaxy clusters. About one-tenth of elliptical galaxies have a shell-like structure, which has never been observed in spiral galaxies. The shell-like structures are thought to develop when a larger galaxy absorbs a smaller companion galaxy. As the two galaxy centers approach, the centers start to oscillate around a center point, the oscillation creates gravitational ripples forming the shells of stars, similar to ripples spreading on water.

For example, galaxy NGC has over twenty shells. Though the stars and other visible material contained in such a galaxy lie mostly on a plane, the majority of mass in spiral galaxies exists in a roughly spherical halo of dark matter that extends beyond the visible component, as demonstrated by the universal rotation curve concept.

Extending outward from the bulge are relatively bright arms. In the Hubble classification scheme, spiral galaxies are listed as type S, followed by a letter a, b, or c that indicates the degree of tightness of the spiral arms and the size of the central bulge. An Sa galaxy has tightly wound, poorly defined arms and possesses a relatively large core region.

At the other extreme, an Sc galaxy has open, well-defined arms and a small core region. Like the stars, the spiral arms rotate around the center, but they do so with constant angular velocity.

The spiral arms are thought to be areas of high-density matter, or " density waves ". The velocity returns to normal after the stars depart on the other side of the arm.

This effect is akin to a "wave" of slowdowns moving along a highway full of moving cars. The arms are visible because the high density facilitates star formation, and therefore they harbor many bright and young stars.

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Bars are thought to be temporary structures that can occur as a result of a density wave radiating outward from the core, or else due to a tidal interaction with another galaxy. They are very large with an upward diameter of , light-years compared to the Milky Way's , light-year diameter. With a mass of billion solar masses, they generate a significant amount of ultraviolet and mid-infrared light.

They are thought to have an increased star formation rate around 30 times faster than the Milky Way. A ring galaxy has a ring-like structure of stars and interstellar medium surrounding a bare core.

A ring galaxy is thought to occur when a smaller galaxy passes through the core of a spiral galaxy.


These are categorized as Hubble type S0, and they possess ill-defined spiral arms with an elliptical halo of stars [78] barred lenticular galaxies receive Hubble classification SB0. Irregular galaxies are galaxies that can not be readily classified into an elliptical or spiral morphology.

An Irr-I galaxy has some structure but does not align cleanly with the Hubble classification scheme.

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Irr-II galaxies do not possess any structure that resembles a Hubble classification, and may have been disrupted. An ultra diffuse galaxy UDG is an extremely-low-density galaxy.

The lack of luminosity is because there is a lack of star-forming gas in the galaxy which results in old stellar populations. Magnitude systems and their relationship to quantitative measurements of luminosity and effective temperature. Observational properties of stars and galaxies: the H-R diagram, stellar clusters, basic description of the structure of the Milky Way; the Hubble classification of galaxies; galaxy luminosity functions.

The equations of stellar structure: hydrostatic equilibrium, virial theorem, convection and energy transport. Structure of main sequence stars; use of scaling relations to derive relationships between stellar masses, luminosities, radii and lifetimes.

The Chandrasekar limit and degenerate stellar cores; introduction to post-main sequence evolution. Galaxies treated as systems of stars in spherically symmetric gravitational potentials. The Collisionless Boltzmann Equation; Jeans' equations; moments of distributions. Stellar velocity dispersions and their use to infer the potential.

Heat death of the universe

Influence of a point mass at the centre of the potential; observational evidence for supermassive black holes in normal galaxies. Textbooks There is not really a course textbook, but the following are useful: Astrophysics for Physicists - A. Tremaine Second Edition Princeton University Press - Note this book is graduate-level and goes well beyond this course Lecture Outline The actual split of topics between lectures may change.

Lecture notes will be posted here shortly PDF format. Lecture 1 Lecture notes PDF. Lecture slides PDF.

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Unit of length, parallax, definition of parsec Choudhuri 1. Solar units. Constrained Motion Page 5 Section: Constrained Motion Page 6 Section: Constrained Motion Page 7 Section: Constrained Motion Page 8 Section: Constrained Motion Page 9 Section: Constrained Motion Page 10 Section: Constrained Motion Page 11 Section: Constrained Motion Page 12 Section: Constrained Motion Page 13 Section: Constrained Motion Page 14 Section:Consequently, these galaxies also have a low portion of open clusters and a reduced rate of new star formation.

Magnetic fields provide the transport of angular momentum required for the collapse of gas clouds and hence the formation of new stars.

Constrained Motion Page 11 Section: The cycle of stellar birth and death slowly increases the abundance of heavy elements, eventually allowing the formation of planets. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that appeared to be similar to stars, rather than extended sources similar to galaxies.

Galaxies treated as systems of stars in spherically symmetric gravitational potentials.