Some Concepts of Physics

Simple concepts, Big Physics

Mass

• Usually defined as the quantity of matter in a body

• Does this definition need improvement?

• Why?

Mass Varies with Velocity

• A body moving at very high speeds has mass depending on its speed, if you believe in relativity.

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Variation of mass with velocity

See in the figure alongside how the mass of a body changes with velocity. Here is the mass of the body at rest.

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Definition of Mass

• Is it, then, correct to say that mass is the quantity of matter contained in a body?

• Is there a better way of defining mass?

An Alternative definition of Mass

• Would it not be better to define mass as a measure of inertia?

• Greater the resistance of a body to a change in its state of motion, greater the inertia and hence the mass.

Unit of Mass

• At present the kg is the only unit which is arbitrarily defined in terms of the mass of a certain body kept at specified conditions somewhere in Paris. Copies are kept in many countries.

Prototype Kilogram

International Prototype Kilogram (IPK),A platinum-Iridium Cylinder.Present Definition Since 1901.

A Better Defintion of a Unit

• It is more natural to construct units from natural physical constants which have some physical significance. Notice that the other two fundamental units, those of length and time, are now no longer arbitrary.

• One metre is defined as the distance travelled by light in vacuum in a time interval of 1/299792458 second.

About the metre

• Remember that the Metre was once based on a measurement of a meridian between Dunkirk and Barcelona. It was defined as one ten-millionth of the length of the Earth's meridian through Paris from the equator to the north pole.

Released into the public domain http://commons.wikimedia.org/

Definition of Metre

The figure is based on a figure from

www.npl.co.ukEquator

North Pole

Meridian through Paris

A bar with a rectangular cross section, made of 90% platinum and 10% iridium, with polished parallel ends, and kept at 0 degree C, was made to represent the meter.

Standard of Length• In 1960 the General Conference

on Weights and Measures redefined the International Standard of Length as 1,650,763.73 vacuum wavelengths of light resulting from certain unperturbed atomic transition of krypton - 86.

Refinement in the Definition of the Unit of Length

• In 1983 the meter was redefined again to further reduce uncertainty. The metre was defined in terms of the speed of light and time. It is now the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.

Definition of Second

• In 1956 the second was defined in terms of the period of revolution of the Earth around the Sun for a particular epoch, because by then it had been recognized that the Earth's rotation on its own axis was not sufficiently uniform as a standard of time

Equator

Ecliptic

Earth

Vernal Equinox

Sun

Earth

The time taken by the Sun to go round from vernal equinox and back to it is called a tropical year.

GNU Free Documentation License. commons.wikimedia.org

The tropical year is not a constant interval of time.

Unit of Time

• The second thus defined was

–the fraction 1/31,556,925.9747 of the tropical year for epoch1900 January 0 at 12 hours ephemeris time.

Ephemeris Time (ET) is the closest approximation to a uniform time. It uses the best available theory of the earth's rotation which removes the known changes in rotation rate. The use of Ephemeris Time continued until 1984.

Refinement in the Unit of Time

• With the development of the atomic clock, it was decided to use atomic clocks as the basis of the definition of the second, rather than the revolution of the Earth around the Sun.

Second Defined

• As a result, in 1967 the General Conference on Weights and Measures defined the second of time in the International System of Units as–the duration of 9,192,631,770

periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

Latest Defintion of Second

• One second is the time required for a Cesium – 133 atom (at rest at 0 K) to undergo 9192631770 vibrations between two hyperfine levels of its ground state.

Goal Of Changes

• In all of these changes in definitions, the goal was not only to improve the precision of the definition, but also to change its magnitude as little as possible.

Unit of Mass

• The mass is still defined in terms of a man-made body. This worries scientist.

• There are reports that the mass of the prototype kilogram is decreasing. The cause is not known.

A Possibility• A quantity

consisting of a combination of physical constants has dimensions of mass. However, its value 2.1765 × 10-8 kg is very inconvenient for every - day use.

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G

c

IUPAP Commission

• Efforts be continued to refine experiments that link the unit of mass to fundamental constants with a view to improving the connection between macroscopic and microscopic masses and the realization of macroscopic mass measurements in terms of a fundamental definition of the kilogram.

Mass – Energy Equivalence• Just one more

trivial thing: In particle physics, the mass is routinely stated in terms of energy using the relation between mass and energy.

2mcE

Mass in Terms of Energy

• It is more convenient to say that the mass of an electron is 0.5 Mev, rather than saying me = 9 × 10-31

kg. This is also a good exercise for the students to calculate the mass of an electron and a proton (940 Mev) in terms of energy.

"The most likely Higgs mass has now been increased from 96 to 117 GeV/c²" ? GeV/c² is a common particle-physics unit of mass; the mass of the proton measures about 1 GeV/c²? “Which means it's probably beyond the sensitivity of current experiments, but very likely to be found in future experiments at the Large Hadron Collider being built at CERN."

June 2004

Centre of Mass

• Exercise: Where would be the CM of the sun-earth system?

• Mass of the sun: 2 × 1030 kg• Mass of the earth: 6 × 1024 kg• Would it be close to the centre of

the earth, or that of the sun, or somewhere in between?

Common Centre of Mass

• We must also remember that the earth and the sun must revolve round their common centre of mass. We are used to considering only the earth revolving round the sun.

Two stars move about their common CM

For animation, visit http://upload.wikimedia.org/wikipedia/commons/7/73/Orbit1.gif

CM

Centre of Mass of the Sun – Earth System

• If the centre of mass of the sun-earth system lies close to the centre of the sun (only 449 km away from the centre of the sun of radius 696000 km), what is the implication?

CM of the Sun-Earth SystemNotice slight displacement from

the centre of the sun.

Sun

Earth

Based on zebu.uregon.edu

Doppler Shift

• Illustration of Doppler Shift

Source: http://www.astrosociety.org/education/publications/tnl/67/music.html

Doppler Shift

• Notice that the spectral lines shift towards red when the object is moving away from us, and towards blue when it moves towards us.

Source of Fig. spheroid.wordpress.com/2007/02/18/astro-seminar-finding-exoplanets/

Wobble of a starThe star wobbles because of the presence of a planet. What we see is the shift in the spectral lines from the star.

For animation, visit www.astronomynotes.com/lifezone/star-wobble.gif

Motion of the Sun seen from Outside

• If alien astronomers began tracking the motion of the Sun in the year 2000, viewing it from its North Ecliptic Pole, this is what they would see over the next 50 years, adjusted for the normal motions of the star and system.

Wobble of the sun

Credit: The New York Times

http://plus.maths.org/issue10/news/planet/wobble.gif

For animation of the wobbling motion, visit:

Velocity Curve of a Wobbling Star

• 51 Peg is a variable star

Source: www.seti.org

Estimate of the Mass

• Once the time period of the wobbling motion is determined, then Kepler’s third law is used to get the combined mass of the star and the planet.

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planetstar

Extrasolar Planets

• More than 150 extrasolar planets have been discovered. Most of them have masses similar to that of Jupiter. Technology not yet sufficiently advanced to detect planets of the size of the earth.

Prerequisite for Life to Exist

• In order to be able to say whether life exists outside our solar system, it is necessary not only to find planets of the size of the earth, but also to detect molecules which form the basis of life.

Complex Molecules Discovered

• Astronomers have found the first signature of complex organic molecules in the dust cloud around a distant star, suggesting that these building blocks of life may be a common feature of planetary systems.

Tholins

• In our solar system, the large carbon molecules, called tholins, have been found in comets and on Saturn's moon, Titan, giving its atmosphere a red tinge.

Titan, A Moon of SaturnA picture of Titan from The Hubble Space Telescope, the orange is caused by a thick atmosphere.

Precursors to Biomolecules

• Tholins are thought to be precursors to the biomolecules that make up living organisms on Earth (though they are no longer found on our planet because the oxygen in our atmosphere would quickly destroy them).

Detection of Tholins

• A new study, reported recently, features observations of the spectrum of the dust disk surrounding the star HR4796A that indicate the presence of tholins there.

Habitable Zone• For life to exist on a palnet, it must

also be in the habitable zone. This is the region in the solar system which is neither too hot nor too cold, but just right. Astronomers believe that in other solar systems, too, such habitable zones exist and life is more probable in those planets which fall in this zone.

Habitable Zone in the Solar System

0.95 – 1.37 AU

1 AU is the distance of Earth fromThe Sun.

Fig from www.dur.ac.uk

Habitable Zones

• But the habitable zone may be larger than originally conceived. The strong gravitational pull caused by large planets may produce enough energy to sufficiently heat the cores of orbiting moons. Life has proven itself tough here on Earth. Perhaps it could thrive in more extreme environments.