Документ взят из кэша поисковой машины. Адрес оригинального документа : http://star.arm.ac.uk/~meb/ras_leaflets2012/Gravity.2012.pdf Дата изменения: Tue Mar 6 03:05:37 2012 Дата индексирования: Tue Oct 2 06:43:36 2012 Кодировка: Поисковые слова: galaxy cluster

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Tycho Brahe and Johannes Kepler
ycho Brahe made observations of the motions of the planets from his great observatory on the island of Hven from 1576 to 1597. He introduced many innovations in technology and observing techniques, and understood the importance of random and systematic errors in his observations. In 1600 Tycho Brahe employed Johannes Kepler, the most distinguished mathematician in Europe, to work on the problem of the orbit of Mars. After Brahe died in 1601, Kepler set about analysing Brahe's magnificent data. Kepler fully appreciated the significance of these precise observations. In his words: "Divine providence has granted us such a diligent observer in Tycho Brahe that his observations convicted this Ptolemaic calculation of an error of 8 arcmin; it is only right that we should accept God's gift with a grateful mind... because these 8 arcmin could not be ignored, they alone have led to a total reformation of astronomy." Tycho's observations were 10 times more accurate than all previous observations and they led to Kepler's laws of planetary motion: Kepler 1: The orbits of the planets are ellipses with the Sun at one focus. Kepler 2: The line joining the Sun to a planet sweeps out equal areas in equal times. Kepler 3: The square of the period T of the planet about the Sun is proportional to the cube of the length of its semi-major axis r; T2 r3.

Tycho Brahe in his observatory with his instruments, including the great mural quadrant (1582). (ROE)

2.0 orbital period/years 1.5 1.0
Venus Mercury

Mars

Earth

0.5 0

Kepler's Third Law can be demonstrated using the average distances of planets from the Sun and their average period of revolution about the Sun.

0

0.5

1.0

1.5

(average distance from Sun)

3/2

2.0


igures in Gravitational Scie
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Isaac Newton
where G is the gravitational constant, M1 and M2 are the masses of the objects and r is their separation. The third book of the Principia lays out the Newtonian "System of the World", a celestial dynamics system based on the action of universal gravity. Newton presented results on the shape of the Earth and the variation of its surface gravity with latitude, showed that the complex motion of the Moon arises from the action of the Sun's gravity superposed on that of the Earth's, explained the way that the gravitational forces of the Sun and Moon act together to produce the ocean tides, and provided the first method for determining the trajectories of comets from limited observations. It is not an exaggeration to say that modern astronomy, and modern science, began with the publication of the Principia. n 1687 Isaac Newton published the Principia in which he set out his concept of the universal nature of gravity and also his law of gravity. The line of thought leading to his mature theory of gravity started with an exchange of letters with Robert Hooke in 1679­80, but it did not become precise until after a visit from Edmund Halley in 1684. Halley, like Hooke before him, asked about the trajectory of a body under the influence of inverse-square law forces directed towards a given centre. The Principia contains Newton's contributions to mechanics and celestial dynamics. He formulated the concepts of mass and centripetal force and set forth his three famous "Laws of Motion". Newton also showed the physical significance of Kepler's laws by relating them to centripetal forces. Today we write this as: F = GM1M2/r2

Sir Isaac Newton and the title page of his Principia (1687), which set out his law of gravity.


nce
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Albert Einstein
Gravitational radiation Einstein predicted that when two masses rotate about each other they will emit gravitational radiation, causing the bodies to move closer together and the period of rotation to decrease. This has been observed in the binary pulsar PSR 1913 + 16, in which two neutron stars, each no more than 20 km in diameter, orbit each other every 7.7 hours. Eventually the two stars will merge, releasing an intense burst of gravitational radiation and more energy than the supernova explosion that formed them. Gravitational wave detectors have been built in laboratories, but so far no detections have been made. lbert Einstein's great papers on Special Relativity and General Relativity, written at the beginning of the 20th century, extend Newton's theory of gravitation to much more extreme physical conditions. In his Special Theory of Relativity, published in 1905, Einstein showed that we live in a fourdimensional space-time. His famous formula E = mc2 is a consequence of this. His General Theory, completed in 1915, showed that matter bends space-time and that matter moves along paths in bent spacetime, making the theory somewhat complex. In the theory, the idea of gravity being a mysterious force is replaced by the idea of curved space-time. General Relativity predicted that the perihelion of Mercury would advance faster than predicted by Newtonian theory by a tiny but measurable rate. It also predicted that the paths of light rays would be bent by the Sun, which was first observed during the total eclipse of 1919. This effect is now seen much more dramatically in gravitational lenses. Einstein also showed that moving clocks would run more slowly, an effect that has been demonstrated by clocks placed in artificial satellites circling the Earth and by the greatly increased lifetimes of particles circling in accelerators.

0
accumulated orbital phase shift/s prediction of General Relativity

­4

­8

­12 1975 1980 1985 year 1990

As the two neutron stars of PSR 1913 + 16 get closer together, their orbit speeds up.


The

Tides
daily rotation about O Earth A O G in orbit around G B Moon orbital motion of the Moon about G

in orbit around G bulge due to solid and ocean tides

bulge due to solid and ocean tides

M

How the rotations of the Earth and the Moon lead to two tides each day.

ost of the Earth's seas experience two high and two low tides each day. There is also a tide in the solid surface of the Earth with a height of about half a metre. Tides are caused by the gravitational pull of the Moon and the Sun. To understand why there are two tides each day we must consider the force of gravity acting on the sea and the fact that the whole system is in rotation. Each month, the Earth and the Moon both orbit their common centre of gravity, G, located about 4600 km from the centre of the Earth, O, in the direction of the Moon. Consider the point B on the Earth's surface nearest the Moon. Here the pull of the Moon's gravity is greatest. On the opposite side of the Earth at A, the pull of the Moon's gravity is weakest. We must also include the effect of the centripetal force associated with points B and A rotating once a month about point G, which

is below the Earth's surface. The overall result is that there are equal-sized oceanic bulges on opposite sides of the Earth. The oceanic tidal bulges are fixed with respect to the direction of the Moon, while the solid Earth rotates about point O, beneath the oceans, giving rise to two high tides each day. Exactly the same types of tidal bulge are created by the interaction of the Sun and the Earth. The sizes of the tidal bulges due to the Sun are slightly less than half the size of those due to the Moon, giving rise to the phenomena of spring and neap tides. Roughly twice a month, the Sun and Moon line up and then the effects of the Sun and Moon reinforce each other to produce the largest tides, the spring tides. When the effects of the Sun and Moon are at right angles to each other, the sizes of the tidal bulges are at a minimum, corresponding to the neap tides.


Gravity

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DESIGN: Paul Johnson (higgs-boson.com)

ll matter experiences the force of gravity. It is the weakest of all the forces of Nature, but is the dominant force in astronomy and cosmology, controlling the movement of planets in our solar system, the structure of stars, the shapes of galaxies and the ultimate fate of our universe. The concept of a universal law of gravity was first presented by Isaac Newton in the 17th century and it can explain the properties of most astronomical systems. However, when bodies are moving at high speeds or in strong gravitational fields, Newton's theory is inadequate and we need Einstein's theories of relativity. Einstein's special and general theories of relativity play an essential role in understanding black holes, active galaxies and quasars.
This is one in a series of leaflets prepared by the Education Committee of the Royal Astronomical Society and produced with the aid of a grant from COPUS, the Committee on the Public Understanding of Science. It may be copied for educational use. It was written by E Baldwin, R Catchpole and M S Longair. The text on Newton benefited from comments by I B Cohen, Tufts University, and G Smith, Harvard University. © RAS 2003. Published by the RAS, Burlington House, Piccadilly, London W1J 0BQ. Reprinted 2012 by Armagh Observatory with funding from the Northern Ireland Department of Culture, Arts and Leisure (DCAL).


Solar System
The
Saturn Jupiter Uranus Neptune Sun Pluto

I

Halley's Comet

t can be shown that Newton's law of gravity allows the planets and other objects to take only certain types of orbit. These are circular, elliptical, parabolic or hyperbolic orbits. This list is in order of increasing energy for a given distance of closest approach to the Sun (perihelion). Both parabolic and hyperbolic orbits are open. Objects on parabolic orbits start out more or less at rest at a great distance from the Sun and are typical of comets from the Oort cloud which pass only once through the inner solar system. No comet has been seen coming into the solar system on a significantly hyperbolic orbit, but some comets come close to planets and are given hyperbolic orbits, leaving the solar system for ever. At the age of 26, Edmund Halley was inspired by the great comet of 1682 and used Newton's new theory to calculate the orbits of 24 comets. He realised that the comets of 1531, 1607 and 1682 were the same object and predicted its return in 1759. In fact, it reappeared on 25 December 1758. This was a major triumph for Newton's theory and the comet was named after Halley. Halley's Comet will make its 31st recorded appearance in 2061. Jupiter is the largest planet in the solar system and can have dramatic effects on the orbit of comets. On 8 July 1992 a comet, later known as Shoemaker-Levy 9, passed within 20 000 km of Jupiter. The tidal stress of Jupiter acting on the comet caused it to break up into 21 large fragments, each of which then continued on its own orbit. Two years later, the comet fragments had formed into a long line and between 16 and 22 July 1994 they plunged into Jupiter. Comets and asteroids occasionally hit the Earth. One famous impact occurred 65 million years ago, probably ending the reign of the dinosaurs and opening the era of the A montage (not to scale) showing fragments of the comet mammals. The impact crater associated with this catastrophic event has been identified at Chicxulub on the Yucatan Shoemaker-Levy 9 approaching peninsula in the Gulf of Mexico. Jupiter. (HST)


How
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tars are born when gravity causes a comparatively dense interstellar gas and dust cloud to collapse. The thermal pressure centre of the collapsing protostar becomes hotter and denser, until it is hot enough to ignite the nuclear fusion gravity reactions that convert hydrogen into helium. These reactions release energy that heats the gas at the centre of the star, producing a pressure which resists the force of gravity. As long as the fuel lasts, the star adjusts its internal structure so that there is an exact balance radiation escapes from the surface between the force of gravity and the force generated by nuclear energy of the star the pressure of the hot gas. generation Outside the protostar, the remains of the cloud forms into a rotating disc. By collisions and the action of gravity the Illustrating the structure of stars like the Sun. dust and gas slowly forms into ever-larger clumps. Eventually planets, moons, asteroids and comets are created. The ultimate fate of a star depends on its mass. A star about the same mass as the Sun will first become a red giant before ejecting its outer atmosphere, enriched with elements it has made, into the space between the stars. There the matter will be ready to form a new generation of stars, while the Sun becomes a white dwarf and slowly fades away. A star more than about eight times the mass of the Sun will finally destroy itself in a supernova explosion, which can be as bright as the light of an entire galaxy of stars. The force of gravity causes the central regions of the star to collapse, releasing vast amounts of gravitational potential energy. During the first few minutes of the supernova, heavy elements are created by nuclear fusion and dispersed into space in the explosion. In a supernova explosion, the central regions of the star collapse to form either a black hole or a rapidly rotating neutron star. Often neutron stars emit intense beams of radio energy. If the orientation of the neutron star is right then as the radio beam sweeps past the Earth, typically many times a second, the remnant is observed as a radio pulsar.

Stellar evolution

Supernova 1987A exploded in the Large Magellanic Cloud on 24 February 1987. Shown before (left) and after (right). (AAO)


Gravity Affects Our Univer e
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alaxies typically contain about 100 billion stars. Nearby, 99% of all galaxies are spirals or ellipticals. The spiral galaxies have prominent spiral arms which are defined by young, hot, blue stars and regions of star formation. The elliptical galaxies are featureless and appear to be mostly devoid of young stars. In spiral galaxies the characteristic spiral arms lie in a flattened, rotating disc held together by the overall gravitational field of the galaxy. In elliptical galaxies, which are also held together by gravity, the The spiral stars have much higher random velocities, with a galaxy NGC4414. substantial non-circular component. (HUBBLE HERITAGE TEAM [AURA/STSCI/NASA]) In many galaxies, there must be a large amount of dark matter present. The evidence for this comes from the rotation curves of the discs of the spirals, that is, the variation in the speed of rotation of the stars and gas of the galaxy with the distance from its centre. In many cases, the rotation curves are "flat" as far as they can be measured. It can be shown that this type of rotation curve means that the mass of the galaxy must continue to increase to large distances, despite the fact that the light falls off very rapidly. Consequently, there must be dark matter in the outer regions of galaxies. The nature of dark matter is one of the great unsolved problems in total enclosed mass cosmology. It is no longer thought rotation curve to consist of dead stars or brown dwarfs but may be some form of as yet undiscovered elementary particle.
speed of rotation
variation of brightness distance from centre of galaxy

Galaxies

Comparing the speeds of rotation of matter in the galaxy with the light emitted provides evidence for dark matter.


se rse
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few galaxies cannot be classified as spiral or elliptical. When two galaxies collide, their gravity pulls them into very strange shapes. The system known as the Antennae was formed when two spiral galaxies passed by each other in the same sense as the rotation of each disc of stars, that is, in the "prograde" direction. The stars in the outer rings felt the same outward force acting in the same direction for a prolonged period, and so were ripped off. Since nearly all galaxies occur in clusters, similar encounters between galaxies are quite common on a less spectacular scale. Within the Local Group of galaxies, the Large and Small Magellanic Clouds are currently being torn apart by the gravitational influence of our galaxy and eventually some of this debris will be assimilated by our galaxy, the Milky Way. In rich clusters of galaxies, massive galaxies can form at their centres, due to the collision and coalescence of smaller galaxies. Collisions are important in explaining the formation and evolution of galaxies.

Colliding Galaxies

The Antennae galaxy. (AAO)

1

2

Computer simulations of the collision of two spiral galaxies. In order of increasing time 1 to 3.
(A AND YU TOOMRE)

3


Clusters of Galaxies

Hubble Space Telescope image of the cluster Cl0024 + 1654, showing the multiple images of a distant blue galaxy lensed by the cluster. (HST)

X-ray image of the Coma Cluster in the 0.5­2.4 keV energy band observed by the ROSAT observatory.

C

lusters of galaxies are the largest gravitationally bound systems in the universe. The largest clusters contain thousands of galaxies. Just like the stars in elliptical galaxies, the random velocities of the galaxies in the cluster balance the attractive gravitational force of the cluster as a whole. In addition to galaxies, clusters of galaxies possess hot intergalactic gas and large amounts of dark matter. Evidence for hot gas in clusters comes from X-ray observations. The gravitational pull of the total mass of the cluster is so strong that the gas has to be very hot indeed to form a stable atmosphere within the cluster. The temperature of the hot gas in a massive cluster is typically about 10 million degrees. It turns out that there is as much mass in the hot diffuse intergalactic gas as there is in the galaxies themselves. However, the total mass

of the cluster is about 10 times the obervable mass of the galaxies and the hot intergalactic gas, so there must be large amounts of dark matter present. The distribution of the hot gas enables the distribution of the dark matter in the cluster to be determined. X-ray observations have suggested that the distribution of the dark matter is similar to that of the galaxies and the hot gas. Another remarkable aspect of the gravitational influence of clusters of galaxies is that they act as giant gravitational lenses, which can magnify and distort the images of distant background galaxies. This enables the mass of the cluster to be determined, and also the observation of the distant background galaxies, which would otherwise be too faint to be detected.


A

in the form of intense X-rays. black hole is a region of space-time Black holes have been found in some containing enough matter to create a double-star systems and in the centres of gravitational field sufficiently strong to galaxies. Those in double-star systems are prevent light escaping from it. This idea probably about 10 times the mass of the Sun was first suggested by John Michell in 1783, and the radius of the but a detailed event horizon is about understanding of the 30 km. They are the properties of black remnants of more holes only came with massive stars that the discovery of eventually exhausted General Relativity. It is their nuclear fuel and now known that black were crushed into a holes can have only black hole by the three properties: mass, overwhelming force angular momentum of gravity. and electric charge. Quasars are the Although black most luminous objects holes are themselves in the universe and invisible, they are the belong to a class of most efficient sources galaxies that have of energy known in A 5000 light year long jet emerging from a black holes, typically the universe, capable 9 2.4в 10 solar-mass black hole at the centre of 109 times the mass of of converting almost the giant elliptical galaxy M87. (HST) 50% of the rest-mass the Sun, at their that falls into them centres. Our own into energy. In contrast, radiation from hottest galaxy has a black hole mass of black hole gas is emitted close to v 2r hydrogen fusion in at its centre. It is quiet M= the last stable orbit G stars only converts 1% at the moment as of rest mass into there is no matter r v energy. As matter falls falling into it. towards a black hole, Black holes in the the principle of the nuclei of galaxies are conservation of responsible for a wide The accretion disc surrounding a black hole. angular momentum range of exotic highdemands that its energy astrophysical velocity of rotation increases. Thus the matter processes, including jets such as that seen in forms a rapidly rotating accretion disc around the nearby galaxy M87, as well as intense the black hole. Within the accretion disc radio, X-rays and -rays. These observations there are many collisions that raise the enable Einstein's theory to be tested in strong temperature so high that energy is released gravitational fields.

Black Holes


I

n 1929 Edwin Hubble discovered that the galaxies are all moving away from each other. The more distant they are, the greater their speed of recession v. This is known as Hubble's Law, v = H0r, where r is the distance. The Hubble constant, H0, was found using measurements of nearby galaxies. The formula then allowed the distance of far-away galaxies to be calculated. This enabled astronomers to map the universe. It has a foam-like structure with the galaxies arranged in sheets and clusters. Each structure is about 300 million light years across. On even larger scales the universe is uniform. However, at a distance of about 8 billion light years, Hubble's law underestimates galaxy distances. It seems that the universe is now expanding faster than it was in the past. It is probably accelerating, driven by a mysterious form of energy, dubbed dark energy. Observations show the universe to be 73% dark energy and 4% matter like ourselves. The other 23% is dark matter that is very different from the atoms around us. It cannot be seen but can be detected by the effect of its gravity. When the universe was young, the much higher density of matter allowed gravity to slow the rate of expansion. The above-average density of matter inside galaxies and even in clusters of galaxies halted the expansion of space, but elsewhere gravity has lost control and the universe may well expand for ever. We believe the universe came into being 13.7 billion years ago in a very-high-energy event known as The Big Bang from which it has expanded and cooled. It became transparent to photons when it was 380 000 years old. These energetic photons cooled to give us the view we see today as the cosmic microwave background. Its average temperature is only 2.735 degrees above absolute zero. The slight fluctuations in this temperature have their origins in quantum fluctuations in the early universe. These fluctuations have become the large-scale structures we now see in the universe.

Cosmology
cosmic time in units of present age of universe 0.99 0.95 0.9 0.8 0.7 0.3 redshift (z) 0.1 0.03 0.01 1000 20 15 10 (brighter) magnitude (fainter) 10 000 100 000 velocity of recession (km s­1)

0.003

A modern version of Hubble's law. (SANDAGE)
accelerating expansion less than critical density: expands forever

size

critical density: expands to rest at infinty

greater than critical density: collapses to a big crunch

today age of universe (depends on model)

time

Models of the expanding universe.

An allsky view of the cosmic background radiation. The mottled pattern is evidence of the quantum fluctuations in the early universe, now seen as tiny (1 in 100 000) variations in the intensity of the microwave radiation. (NASA/WMAP SCIENCE TEAM)