## Sunday, 16 December 2007

### Gravitasi

Arip Nurahman
Department of Physics, Faculty of Sciences and Mathematics
Indonesia University of Education
&
Follower Open Course Ware at MIT-Harvard University, USA.

Gravitation is a natural phenomenon by which all objects with mass attract each other. In everyday life, gravitation is most familiar as the agency that gives objects weight. It is responsible for keeping the Earth and the other planets in their orbits around the Sun; for keeping the Moon in its orbit around the Earth, for the formation of tides; for convection (by which hot fluids rise); for heating the interiors of forming stars and planets to very high temperatures; and for various other phenomena that we observe. Gravitation is also the reason for the very existence of the Earth, the Sun, and most macroscopic objects in the universe; without it, matter would not have coalesced into these large masses and life, as we know it, would not exist.

Modern physics describes gravitation using the general theory of relativity, but the much simpler Newton's law of universal gravitation provides an excellent approximation in most cases.

In scientific usage gravitation and gravity are distinct. "Gravitation" is the overall theory dealing with the attractive influence that all objects exert on each other, while "gravity" specifically refers to a force produced by a massive object (i.e., an object with mass). The terms are mostly interchangeable in everyday use. In general relativity, gravitation is due to spacetime curvatures which causes inertially moving objects to tend to accelerate towards each other. Another (discredited) example is Le Sage's theory of gravitation, in which massive objects are effectively pushed towards each other.

## History of gravitational theory

### Early history

Efforts to understand gravity began in ancient times. Philosophers in ancient India explained the phenomenon from the 8th century BC.[1] According to Kanada, founder of the Vaisheshika school, "Weight causes falling; it is imperceptible and known by inference."[2]

In the 4th century BC, the Greek philosopher Aristotleeffect without a cause, and therefore no motion without a force. He hypothesized that everything tried to move towards its proper place in the crystalline spheres of the heavens, and that physical bodies fell toward the center of the Earth in proportion to their weight. believed that there was no

Brahmagupta, in the Brahmasphuta Siddhanta (628 AD), responded to critics of the heliocentric system of Aryabhata (476–550 AD) stating that "all heavy things are attracted towards the center of the earth" and that "all heavy things fall down to the earth by a law of nature, for it is the nature of the earth to attract and to keep things, as it is the nature of water to flow, that of fire to burn, and that of wind to set in motion... The earth is the only low thing, and seeds always return to it, in whatever direction you may throw them away, and never rise upwards from the earth."[3][4]

In the 9th century, the eldest Banū Mūsā brother, Muhammad ibn Musa, in his Astral Motion and The Force of Attraction, discovered that there was a force of attraction between heavenly bodies,[5] foreshadowing Newton's law of universal gravitation.[6] In the 1000s, the Iraqi scientist Ibn al-Haytham (Alhacen), in the Mizan al-Hikmah, discussed the theory of attraction between masses, and it seems that he was aware of the magnitude of acceleration due to gravity.[7] In 1121, Al-Khazini, in The Book of the Balance of Wisdom, differentiated between force, mass, and weight,[8] and discovered that gravity varies with the distance from the centre of the Earth,[9] though he believed that the weight of heavy bodies increase as they are farther from the centre of the Earth.[10]

Scientific revolution

Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th century and early 17th century. In his famous (though probably apocryphal) experiment dropping balls from the Tower of Pisa, and later with careful measurements of balls rolling down inclines, Galileo showed that gravitation accelerates all objects at the same rate. This was a major departure from Aristotle's belief that heavier objects are accelerated faster. (Galileo correctly postulated air resistance as the reason that lighter objects may fall more slowly in an atmosphere.) Galileo's work set the stage for the formulation of Newton's theory of gravity.

### Newton's theory of gravitation

In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square law of universal gravitation. In his own words, “I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centers about which they revolve; and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly.”

Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted by the actions of the other planets. Calculations by John Couch Adams and Urbain Le Verrier both predicted the general position of the planet, and Le Verrier's calculations are what led Johann Gottfried Galle to the discovery of Neptune.

Ironically, it was another discrepancy in a planet's orbit that helped to point out flaws in Newton's theory. By the end of the 19th century, it was known that the orbit of Mercury could not be accounted for entirely under Newton's theory, but all searches for another perturbing body (such as a planet orbiting the Sun even closer than Mercury) had been fruitless. The issue was resolved in 1915 by Albert Einstein's new General Theory of Relativity, which accounted for the discrepancy in Mercury's orbit.

Although Newton's theory has been superseded, most modern non-relativistic gravitational calculations are still made using Newton's theory because it is a much simpler theory to work with than General Relativity, and gives sufficiently accurate results for most applications.

General relativity

In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of a force. The starting point for general relativity is the equivalence principle, which equates free fall with inertial motion. The issue that this creates is that free-falling objects can accelerate with respect to each other. In Newtonian physics, no such acceleration can occur unless at least one of the objects is being operated on by a force (and therefore is not moving inertially).

To deal with this difficulty, Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. (This type of path is called a geodesic.) More specifically, Einstein discovered the field equations of general relativity, which relate the presence of matter and the curvature of spacetime and are named after him. The Einstein field equations are a set of 10 simultaneous, non-linear, differential equations. The solutions of the field equations are the components of the metric tensor of spacetime. A metric tensor describes a geometry of spacetime. The geodesic paths for a spacetime are calculated from the metric tensor.

Notable solutions of the Einstein field equations include:

General relativity has enjoyed much success because of how its predictions of phenomena which are not called for by the theory of gravity have been regularly confirmed. For example:
Gravity and quantum mechanics
Main articles: Graviton and Quantum gravity

Several decades after the discovery of general relativity it was realized that general relativity cannot be the complete theory of gravity because it is incompatible with quantum mechanics.[11] Later it was understood that it is possible to describe gravity in the framework of quantum field theory like the other fundamental forces. In this framework the attractive force of gravity arises due to exchange of virtual gravitons, in the same way as the electromagnetic force arises from exchange of virtual photons.[12][13] This reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the Planck length,[14] where a more complete theory of quantum gravity is required. Many believe the complete theory to be string theory,[15] or more currently M Theory.

## Specifics

### Earth's gravity

Main article: Earth's gravity

Every planetary body (including the Earth) is surrounded by its own gravitational field, which exerts an attractive force on all objects. Assuming a spherically symmetrical planet (a reasonable approximation), the strength of this field at any given point is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body.

The strength of the gravitational field is numerically equal to the acceleration of objects under its influence, and its value at the Earth's surface, denoted g, is approximately 9.81 m/s² as the standard average. This means that, ignoring air resistance, an object falling freely near the earth's surface increases its velocity with 9.81 m/s (32 ft/s or 22 mi/h) for each second of its descent. Thus, an object starting from rest will attain a velocity of 9.81 m/s (32 ft/s) after one second, 19.6 m/s (64 ft/s) after two seconds, and so on, adding 9.8 m/s to each resulting velocity. According to Newton's 3rd Law, the Earth itself experiences an equal and opposite force to that acting on the falling object, meaning that the Earth also accelerates towards the object. However, because the mass of the Earth is huge, the acceleration of the Earth by this same force is negligible, when measured relative to the system's center of mass.

### Equations for a falling body

The kinematical and dynamical equations describing the trajectories of falling bodies are considerably simpler if the gravitational force is assumed constant. This assumption is reasonable for objects falling to Earth over the relatively short vertical distances of our everyday experience, but does not hold over larger distances, such as spacecraft trajectories, since the acceleration due to Earth's gravity is much smaller at large distances.

Under an assumption of constant gravity, Newton’s law of gravitation simplifies to F = mg, where m is the massg is a constant vector with an average magnitude of 9.81 m/s². The acceleration due to gravity is equal to this g. An initially-stationary object which is allowed to fall freely under gravity drops a distance which is proportional to the square of the elapsed time. The image on the right, spanning half a second, was captured with a stroboscopic flash at 20 flashes per second. During the first 1/20th of a second the ball drops one unit of distance (here, a unit is about 12 mm); by 2/20ths it has dropped at total of 4 units; by 3/20ths, 9 units and so on. of the body and

Under the same constant gravity assumptions, the potential energy, Ep, of a body at height h is given by Epmgh (or Ep = Wh, with W meaning weight). This expression is valid only over small distances h from the surface of the Earth. Similarly, the expression h = v2 / 2g for the maximum height reached by a vertically projected body with velocity v is useful for small heights and small initial velocities only. In case of large initial velocities we have to use the principle of conservation of energy to find the maximum height reached. This same expression can be solved for v to determine the velocity of an object dropped from a height h immediately before hitting the ground,
$v=\sqrt{2gh}$, assuming negligible air resistance. =

### Gravity and astronomy

Main article: Gravity (astronomy)

The discovery and application of Newton's law of gravity accounts for the detailed information we have about the planets in our solar system, the mass of the Sun, the distance to stars, quasars and even the theory of dark matter. Although we have not traveled to all the planets nor to the Sun, we know their masses. These masses are obtained by applying the laws of gravity to the measured characteristics of the orbit. In space an object maintains its orbit because of the force of gravity acting upon it. Planets orbit stars, stars orbit galactic centers, galaxiessuperclusters. The force of gravity is proportional to the mass of an object and inversely proportional to the square of the distance between the objects.

Main article: Gravitational wave

In general relativity, gravitational radiation is generated in situations where the curvature of spacetime is oscillating, such as is the case with co-orbiting objects. The gravitational radiation emitted by the solar system is far too small to measure. However, gravitational radiation has been indirectly observed as an energy loss over time in binary pulsar systems such as PSR 1913+16. It is believed that neutron star mergers and black hole formation may create detectable amounts of gravitational radiation. Gravitational radiation observatories such as LIGO have been created to study the problem. No confirmed detections have been made of this hypothetical radiation, but as the science behind LIGO is refined and as the instruments themselves are endowed with greater sensitivity over the next decade, this may change.

## Notes

• Note 1: Proposition 75, Theorem 35: p.956 - I.Bernard Cohen and Anne Whitman, translators: Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy. Preceded by A Guide to Newton's Principia, by I. Bernard Cohen. University of California Press 1999 ISBN 0-520-08816-6 ISBN 0-520-08817-4

• Note 2: Max Born (1924), Einstein's Theory of Relativity (The 1962 Dover edition, page 348 lists a table documenting the observed and calculated values for the precession of the perihelion of Mercury, Venus, and Earth.)

## References

1. ^ Dick Teresi (2002), Lost Discoveries: The Ancient Roots of Modern Science - from the Babylonians to the Maya, Simon & Schuster, New York, ISBN 0-684-83718-8:

"Two hundred years before Pythagoras, philosophers in northern India had understood that gravitation held the solar system together, and that therefore the sun, the most massive object, had to be at its centre."

2. ^ Brahmagupta (628 AD). Brahmasphuta SiddhantaThe Opening of the Universe"). ("

3. ^ Al-Biruni (1030). Ta'rikh al-Hind (Indica).

4. ^ K. A. Waheed (1978). Islam and The Origins of Modern Science, p. 27. Islamic Publication Ltd., Lahore.

5. ^ Robert Briffault (1938). The Making of Humanity, p. 191.

6. ^ Dr. Nader El-Bizri, "Ibn al-Haytham or Alhazen", in Josef W. Meri (2006), Medieval Islamic Civilization: An Encyclopaedia, Vol. II, p. 343-345, Routledge, New York, London.

7. ^ Donald Routledge Hill (1993), Islamic Science and Engineering, p. 61, Edinburgh University Press. (cf.Merv, p. 5, Foundation for Science Technology and Civilization.) Salah Zaimeche PhD (2005),

8. ^ Professor Mohammed Abattouy (2002). "The Arabic Science of weights: A Report on an Ongoing Research Project", The Bulletin of the Royal Institute for Inter-Faith Studies 4, p. 109-130.

9. ^ N. Khanikoff, ed. and trans. (1858-1860), "Analysis and Extracts of ... Book of the Balance of Wisdom, An Arabic Work on the Water-Balance, Written by 'Al-Khâzinî in the Twelfth Century", chap. 5, sect. 3.1, Journal of the American Oriental Society 6, p. 36.

10. ^ Randall, Lisa (2005). Warped Passages: Unraveling the Universe's Hidden Dimensions. Ecco. ISBN 0-06-053108-8.

11. ^ Feynman, R. P.; Morinigo, F. B., Wagner, W. G., & Hatfield, B. (1995). Feynman lectures on gravitation. Addison-Wesley. ISBN 0201627345.

12. ^ Zee, A. (2003). Quantum Field Theory in a Nutshell. Princeton University Press. ISBN 0-691-01019-6.

13. ^ Randall, Lisa (2005). Warped Passages: Unraveling the Universe's Hidden Dimensions. Ecco. ISBN 0-06-053108-8.

14. ^ Greene, Brian (2000). The elegant universe: superstrings, hidden dimensions, and the quest for the ultimate theory. New York: Vintage Books. ISBN 0375708111.

• Halliday, David; Robert Resnick; Kenneth S. Krane (2001). Physics v. 1. New York: John Wiley & Sons. ISBN 0-471-32057-9.

• Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers, 6th ed., Brooks/Cole. ISBN 0-534-40842-7.

• Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics, 5th ed., W. H. Freeman. ISBN 0-7167-0809-4.

### Alternative Theory of Gravity Explains Large Structure Formation Without Dark Matter

Arip Nurahman

(Teacher and Professional Lecturer)
Department of Physics, Faculty of Sciences and Mathematics, Indonesia University of Education

and

Follower Open Course Ware at MIT-Harvard University, Massachusetts. U.S.A.

The light from galaxies in the background has been warped and “arced” by the galaxy cluster Abell 1689 in the foreground, and perhaps with some help by either dark matter or a stronger type of gravity on this large scale. Image Source: NASA, N. Benitez (JHU), T. Broadhurst (Racah Institute of Physics/The Hebrew University), H. Ford (JHU), M. Clampin (STScI),G. Hartig (STScI), G. Illingworth (UCO/Lick Observatory), the ACS Science Team and ESA.

In the standard theory of gravity—general relativity—dark matter plays a vital role, explaining many observations that the standard theory cannot explain by itself. But for 70 years, cosmologists have never observed dark matter, and the lack of direct observation has created skepticism about what is really out there.

Lately, some scientists have turned the question around, from “is dark matter correct?” to “is our standard theory of gravity correct?” Most recently, Fermilab scientists Scott Dodelson and former Brinson Fellow Michele Liguori demonstrated one of the first pieces of theoretical evidence that an alternative theory of gravity can explain the large scale structure of the universe.

CURRICULUM VITAE

ScottDodelson

Fermi National Accelerator Laboratory

Box500MS-209

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EMPLOYMENT

Fermi National Accelerator Laboratory
Interim Director, CenterforParticleAstrophysics(2006-2008)
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ScientistI(1999-2004)
AssociateScientist(1994-1999)
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UniversityofChicago
Professor,PartTime,DepartmentofAstronomyandAstrophysics
(2004-present)
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EDUCATION

Columbia University, PhD in Theoretical Physics, Advised by Gerald Feinberg(1988)
Joint BA/BS in Applied Physics, Columbia College
and School of Engineering and Applied Science(1983)

“To definitively claim that dark matter is the answer, we need to find it,” Dodelson explained to PhysOrg.com. “We can do this in one of three ways: produce it in the lab (which might happen at Fermilab, the soon-to-start LHC, or ultimately the International Linear Collider), see a pair of dark matter particles annihilate and produce high energy photons (there are about a half dozen experiments designed to look for this), or see a dark matter particle bump a nucleus in a large underground detector (again, about 10 experiments are looking for this). Until one or more of these things happen, skeptics are still allowed. … After they happen, skeptics will become crackpots.”

Although cosmologists have never directly observed dark matter, they have many good reasons for not giving up hope. The ways that galaxies rotate and starlight bends (gravitational lensing) stray from predictions based on visible matter. Further, the formation of large cosmic structures (such as galaxies and galaxy clusters) would have required significantly large matter perturbations when the Universe was less than a million years old that simply don’t exist in a theory of general relativity before “tacking on” dark matter.

“It is extremely important to see how well a no-dark-matter cosmology does,” said Dodelson. “[In the standard theory,] we are asking the community to believe in the existence of a particle that has never been seen. We have to be damned sure that you can't explain the universe without this huge leap. Our Figure 1 [see citation below] illustrates that, in standard gravity, a no-dark-matter model does not do well at all.”

While altering the theory of gravity may seem like pulling the rug out from under a century of observations and pain-staking calculations, an alternative theory may simply be “more correct” than today’s standard theory. Just as Einstein’s theory was “more correct” than Newton’s because it improved upon the older one by noticing more specific details (e.g. extraordinary masses and speeds), a new alternative theory may only drastically change gravity at certain scales.

“Perhaps a fundamental theory of gravity which differs from general relativity on large scales can explain the observations without recourse to new, unobserved particles,” wrote Dodelson and Liguori in their study published in Physical Review Letters. “Now more than ever before, there are very good reasons to explore this idea of modifying gravity. For, the case of dark energy also hinges on the assumption that general relativity describes gravity on larges scales. Dark energy is even more difficult to explain than dark matter, so it seems almost natural to look at gravity as the culprit in both cases.”

The new theory (or groundwork for it) under investigation would be Jacob Bekenstein’s relativistic covariant theory of gravity (TeVeS), published in 2004. Bekenstein based his theory on a modified version of Newtonian theory from the early ‘80s, dependent on gravitational acceleration and called modified Newtonian dynamics (MOND) by its founder, Mordecai Milgrom.

“MOND, the original theory on which TeVeS is based, was already quite successful at explaining galactic dynamics (even better, in some cases, than the dark matter paradigm), but it failed completely at explaining other observations—gravitational lensing in particular,” explained Liguori. “For this reason, it couldn't be considered a real alternative to dark matter. Bekenstein’s theory, by generalizing MOND, retains its good features while overcoming its main problems at the same time. This makes TeVeS a much more interesting theory than MOND. It is then worthwhile (and necessary) to test TeVeS’ predictions in detail and compare them to the standard dark matter paradigm to see if TeVeS can be a viable alternative.”

Dodelson and Liguori find Bekenstein’s theory intriguing in this context because, for one, the gravitational acceleration scale in the theory is very close to that required for the observed acceleration of the Universe. The scale is also very similar to that proposed in “post hoc” theories such as dark energy. Even more interesting is the fact that the origins of Bekenstein’s theory had nothing to do with cosmic acceleration.

But the feature of Bekenstein’s theory that Dodelson and Liguori focus on most is that the theory—unlike standard general relativity—allows for fast growth of density perturbations arising from small inhomogeneities during recombination. Building on this finding from scientists Skordis et al. earlier this year, Dodelson and Liguori have found which aspect of the theory actually causes the enhanced growth—the part that may solve the cosmological structure problem.

The pair has discovered that, while Bekenstein’s theory has three functions which characterize space-time—a tensor, vector and scalar (TeVeS)—it’s the perturbations in the vector field that are key to the enhanced growth. General relativity describes space-time with only a tensor (the metric), so it does not include these vector perturbations.

“The vector field solves only the enhanced growth problem,” said Dodelson. “It does so by exploiting a little-known fact about gravity. In our solar system or galaxy, when we attack the problem of gravity, we solve the equation for the Newtonian potential. Actually, there are two potentials that characterize gravity: the one usually called the Newtonian potential and the perturbation to the curvature of space. These two potentials are almost always very nearly equal to one another, so it is not usually necessary to distinguish them.

“In the case of TeVeS, the vector field sources the difference between the two,” he continued. “As it begins to grow, the difference between the two potentials grows as well. This is ultimately what drives the overdense regions to accrete more matter than in standard general relativity. The quite remarkable thing about this growth is that Bekenstein introduced the vector field for his own completely independent reasons. As he remarked to me, ‘Sometimes theories are smarter than their creators.’"

Dodelson and Liguori see this solution to large structure formation as an important step for a gravity theory based on baryon-only matter. Other problems that their theory (or any alternative theory) will have to confront include accounting for the mismatch in galaxy clusters between mass and light. Also, the theory must conform to at least two observations: the galaxy power spectrum on large scales, and the cosmic microwave background fluctuations, which correspond to baby galaxies and galaxy clusters.

“As Scott says, until dark matter will be observed, skeptics will be allowed,” said Liguori. “Despite the many and impressive successes of the dark matter paradigm, which make it very likely to be correct, we still don't have any final and definitive answer. In light of this, it is important to keep an eye open for possible alternative explanations. Even when, after the analysis, alternative theories turn out to be wrong, the result is still important, as it strengthen the evidence for dark matter as the only possible explanation of observations.”

References:

1. ^ a b Bertone, G.; Merrit, D. (2005). "Dark matter dynamics and indirect detection". Modern Physics Letters A 20: 1021-1036. doi:10.1142/S0217732305017391. arΧiv:astro-ph/0504422.
2. ^ Kane, G.; S. Watson (2008). "Dark Matter and LHC: What is the Connection?". Modern Physics Letters A 23: 2103-2123. doi:10.1142/S0217732308028314. arΧiv:0807.2244.
3. ^ R. Bernabei et al., First results from DAMA/LIBRA and the combined results with DAMA/NaI , Eur. Phys. J. C 56:333-355 (2008), articlepreprint
4. ^ Stecker, F.W.; Hunter, S.D. et al. (2008). "The likely cause of the EGRET GeV anomaly and its implications". Astroparticle Physics 29: 25-29. doi:10.1016/j.astropartphys.2007.11.002. arΧiv:0705.4311.
5. ^ Atwood, W.B.; Abdo, A.A. et al. (2009). "The large area telescope on the Fermi Gamma-ray Space Telescope Mission". Astrophysical Journal 697: 1071-1102. doi:10.1088/0004-637X/697/2/1071. arΧiv:0902.1089.
6. ^ >Adriani, O.; et al. (2009). "An anomalous positron abundance in cosmic rays with energies 1.5–100 GeV". Nature 458: 607-609. doi:10.1038/nature07942.
7. ^ NASA (2006-08-21). "NASA Finds Direct Proof of Dark Matter". Press release.
8. ^ Brownstein, J.R.; Moffat, J.W. (2007). "The Bullet Cluster 1E0657-558 evidence shows modified gravity in the absence of dark matter". Monthly Notices of the Royal Astronomical Society 382: 29-47. doi:10.1111/j.1365-2966.2007.12275.x. arΧiv:astro-ph/0702146.
9. ^ Reuter, M.; H. Weyer (2004). "Running Newton Constant, Improved Gravitational Actions, and Galaxy Rotation Curves". Physical Review D 70: 124028. doi:10.1103/PhysRevD.70.124028. arΧiv:hep-th/0410117.
10. ^ Th. M. Nieuwenhuizen (2009). "Do non-relativistic neutrinos constitute the dark matter?". Europhysics Letters 86: 57001.

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