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![F = GMm
r2
where,
– F = Force of attraction between the two particles.
– M = mass of first particle.
– m = mass of second particle.
– r = distance between the centers of the first and second particle.
– G = Universal gravitational constant. = 6.67 × 10-11
N·m2
/kg
Dimensional formula of F is [MLT-2
]
S.I. Unit = N (Newton)
C.G.S. Unit = dyne](https://image.slidesharecdn.com/akshatsaxenaphysics-160226171940/85/Newton-s-Law-of-Universal-Gravitation-11-320.jpg)
Uploaded byakshat saxena
Newton's Law of Universal Gravitation
The document discusses Sir Isaac Newton's contributions to the understanding of force and gravitational law, detailing his three laws of motion and the formulation of the law of universal gravitation. It explains how Newton connected the force of gravity to both terrestrial and celestial bodies, supported by experiments including those conducted by Henry Cavendish to measure the gravitational constant. The text highlights the implications of gravitational force on various phenomena, such as tides and satellite orbits.
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Newton's Law of Universal Gravitation
- 1. Presented By:- Name –Akshat Saxena
- 2. What isForce? Who discovered Gravitational law? Discovery of Gravitational Force. Calculation used by Newton. Calculating the constant. Gravity- A special Case. Effect of Gravity and its Uses.
- 3. Sir Issac newtongave many laws of nature. In his First law of motion, he described the inherent property of matters,qualitatively. In his second law,he wrote “A force action on a body gives it an accelaration which is in the direction of force and has a magnitude given by ma.” So,it describes force quantitatively also. In his third law,he describes how force are exerted. Therefore,we can say he discovered “Force”.
- 4. The force isan external effort(cause) in the form of a push or pull which either changes or tends to change the state of rest or the uniform motion of a body along a straight line. They are classified into two categories:- (i) Contact Force. - Frictional force, normal reaction,tensile force etc. (ii) Non-Contact Force. - electric,magnetic,gravitational force.
- 5. Sir IsaacNewton (1642-1727) Perhaps the greatest genius of all time Invented the reflecting telescope Invented calculus Connected gravity and planetary forces Philosophiae naturalis principia mathematica
- 6. In 1665,Issac Newton performed brilliant theoretical and experimental tasks in mechanics and optics. In this year, he focused his attention on the motion of the moon about the earth. While doing so, he had a question that what is the force that makes moon to revolve.
- 7. He had datathat moon revolves round the earth in 27.3 days. Its distance from earth is R = 3.85 ×105 km. The acceleration of moon is ,therefore, α = ω2 R α = 2π 2 × R ( velocity = disp. ) T time = 4π2 ×(3.85 ×105 km) (27.3 days)2 Displacement and time were converted into SI units. He had a belief that earth is making the moon to revolve.But How? = 0.0027 m/s2
- 8. Newton was sittingunder an apple tree when an apple fell down from the tree on the earth. This sparked the idea that the earth attracts all bodies towards its centre. He declared that the laws of nature are same for earthly and celestial bodies.
- 9. The acceleration ofa body falling near the earth’s surface is about 9.8 m/s2 and moon’s acceleration is 0.0027m/s2 .Thus, aapple amoon = 9.8 m/s2 0.0027 m/s2 Also, distance of the moon from the earth distance of the apple from the earth dmoon dapple 3.85 ×105 km 6400 km = 3600. ....(i) aapple amoon = dmoon dapple 2 = = = 60 ….(ii) By comparing (i)&(ii)
- 10. Newton guessed that, accelerationa ∝ 1 r2 …..(1) He had, F ∝ ma ; (Newton’s second law) …..(2) . ˙ . F ∝ m . ( From (1) ) r2 …..(3) By Newton’s Third law of motion, F ∝ M …..(4) Combining 3 & 4, F ∝ Mm r2
- 11. F = GMm r2 where, –F = Force of attraction between the two particles. – M = mass of first particle. – m = mass of second particle. – r = distance between the centers of the first and second particle. – G = Universal gravitational constant. = 6.67 × 10-11 N·m2 /kg Dimensional formula of F is [MLT-2 ] S.I. Unit = N (Newton) C.G.S. Unit = dyne
- 12. m1 m2 ř12 ř21 r F12= - Gm2m1 r2 F21 = - Gm1m2 r2 ř21 ř12 Note : -(minus) sign denotes that opposite direction of force and Distance.
- 13. Always actsas “Force of Attraction”. Form an action-reaction pair. Central Forces. Independent of the presence of other bodies and properties of the intervening medium. Weakest Force.
- 14. The force ofattraction between any two material particles is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. It acts along the line joining the two particles. i.e, F ∝ Mm r2
- 15. First measurementwas done by Cavendish in 1798,about 71 years after the law was formulated. The Gravitational constant G is a small quantity and its measurement needs very sensitive arrangement. Value of G was given through Cavendish Experiment. Calculating the Gravitational Constant
- 16. In 1798 SirHenry Cavendish suspended a rod with two small masses (red) from a thin wire. Two larger mass (silver) attract the small masses and cause the wire to twist slightly, since each force of attraction produces a torque in the same direction. By varying the masses and measuring the separations and the amount of twist, Cavendish was the first to calculate G. G = 6.67 × 10-11 N·m2 /kg2 Cavendish’s Experiment
- 17. Earth wastreated as a single particle placed at its centre. Newton spent several years to prove that a spherically symmetric body can be replaced by a point particle as its centre. In this process he discovered the methods of Calculus. He did it by use of Calculus. It was then, applicable for the bodies if their entire mass were concentrated at their centre of mass. Hence, it is applicable to all, whatever the size may be. Assumptions
- 18. It isa Universal Law. It explains motion of heavenly bodies. The predictions of eclipses comes true. Tides in oceans because of attraction between moon and ocean water. The predictions about orbits and time periods of artificial satellites found to be correct.
- 19. Gravity is theforce by which earth attracts a body towards its centre. F e= GMem Re 2 where, – Fe = forces of attraction between Earth and particle of mass m. – Me = mass of Earth. – m = mass of particle. – Re = distance between the centers of the Earth and particle. – G = Universal gravitational constant. = 6.67 × 10-11 N·m2 /kg
- 20. Follows Newton'sLaw of Universal Gravitation By Newton’s second law , F = mg Compare with F = mg so g = GM/r2 g depends inversely on the square of the distance g depends on the mass of the planet Nominally, g = 9.81 m/s2 or 32.2 ft/s2 • At the equator g = 9.78 m/s2 • -At the North pole g = 9.83 m/s2 • g on the Moon is 1/6 of g on Earth.
- 21. Provides necessarycentripetal force to moon to revolve. Provides force to Satellites to revolve round the earth. To make the bodies fall from height. Formation of Tides in the ocean.
- 22. Fg,lead = GMEarthMlead REarth 2 Fg,wood = GMEarthMwood REarth 2 22 ,1 • Earth earth leadEarth leadearth lead leadg lead R GM MR MGM M F a === 22 , 1 • Earth earth woodEarth woodearth wood woodg wood R GM MR MGM M F a === Lead Wood aawoodwood aaleadlead Q. If two bodies one of lead and other of wood of same volume are fallen from same height from the state of rest. Then which will strike to the ground first?(Neglect air-resistance) Sol. …..(a) …..(b)
- 23. Let, h betheir height above the ground. By second equation of motion, S = ut + 1/2at2 For lead, h = 1/2aleadt1 2 ; …..(c) For wood, h = 1/2awoodt2 2 ; ..…(d) Equating (c)&(d), 1/2aleadt1 2 = 1/2awoodt2 2 t1 2 = t2 2 Or, t1 = t2 Thus, they will reach earth at same instant. (From (a) &(b))
- 24. www.wikipedia.org/Gravitation www.physicsclassroom.com www.google.books.com Books Prof. H.C.Verma : Concept of Physics Vol. I Kumar,Mittal : ISC PHYSICS Class XI Modern ABC : Physics Vol.I
- 25.
Editor's Notes
- #12 The birth of the Principia may be traced back to a discussion in 1684 at the Royal Society. Astronomer Edmund Halley and architect Sir Christopher Wren suspected that there was an inverse square relation governing celestial motions based on Kepler's Third Law of elliptical orbits, but no one could prove it. They brought the question before Newton's arch rival Robert Hooke, who claimed that he could prove the inverse square law and all three of Kepler's laws. His claim was met with scepticism, and Wren offered a forty-shilling book as a prize for the correct proof within a two-month limit. Hooke failed to produce the calculation, and Halley travelled to Cambridge to ask for Newton's opinion. Newton responded with a typical lack of interest in work that he had already completed, that he had already solved the problem years before. He could not find the calculation among his papers and promised to send Halley a proof. Halley, suspecting the same bogus claim he had received from Hooke, left frustrated and returned to London. Three months later he received a nine page treatise from Newton, written in Latin, De Motu Corporum, or On the Motions of Bodies in Orbit. In it, Newton offers the correct proof of Kepler's laws in terms of an inverse square law of gravitation and his three laws of motion. Halley suggested publication, but Newton, reluctant to appear in print, refused. At Halley's insistence, Newton finally began writing and, with typical thoroughness, worked for 18 months revising and rewriting the short paper until it grew into three volumes. The Royal Society, having exhausted available funds on an extravagant edition of De Historia Piscium, or The History of Fishes, could not pay for the publication and so it was at Edmund Halley's expense that Philosophiæ Naturalis Principia Mathematica was finally published. The Mathematical Principles of Natural Philosophy, or The Principia as it came to be commonly known, begins with the solid foundation on which the three books rest. Newton begins by defining the concepts of mass, motion (momentum), and three types of forces: inertial, impressed and centripetal. He also gives his definitions of absolute time, space, and motion, offering evidence for the existence of absolute space and motion in his famous "bucket experiment". These absolute concepts provoked great criticism from philosophers Leibnitz, Berkeley, and others, including Ernst Mach centuries later. The three Laws of Motion are proposed, with consequences derived from them. The remainder of The Principia continues in rigorously logical Euclidean fashion in the form of propositions, lemmas, corollaries and scholia. Book One, Of The Motion of Bodies, applies the laws of motion to the behaviour of bodies in various orbits. Book Two continues with the motion of resisted bodies in fluids, and with the behaviour of fluids themselves. In the Third Book, The System of the World, Newton applies the Law of Universal Gravitation to the motion of planets, moons and comets within the Solar System. He explains a diversity of phenomena from this unifying concept, including the behaviour of Earth's tides, the precession of the equinoxes, and the irregularities in the moon's orbit. The Principia brought Newton fame, publicity, and financial security. It established him, at the age of 45, as one of the greatest scientists in history.
- #16 No one could figure out what G was until Henry Cavendish discovered it in the late 18th century. Newton stated this law of gravitation, but he did not attempt to explain, or prove it.
- #23 Galileo Experimented