Gravity. A. Law of Gravity. Gravity. Physics: Mechanics. A. The Law of Gravity. Dr. Bill Pezzaglia. B. Gravitational Field. C.

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1 Physics: Mechanics 1 Gavity D. Bill Pezzaglia A. The Law of Gavity Gavity B. Gavitational Field C. Tides Updated: 01Jul09 A. Law of Gavity 3 1a. Invese Squae Law 4 1. Invese Squae Law. Newton s 4 th law 3. Acceleation of Gavity 1b. Invese Squae Law 5 Appaent Luminosity dops off invesely popotional to squaed distance. Sun at planet Satun (10 futhe away than eath) would appea 1/100 as bight. Sound behaves the same way So do electic and magnetic foces 1c Gavity obeys invese squae law 6 Acceleation of gavity is invesely popotional to distance (fom cente of eath) Example: At the suface of the eath (one eath adii distance) the acceleation of gavity is nealy g=10 m/s The moon is 60 futhe away Acceleation of moon towads eath is hence 60 smalle (about a=0.003 m/s ). 1 g g g a

2 . Gavity: Newton s 4 th Law (a) The apple tee stoy "Afte dinne, the weathe being wam, we went into the gaden and dank tea, unde the shade of some apple tees," wote Stukeley, in the papes published in 175 and peviously available only to academics. "He told me, he was just in the same situation, as when fomely, the notion of gavitation came into his mind. It was occasion'd by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend pependiculaly to the gound, thought he to himself." 7 (b) The Law of Gavitation The mutual foce between two bodies is popotional to thei masses, and invesely popotional to squae of distance. Newton could not detemine the Gavitation Constant G 8 (c) Cavendish Expeiment: The Acceleation of Gavity (a) Galileo s Law of Falling Bodies 10 Ove 100 yeas late Cavendish measues the constant: G= N m /kg Vey Small! To have 1 N of foce would need 10 kg masses 1 cm apat! Combining Newton s nd and 4 th laws, we see that the mass of the test body cancels out! Hence we deive Galileo s law that all test bodies fall at the same acceleation g, independent of thei mass m GmM ma F GM a g 3b. Measue Mass of Eath 11 3c. Escape Speed 1 Hence if we measue g, and know the adius of the eath (measued by ancient geeks), we can detemine the mass of the eath! GM g The gavitational potential enegy is the amount of wok we would have to do to lift a mass m fom suface of eath to infinity. Equivalently, it s the amount of Kinetic Enegy an meteooid would have if it fell to the eath. U GmM g M G m m s m kg s kg Note mass m cancels out (all bodies fall at same ate!). Hence, thee is a minimum escape speed such that a body will not fall back to eath! [about 11 km/sec o 5,000 miles pe hou] 1 mv GmM GM v g

3 B. Gavity Field Action at a Distance 14 Action at a Distance (no touching) 1. Action at a Distance. Gavitational Field 3. Black Holes etc. Huygens citicized: How can one believe that two distant masses attact one anothe when thee is nothing between them? Nothing in Newton's theoy explains how one mass can possible even know the othe mass is thee. actio in distans (action at a distance), no mechanism poposed to tansmit gavity Newton himself wites: "...that one body may act upon anothe at a distance though a vacuum without the mediation of anything else, by and though which thei action and foce may be conveyed fom one to anothe, is to me so geat an absudity that, I believe no man, who has in philosophic mattes a competent faculty of thinking, could eve fall into it.". The field concept 15 b. Definition of Mass Faaday poposes ideas of Lines of Foce Example: ion filings ove a magnetic show field lines Thee ae 3 ways to think about mass 1. Inetial Mass F=ma. Passive Gavitational Mass F=mg Gavitational Analogy: Eath s mass M ceates a gavity field g Foce of field on mass m is: F=mg (i.e. weight ) This eliminates action at a distance Michael Faaday Active Gavitational Mass GM g The Weak Equivalence pinciple says that inetial mass equals passive gavitational mass 3a. The Equivalence Pinciple Refeence at est with Gavity is indistinguishable to a efeence fame which is acceleating upwad in gavity fee envionment. 17 3b. Bending of Stalight Newton: Light is NOT affected by gavity Einstein: Elevato example shows light must be affected by gavity. Pedicts stalight will be bent aound sun! 1919 Measued by Eddington! 18 The apple acceleating downwad due to gavity looks the same as an apple at est in space, with the floo acceleating upwad towads it. 3

4 3c. Black Hole 19 3d. Obseving a Black Hole 0 If the mass of a sta is vey big and its size shinks vey small the escape speed becomes bigge than the speed of light, and not even light can escape! Any mass is compessed into a size smalle than the Schwazschild Radius R s, it will become a black hole This can happen duing a supenova explosion, o late by additional mass falling on a neuton sta. If black how do we see them? Mateial shed fom anothe sta falls towads black hole. Not all the mateial falls into the hole. Some is ejected at vey high enegies out jets along the axis of the black hole. Anything that comes close than the Schwazschild Radius, will fall in and neve escape. 3e. Radio Lobes fom galaxy Centauus A 1 Black holes at the cente of galaxies have a mass of ove a billion stas combined! C. Tidal Foces 1. Histoy. Tidal Foce 3. Cycle of Tides 1. Discovey of Tides Alexande the Geat knew nothing about tides and his entie fleet was standed on a sand ba in the Indian Ocean 3. Tidal Foces 4 This animation illustates the oigin of tidal foces. Imagine thee identical billiad balls placed some distance fom a planet and eleased. The close a ball is to the planet, the moe gavitational foce the planet exets on it. Thus, a shot time afte the balls ae eleased, the yellow 1-ball has moved a shot distance, the geen -ball has moved a longe distance, and the ed 3-ball has moved a still longe distance. Fom the pespective of the cente ball (the -ball), a foce seems to have pushed the 1-ball away fom the planet, and a foce seems to have pulled the 3-ball towad the planet. These foces ae called tidal foces. 4

5 b. Two Tides! 5 You get a high tide on BOTH sides of the eath! c Tides (continued) The fiction of tides ae slowing the eath down (day is getting longe!), causes the moon to move futhe away by 1 cm a yea (to conseve angula momentum) 6 d. Tidal Stength Sun s tides ae only half as stong because its futhe away 7 3a Cycle of Tides: Daily High tides twice a day, at (nea) tansit (uppe culmination) and lowe culmination of moon (Luna) Tides ae 5/= 1.5 hous apat Tides can be ealy/late by half hou o moe because of influence of sun pulling it off to side. 8 3b Tides fom BOTH moon AND sun 9 3c Sping Tides 30 At Full Moon the tidal foces add, and you get a eally BIG sping o king tide. Since tides ae ceated on both sides of eath, you also get a sping tide at New Moon when the sun and moon ae on same side of eath 5

6 3d Neap Tides At Fist Quate and Last Quate Moon, the weake tidal foce of the sun patially cancels out the luna tide, and you get a eally small NEAP tide. 31 Refeences x 3 6

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