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Newton’s Universal Law of Gravitation

Newton’s Universal Law of Gravitation. Physics 100 Chapt 10. Very fast horizontal toss. t = 0s. t = 1s x= 8km. t = 2s x=16km. t = 3s x=24km. V=8km/s. 5m. 20m. 45m. Centripetal acceleration. a = v 2 /r for a circular orbit (v = 8km/s = 8x10 3 m/s). (8 x10 3 m/s) 2

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Newton’s Universal Law of Gravitation

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  1. Newton’s Universal Law of Gravitation Physics 100 Chapt 10

  2. Very fast horizontal toss t = 0s t = 1s x= 8km t = 2s x=16km t = 3s x=24km V=8km/s 5m 20m 45m

  3. Centripetal acceleration a = v2/r for a circular orbit (v = 8km/s = 8x103m/s) (8 x103 m/s)2 6.4 x 106 m 64 x106 m2/s2 6.4 x 106 m a = = = g = 10 m/s2 Toward Earth’s center

  4. Orbital motion is free fall Circular Orbit! Eliptical Orbit V = 4km/s V = 6km/s V = 8km/s V = 10km/s

  5. Artificial satellite a = v2/r = g v a

  6. Moon-earth v a=v2/r

  7. Is the Moon in free-fall around the Earth? v a=v2/r r=3.84x105km what is v? 2pr 28d 2x3.14x 3.84x108 m 28dx(24h/d)x3.6x103s v=dist/time= = 24 x 108 m 2.4x106s = = 1.0 x 103 m/s

  8. Moon’s centripetal acceleration amoon = v2/r; v = 1.0 x103 m/s) (1.0 x103 m/s)2 3.84 x 108 m 1.0x106 m2/s2 3.84 x 108 m amoon= =  g 1 3600 = 2.7 x 10-3 m/s2 Toward Earth’s center

  9. Newton’s dreams Hmmmmm……. The Moon is in free-fall around the Earth It’s acceleration is only 1/3600 g (accel at the Earth’s surface)

  10. Distances The moon is 60x further from the Earth’s center than objects on (near) the Earth’s surface r=3.84x108m  60 x (6.4x106 m) = 60 x RE 1 60 1 3600 ( )2= RE = 6.4x106m

  11. Newton’s big idea The force of gravity gets weaker as distance squared The moon is 60x further from the Earth’s center than objects on (near) the Earth’s surface The strength of Earth’s gravity near the Moon is (1/60)2 =1/3600 times weaker

  12. Gravity gets weaker as 1/dist2

  13. Universal law of gravity M m r F  m F  M Proportionality constant: 1 r2 F  “Newton’s Constant” mM r2 mM r2 combine: F  F = G

  14. Universal applies to all objects!!! Universal:

  15. What is G? mME RE2 W= G W GME RE2 W= m W= mg GME RE2 g=

  16. Determine G from g, RE & ME gRE2 ME G = 10m/s2x(6.4x106m)2 6x1024kg G = 10m/s2x 41x1012m2 6x1024kg G = 410x1012m3/s2 6x1024kg G = G = 6.7.x10-11m3/kg s2 G = 6.7x10-11 Nm2/kg2 A very small number

  17. Force of gravity between “ordinary-sized” objects mM r2 F = G 80kg 60kg 1m 60 kg 80kg (1m)2 F = 6.7x10-11Nm2/kg2 F = 6.7x60x80x10-11N F = 32160.x10-11N =3.2x10-7N  30x109 times bigger! Boy’s weight = mg = 80kg x 10m/s2 = 800 N

  18. Measuring gravity force between “ordinary-sized” objects is very hard

  19. Cavendish’s measured the gravitational Force between known masses & from this deduced the value of Newton’s Constant G. From this and the relation for g he deduced ME, the mass of the Earth, which turned out to be about twice the value people had guessed it to be at that time. I weighed the Earth

  20. Moon’s gravity causes tides

  21. So does the Sun’s Half Moon New Moon Full Moon

  22. Measuring Weight N mg

  23. Weightlessness N =0 N =mg N >mg N <mg

  24. Weightlessness means =0 N compensating upward

  25. Weightlessness in action

  26. “Floating” is space isreally free-falling in space

  27. What is g on the moon? mMM RM2 W= G m RM=1.7 x 106m GMM RM2 W W= m W= mgM MM GMM RM2 gM=

  28. gM on the Moon GMM RM2 g = 6.7x10-11Nm2/kg2 x7.4x1022Kg (1.7x106m)2 = gM = 1.7m/s2 1/6x gEarth

  29. Eotvos experiment Does Minertial = Mgravitational ? .. .. .. .. Lorand Eotvos 1848-1919 Devised a sensitive test of the equality between inertial & gravitational mass

  30. q Miv2/r Mi MG MGg q If Mi = MG, q is the same for every object

  31. If Mi = MG, different materials twist different amounts inertia same masses different materials

  32. .. .. Eotvos saw no effect, all materials felt the same twist to 1 part in 109 Minertial = Mgravitational to very high precision

  33. summary Obey the law!

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