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

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

  4. 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

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

  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 t=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? W mME RE2 W= G GME RE2 W= m W= mg GME RE2 g=

  16. 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

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

  18. Moon’s gravity causes tides

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

  20. Measuring Weight N mg

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

  22. Weightlessness means =0 N compensating upward

  23. Weightlessness in action

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

  25. 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=

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

  27. summary Obey the law!

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