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SHAILESH RAJ
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- 4. + 38 10 ForcenalGravitatio ForceneticElectromag proton electron rˆ r mm GF 2 21 r MmG )r(Ug 1.Newton’s Law of Universal Gravitation 2.Gravitational Potential Energy (long-range form)
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- 6. Old: )yy(gm)y(U 0g New: r MmG )r(Ug How could these be the same? Consider a location near the surface of the earth, y0 = R, y = R+h. The only thing that matters is U, not U itself. Old: hgm)RhR(gmUg + New: + + hR 1 R 1 MmG R MmG hR MmG Ug + + hRR h MGm hR 1 R 1 MGm 2 (h << R) hgmh R MG m R h MGm 22
- 7. “Acceleration due togravity” Ball Earth
- 8. Newton’s 2ndlaw force (F) is acting on falling ball (mass = m) All masses have same acceleration . . . so more mass means more force needed: mF F m Ball Earth
- 9. F Newton’s 3rdlaw ball pulls on Earth Ball F Does Earth accelerate? Earth
- 10. All bits ofmatter attract all other bits of matter . . . M1 M2 d F F “Inverse square law” d 1 F2. MMF1. 2 21
- 11. 1. Increaseone or both masses, and force increases. 2. Force decreases as distance increases. Force Distance 400 N 10 m 100 N 20 m 25 N 40 m 16 N 50 m 4 N 100 m d M1 M2F F 4 400 2 400 100 2
- 12. Force Distance 400 10 17815 100 20 44.4 30 25 40 16 50 11.1 60 8.2 70 6.25 80 4 100 0 20 40 60 80 100 120 0 100 200 300 400 500 Distance Force Force never becomes zero.
- 13. Putting the twoparts of the force law together . . . 2 21 d MGM F (G = gravitational constant) Acts through empty space “action at a distance” Explains how gravity behaves – but not why
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- 15. Weight Measure ofgravitational attraction of Earth (or any other planet) for you. Earth R F m M Weight 2 R GMm FW
- 16. Other planets: Mand R change, so your weight must change Mars: R = 0.53 x Earth’s radius M = 0.11 x Earth’s mass Earth Mars Weight 150 lbs 59 lbs A real planet . . .
- 17. “Weight” can be madeto apparently increase . . . upward acceleration
- 18. . . .or decrease! downward acceleration “Weightlessness” 9.8 m/s/s Free-fall
- 19. 2 R GMm W your weight yourmass Earth’s radius Earth’s mass M = 6 x 1024 kg
- 20. By 1915, Einsteinhad worked through all the math (with some help) to show that his postulates led to a new theory of gravity based on the effect of mass and energy to curve the structure of space and time. His theory has some startling implications, one being the existence of “black holes” – regions of space where the gravity field is so high that even light cannot escape. The predictions of General Relativity, including the existence of black holes, have been confirmed by all experiments to date.
- 21. Any motioncontrolled only by gravity is an orbit Without gravity With gravity NEWTON: Gravity explains how planets (and moons & satellites & etc.) go. Sun
- 22. . Object is effectively continuouslyfalling toward the sun . . . . . . But never gets there! Circle F
- 23. Imagine launching a ballsideways near Earth . . .
- 24. Johannes Kepler (1571 – 1630) 1.Planets move in elliptical orbits with the sun at one focus X Sun (Focus) Focus Semi-major axis (a) c
- 26. M m 2 3 P a 1 2 3 P a mM + unitsof the Sun’s mass
- 27. 3 2 2 a m)G(M 4 P + 1 yr 1AU Earth’s massSun’s Mass
- 28. CENTER OF MASSORBITS We left something out . . . Sun Planet Sun pulls on planet . . . planet pulls on sun Sun moves a little, too!
- 29. Exaggerated view: X S P X =center of both orbits Circular orbits
- 30. Consider Jupiter &the Sun . . . X 5.2 AU0.0052 AU Sun’s motion is small! Center of Mass Gravitational Orbits Animation
- 31. Earth & Moon: X 2900mi 235,500 mi 2900 mi < Earth’s radius! Gravitational Orbits Animation