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A History of Universal Gravitation

A History of Universal Gravitation. Realize that by the time Newton was a young man, An understanding that the Earth did something to make objects fall or heavy (Greek word: gravitas) is mentioned in recorded history as far back as the 5 th C

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A History of Universal Gravitation

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  1. A History of Universal Gravitation Realize that by the time Newton was a young man, An understanding that the Earth did something to make objects fall or heavy (Greek word: gravitas) is mentioned in recorded history as far back as the 5thC Galileo had given us, more than 50 years earlier, the idea that, in the absence of air, all objects fall at the same rate. It was well established that the moon circled the Earth at about 60 Earth radii away. An “circling” required a force… but what was it??

  2. A History of Universal Gravitation In 1665, the Great Plague was sweeping through Europe Cambridge University closed for 2 years Newton went home to mother’s farm, Woolsthorpe Contemplated the question: “Is the moon circling the Earth connected to the apple falling from the tree?”

  3. Is the moon circling the Earth connected to the apple falling from the tree? If yes, he considered the inverse square “dilution of gravity” idea says if moon is 60x’s further away, then it should be affected by 1/602 the amount of gravity. Since an object on Earth will fall 4.9m (≈5m) in 1 sec, then the moon should fall 1/602 of 4.9m or 1.4mm in 1 sec He couldn’t quite prove it completely without a few more bits of understanding… like calculus… But 20 years later, when friend Edmund Halley asked, he got it together and published it as…

  4. Universal Gravitation Newton’s Universal Law of Gravitation: every object pulls on every other object with a force of gravity that is proportional to the masses involved and inversely proportional to the square of the distance between their centers. So 3 main points: all things pull on all things! FGα each m FGα 1/r2

  5. So FGα 1/r2 is an example of an inverse square law ISLs very common relationship in science / life as objects get farther apart (r bigger), strength gets A LOT smaller, by the square of r. paint sprayer light from a light bulb electric force around a point charge

  6. Universal Gravitation Try some examples of ISL: FGα 1/r2 And remember,as r gets bigger, FG gets A LOT smaller, by the square of r. Ex If objects twice as far apart, then how did FG change? 1. If 2r, then ___ FG 2. If 4r, then ___ FG 3. If ⅓r, then ___FG 4. If ⅝r, then ___FG

  7. Universal Gravitation So, again, there’s 2 main relationships in UG: FGα each m (the 2 masses pulling on each other) FGα 1/r2 (the distance between those masses) But what’s the equation for UG? 1st let’s put the relationships together in one proportion: FGα m1m2/r2 2nd to turn a proportion into an equation, we need a constant of proportionality…for universal gravitation, it’s official name is the universal gravitation constant, also fondly referred to as “big G” and it has a value of G = 6.67 x 10-11 Nm2/kg2 note that’s a really small number!!

  8. Universal Gravitation Henry Cavendish’s Apparatus 1798 - over 100 years later

  9. Universal Gravitation So the equation for Newton’s Universal Law of Gravitation is: FG = Gm1m2/r2 where m1 is the bigger or main mass m2 is the other mass involved r is the distance between their centers and G = 6.67 x 10-11 Nm2/kg2 Now let’s try some calculations…

  10. Estimate to one sig fig, the force of gravity between you & your partner: Use FG = Gm1m2/r2 m1 = 70 kg (about ½ your pounds) m2 = 60 kg r = .7 m G = 6.67 x 10-11 Nm2/kg2 so FG =small digit x 10-6 N or big digit x 10-7 N Either way, a very small! FG between everyday size objects is really small since the value of G is so small.

  11. Estimate the force of gravity between you & the Earth: m1 is mass of Earth m2 = your mass r is radius of Earth FG = between 500 to 1000 N But what have you just found?? Calculate your weight using Fg = mg How do they compare? Now calculate just Gmearth/rearth2 = That should make sense! Fg= FG on the surface of a planet myoug = Gm1myou/r2 So gplanet = Gmplanet/rplanet2

  12. Estimate the force of gravity between Earth & the moon: m1 is mass of Earth m2 is mass of moon r is distance to moon (do we need re & rm in there?) FG = about 2 x 1020 N Estimate the force of gravity between the sun & the moon: m1 is mass of sun m2 is mass of moon r is distance to sun FG = about 4 x 1020 N Which one’s bigger? What does that mean? The moon is not truly a moon, but a binary (dwarf) planet! We follow an orbital path along our combined CM, which is inside the Earth’s radius since the earth is 100’s more massive than the moon.

  13. One more fascinating revelation: The big problem with Newton’s Universal Law of Gravitation was that masses are applying forces without having to touch each other. So the first answer was to come up with the idea of a force field – the space about an object in which it can apply a force without touching But then Albert Einstein came up with a different explanation: Gravity should not be considered a force, but an effect of space itself.

  14. Einstein said to think of mass as altering the space around it, causing it to be warped or curved. Then bodies wouldn’t move toward a planet because a “mystical” force of gravity was pulling on them, but instead because they were following the curvature of space near the massive object. That’s a lot to ponder!

  15. Unifying the Fundamental Forces Almost since the major forces were discovered, there’s been a drive by physicist (now mostly theoretical physicist) to reduce them to the least number possible. In the 19th C, the electric & magnetic forces where believed to have completely separate causes. But when E&M turned out to have exactly the same source, they were combined – a huge deal at the time! So by the mid 20th C, there were 4 fundamental forces: 1) gravity 2) electromagnetic 3) strong nuclear 4) weak nuclear More recently, weak nuclear was combined with EM, which puts us at 3. There is a real drive to find the single unifying theory that would show all forces are manifestations of a single cause – GUT: grand unified theories. The most prominent of these today is called String Theory…

  16. Kepler’s Laws of Planetary Motion Johannes Kepler German Astronomer 1571-1630 50 years before Newton’s work on UL of G Thru careful analysis of experimental data Worked out detailed descriptions of the motion of the planets around the sun

  17. Kepler’s Laws of Planetary Motion 1st Law: the path of each planet about the Sun is an ellipse with the Sun at one focus

  18. Kepler’s Laws of Planetary Motion 2nd Law: each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal period of time

  19. Kepler’s Laws of Planetary Motion 3rd Law: The ratio of the squares of any two planets revolving about the Sun is equal to the ratio of the cubes of their mean distances from the Sun mean distance refers to half the length of the major (as opposed to minor) axis of the ellipse minor axis major axis point of point of apogee perigee

  20. 2 useful equations from Kepler’s 3rd Law eq’n 1: T12 r13 _____________ _________ T22 r23 where the T’s and r’s are for any 2 objects orbiting the same object in approximately circular motion eq’n 2: r3orbiting Gmorbited ________________ ____________ T2orbiting4π2 where the right side of the eq’n is a constant for any object, so if a suspected orbiting object’s r3/T2 ratio equals the orbited object’s K (Kepler) constant, it is indeed orbiting that object.

  21. Kepler’s Constant for the Earth

  22. Discoveries made thanks to Kepler’s Laws… Newton used measured perturbations in Saturn’s orbit to support his idea that all objects pull on all objects… aka N’s UL of G! Together with his 3 laws of motion, it was clear that heavenly bodies followed the same laws as Earth bound objects – a big deal to make that connection… referred to as “Newton’s synthesis” These (types of) laws known as causal laws… Others used measured perturbations in Uranus’ orbit to predict the existence of Neptune 1846 Neptune’s orbit to predict the existence of Pluto 1930 A star’s wobble to predict existence of orbiting planets - mid 1990’s

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