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Gravity Chapter 7

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Newton Noticed the moon followed a curved path Knew a force was required to allow an object to follow a curved path Therefore, the Earth must exert a force on the moon Needed to develop calculus to fully explain and support his theory

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Law of Universal Gravitation All objects attract each other. This attraction is directly proportional to the product of the masses of the objects and inversely proportional to the square of the distance between them. OR F g = G m 1 m 2 d 2 Where G is the universal gravitational constant = 6.67 x 10 -11 Nm 2 /kg 2.

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So How Can We Use This? Can never be 0 because mass can’t be 0 Since G is so small, gravity is a very weak force (actually, it’s the weakest natural force). Gravity causes the Earth (and all planets) to be round because all parts are pulled equally towards the center. Planets pull each other slightly out of orbit (how most astronomy has advanced) - perturbation

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Gravitational Fields The force of gravity causes an acceleration Surrounds all large objects with varying strengths based on mass and radius. g = Gm r 2 r 2 Ex. Earth’s g = 10 m/s 2 Exists within the Earth also: At the center of the Earth g = 0 because equal force above and below you cancels out.

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Weight A force caused by the acceleration due to gravity acting on your mass (F = ma) Measured as the support force the ground must exert to hold you up Accelerating in an elevator effects your weight: Going up causes more support force on your feet so weight increases. Going down causes less support force on your feet so weight decreases. You can never truly be weightless because gravity always exists You feel “weightless” because you lack a support force to push back on you

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Tides Caused by differences in the pull of the moon’s gravity on different sides of the Earth Moon matters more because it’s closer, so the difference in pull is more Sun does help though, since it’s mass is so large Larger tides occur when sun and moon line up (spring tides), smaller ones occur when they are in opposition (neap tides)

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Black Holes Stars expand as they grow, then become so unstable, that they collapse on themselves. Since the same mass now takes up little distance, the F g is huge. It can become so big that the speed required to escape its gravity is greater than the speed of light = 300000000 km/s (nothing is that fast) The bigger the star, the worse the black hole is.

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Satellites A projectile moving fast enough to fall continuously around an object The curve of it’s path matches the curve of the object’s surface Must go at least 8 km/s to orbit the Earth Would take 90 min to orbit the Earth at this speed Needs to be above the atmosphere or friction would burn it up

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Orbits It’s the horizontal velocity that has to be a certain rate, not vertical So gravity doesn’t slow down the speed of the object Orbits are often elliptical so speed isn’t uniform Moves fastest when closest to the object with gravity, slower when far away

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Escape Speed V = 2Gm d In order to “escape” the curved path that follows the Earth, the speed needs to be at least 11.2 km/s You haven’t really escaped the gravity, just gotten a curve big enough that you aren’t pulled back towards the Earth hard enough to maintain a circle

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