 # Gravity Chapter 7. Newton  Noticed the moon followed a curved path  Knew a force was required to allow an object to follow a curved path  Therefore,

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Gravity Chapter 7

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

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.

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

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.

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

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)

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.

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

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

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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