Gravity

1. Gravity Chapter 7

2. 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

3. 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 Fg = G m1m2 d2 Where G is the universal gravitational constant = 6.67 x 10-11 Nm2/kg2.

4. 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

5. Gravitational Fields • The force of gravity causes an acceleration • Surrounds all large objects with varying strengths based on mass and radius. • g = Gm r2 • Ex. Earth’s g = 10 m/s2 • Exists within the Earth also: • At the center of the Earth g = 0 because equal force above and below you cancels out.

6. 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

7. 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)

8. 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 Fg 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.

9. 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

10. 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

11. 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