Chapter 12 Review

"Universal Gravitation"

12-1: The Falling Apple Pages 168 – 169

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In 1666, Issac Newton discovered the idea of gravity once while he was sitting underneath an apple tree in a garden by his mother's house in Lincolnshire. An apple fell. Some say the apple actually hit Newton's head, and others claim it just fell to the ground. Either way, using the concept of inertia (Galileo), Newton pondered that force is the reason an object has change in speed or direction. The power of gravity must extend higher, maybe to the moon! He realized both the moon and the apple fell because they were pulled by the earth's gravity. Also, Newton discovered the force, decreasing as the inverse square of distance, could be used gto calculate the Moon's orbital period. This force, he guessed, was also responsible for other orbital motions deeming it to be called "univeral gravitation".

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12-2: The Falling Moon Pages 169 – 170

Newton thought more on this falling apple business. He came to the conclusion that the moon must be falling around the earth, falling beneath the straight line it would follow if no force acted on it, a projectile circling the earth. The moon has velocity paralell to the earth. It will continue "falling" around the earth as long as there is no resistance to reduce it's speed. He tested this by finding that mass has no effect on freely falling objects on the earth.

Newton calculated the distance of the moon's orbit below the straight distance the moon WOULD travel. He published the law of universal gravitation, which we will come to shortly.

12-3: The Falling Earth Page 171

Newton's breakthroughs showed the earth was NOT the center of the universe, or even the solar system. It was now clear the earth and other planes orbited the sun. Planets don't crash into the sun do to their tangential velocities. If these velocities were zero, the planets would crash straight into the sun. Those things in the solar system with tangential velocities that were not fit for their survival have already done so.

12-4: Newton's Law of Universal Gravitation Pages 172 – 174

Newton's law of universal gravitation states that every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object. The force also decreases as the square of distance between the centers of masses. This law can be expressed as:

10-11 N m2 / kg2

Cavendish measured forces between lead masses to find this value of G. G is a very weak force. In fact, it is the weakest of the four fundamental forces.
G = 6.67 x 10-11 Nm2 / kg2
Your weight depends on your distance from the center of the earth and your mass.

12-5: Gravity and Distance: The Inverse-Square Law Pages 175 – 176

The inverse-square law occurs when a quantity varies as the inverse square of its distance from its source. It always applies if the effect of a source spreads evenly throughout the surrounding surface. Examples of things that apply this include point sources of gravitational force, electric field, light, sound or radiation. Objects weigh less the further they are from the earth's surface. The gravitational influence of the earth is always with you.

1 / (your number)2

12-6: Univeral Gravitation Pages 177 - 179

The earth is round because the earth had attracted itself before it became solid and its corners were pulled in. This is also true for the sun and the moon. All planets pull on each other. The pulls of the planet disturb the paths of the others, causing perturbation.

In 1845/46, John Adams and Urbain Leverrier both used Newton's law of gravitation to find that a foreign body beyond the orbit of Uranus was perturbing Uranus. Searching the sky for this foreign body, Neptune was found! Following more peturbations, Pluto was discovered in 1930.

The "Big Bang" theory states that the explosion of a fireball 10-15 billion years ago hurled the universe outward, hence an expanding universe.
The "Big Crunch" suggests that the expanding universe way contract and fall back into a single unity, possibly cycling to create an oscillating universe.
Many scientists have followed through from the hope of Newton, such as John Locke. Locke used Newtonian physics and modeled a system of government.