Chapter 4: Ｇｒａｖｉｔｙ

Newton had a theory on gravity, but the planet Mercury was always a bit off... so Einstein helped him out by proposing...

"The only constant in the universe is the speed of light"

Password

"leave"

universal gravitational constant equation:

(It looks really wonky when typed out, but it should be in your notes)

What is the escape speed of earth?

11.2 km/s

At what part of its trajectory does the baseball have minimum speed?

A ball's minimum speed occurs at the top of its trajectory. If it is launched vertically, its speed at the top is zero. If launched at an angle, the verti-cal component of velocity is zero at the top, leaving only the horizontal component. So the speed at the top is equal to the horizontal component of the ball's velocity at any point.

Ellipse

A elongated circle, or oval shape, the shape of the planets orbit.

At the instant a cannon fires a cannonball hori-zontally over a level range, another cannonball held at the side of the cannon is released and drops to the ground. Which ball, the one fired downrange or the one dropped from rest, strikes the ground first?

Both cannonballs hit the ground at the same time, because both fall the same vertical distance.

True or false: Earth satellites normally orbit at altitudes in excess of 150 km to be above both gravity and the atmosphere of Earth.

False. Satellites are above the atmosphere and air resistance—not gravity! It's important to note that Earth's gravity extends throughout the uni-verse in accord with the inverse-square law.

Why is the earth round?

Gravity caused Earth to attract itself together before it became solid. Any "corners" of Earth have been pulled in so that Earth is a giant sphere.

Why is Superman so strong?

His home planet of Krypton is massive! And since there is a ton of mass, there is a ton of gravity! Therefore, Superman's ancestors adapted to that immense amount of gravity. But since Krypton died, Superman was sent to Earth where the gravity is way less. Furthermore, things that would way a lot on Krypton, weigh very little on earth.

Satellites in close circular orbit fall about 5 m during each second of orbit. Why doesn't this distance accumulate and send satellites crashing into Earth's surface?

In each second, the satellite falls about 5 m below the straight-line tangent it would have followed if there were no gravity. Earth's surface also curves 5 m beneath a straight-line 8-km tangent. The process of falling with the curvature of Earth continues from tangent line to tangent line, so the curved path of the satellite and the curve of Earth's surface "match" all the way around Earth. Satellites do, in fact, crash to Earth's surface from time to time when they encounter air resistance in the upper atmosphere that decreases their orbital speed.

The Law of Universal Gravitation was developed by:

Isaac Newton

By how much does the gravitational force between two objects decrease when the distance between their centers is doubled? Tripled? Increased tenfold?

It decreases to 1/4, 1/9, and 1/100 to the original value.

Where is a planet fastest when orbiting a sun in an elliptical shape?

Its highest speed: when closest to the sun Lowest speed: farthest

(Equation) Spacetime=

Matter x Energy

Describe Newton's thought process as the apple fell on his head (supposedly)?

Newton had the insight to see that the force between Earth and a falling apple is the same force that pulls the Moon in an orbital path around Earth, a path similar to a planet's path around the Sun. To test this hypothesis, Newton compared the fall of an apple with the "fall" of the Moon. He realized that the Moon falls in the sense that it falls away from the straight line it would follow if there were no forces acting on it. Because of its tangential velocity, it "falls around" the round Earth

Graviton

Particle that carries the gravitational force. Not yet observed

What was the first probe to escape the solar system?

Pioneer 10

A tossed rock, a cannonball, or any object that is projected by some means and continues in motion by its own inertia is called a ___________.

Projectile

Anything with mass warps...

Spacetime

Why is a black hole invisible?

The escape velocity of the black hole is greater than the speed of light.

A person's weight (not her mass) ___________ as she ___________ her dis-tance from Earth's center.

The person's weight (not her mass) decreases as she increases her dis-tance from Earth's center.

Gravity must travel at... (and no faster!)

The speed of light

Escape speed

The speed that a projectile, space probe, or similar object must reach to escape the gravitational influence of Earth or of another celestial body to which it is attracted.

Why do you feel weightless in a space station?

The station facility and astronauts all accelerate equally toward Earth, at somewhat less than 1 g because of their altitude. This accelera-tion is not sensed at all. With respect to the station, the astronauts experience zero g.

A baseball is batted at an angle into the air. Once the ball is air-borne, and neglecting air resistance, what is the ball's acceleration vertically? Horizontally?

Vertical acceleration is g because the force of gravity is vertical. Horizon-tal acceleration is zero because no horizontal force acts on the ball.

When a supernova explosion results from core collapse in a massive star it appears to leave behind...

a rapidly expanding shell of gas and a central neutron star or black hole

Consider an apple at the top of a tree that is pulled by Earth's grav-ity with a force of 1 N. If the tree were twice as tall, would the force of gravity be only 1/4 as strong? Defend your answer.

no, because an apple at the top of the twice-as-tall apple tree is not twice as far from Earth's center. The taller tree would need a height equal to the radius of Earth (6370 km) for the apple's weight at its top to reduce to 1 4 n. Before its weight decreases by 1%, an apple or any object must be raised 32 km—nearly four times the height of Mt. Everest. So, as a practi-cal matter, we disregard the effects of everyday changes in elevation.

One of the beauties of physics is that there are usually different ways to view and explain a given phenomenon. Is the following explanation valid? "Satellites remain in orbit instead of falling to Earth because they are beyond the main pull of Earth's gravity."

no, no, a thousand times no! If any moving object were beyond the pull of gravity, it would move in a straight line and would not curve around Earth. Satellites remain in orbit because they are being pulled by gravity, not because they are beyond it. For the altitudes of most Earth satellites, Earth's gravitational force on a satellite is only a few percent weaker than it is at Earth's surface.

law of universal gravitation

states that every object in the universe attracts every other object

universal gravitational constant

the constant G in the equation for Newton's law of universal gravitation; measures the strength of gravity

What is weight?

the force of gravity on an object

spacetime

the inseparable, four-dimensional combination of space and time