Conceptual Physics - Chapter 12: Universal Gravitation (Review)

What would be the difference in your weight if you were five times farther from the center of the earth than you are now? Ten times?

1/25; 1/100.

Inverse-square law

A physical quantity varies inversely as another quantity squared

Why did Newton think that a force must act on the moon?

Due to Newton's first law of inertia, Newton thought that a force must act on the moon. Since the moon moves around the earth (even if in a circular path and not a straight linear path) he thought there would be a force acting on it.

Calculate the force of gravity between the earth (mass = 6.0 x 10^24 kg) and the moon (mass = 7.4 x 10^22 kg). The average earth-moon distance is 3.8 x 10^8 m.

F = 2.0 x 10^20 N

Calculate the force of gravity between a newborn baby of mass 4 kg and the obstetrician of mass 75 kg, who is 0.3 m from the baby. Which exerts more gravitational force on the baby, Mars or the obstetrician? By how much?

F = 2.22 x 10^-7 N; the obstetrician exerts more gravitational force than Mars; by 8.31.

Calculate the force of gravity between a newborn baby (mass = 4 kg) and the planet Mars (mass = 6.4 x 10^23 kg), when Mars is at its closest to the earth (distance = 8 x 10^10 m).

F = 2.67 x 10^-8 N

Calculate the force of gravity between the earth and the sun (sun's mass = 2.0 x 10^30 kg; average earth-sun distance = 1.5 x 10^11 m).

F = 3.56 x 10^22 N

What is required before a hypothesis (an educated guess) advances to the status of a scientific theory (organized knowledge)?

For a hypothesis to advance to the status of a scientific theory, it would have to be tested.

Law of universal gravitation

For any pair of objects, each object attracts the other object with a force that is directly proportional to the product of the masses of the objects, and inversely proportional to the square of the distance between their centers of mass

How did Newton check his hypothesis that there is an attractive force between the earth and moon?

Newton checked his hypothesis by detecting the proportion of drop per unit distance away from the Earth. The apple and the moon dropped proportionally to each other in accordance to the distance from the center of the Earth they were.

What did Newton conclude about the force that pulls apples to the ground and the force that holds the moon in orbit?

Newton concluded that the force that pulls apples to the ground and the force that holds the moon in orbit are one and the same - they are both pulled by earth's gravity.

What did Newton discover about gravity?

Newton discovered that gravity is universal.

If the moon falls, why doesn't it get closer to the earth?

Newton proposed that the moon falls AROUND the earth and not toward it. According to his theory, the moon falls in the sense that it falls beneath the straight line it would follow if no force acted on it. In other words, to Newton, the moon was simply a projectile circling the earth under the attraction of gravity.

What causes planetary perturbations?

Planetary perturbations are caused by gravitational interactions between planets.

What is meant by tangential velocity?

Tangential velocity is the velocity at which the object is moving at a line tangent to the circular path.

Universal gravitational constant, G

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

Perturbation

The deviation of an orbiting object from its path around a center of force caused by the action of an additional center of force

What makes the earth round?

The earth is round because of gravitation.

In what way is gravity reduced with distance from the earth?

The strength of gravity is decreased as the distance away from the center a mass is increased.

What are the two masses and the one distance that determine your weight?

The two masses are your own mass and the Earth's mass (or the source of gravity on any other planet/mass) and the distance is equaled to the distance away from the center of the earth.

What does the very small value of the gravitational constant G (in standard units) tell us about the strength of gravitational forces?

The value of G tells us that the force of gravity is a very weak force.

Since the planets are pulled to the sun by gravitational attraction, why don't they simply crash into the sun?

They have tangential velocities.