Review Question

What are Kepler’s laws?

Review Question

What are Newton’s laws?

Discussion

How could Newton tell that a force acting on the Moon was needed to keep it in its orbit?

Speed and distance

The faster you throw something, the farther is goes before it hits the ground.

The Moon is falling

The nearly circular orbit of the Moon is constantly accelerating toward the Earth.

The Moon is constantly falling toward the Earth.

Discussion

Newton’s third law tells us that the force of the Sun on the Earth is the same as the force of the Earth on the Sun. Why then does the Earth orbit the Sun instead of the other way around?

The Sun is more Massive

The force of the Earth on the Sun is the same as the force of the Sun on the Earth. But, the Sun is 333,000 times more massive than the Earth. From Newton’s second law the Earth will be accelerated 333,000 time more than the Sun.

Orbits

Because of Newton’s third law, it is not exactly correct to say that the Earth orbits the Sun or the Moon orbits the Earth. Instead, both objects, the Earth and the Sun or the Moon and the Earth, orbit a common point called the center of mass.

Discussion

If two stars with equal mass are held together by gravity, describe their orbits.

Newton’s Universal Law of Gravity

• Every mass attracts every other mass through a force called gravity

• The force is directly proportional to the product of their masses

• The force is inversely proportional to the square of the distance between them

221

d

MMGF

Newton’s law of gravity

Discussion

Consider the gravitational force between two objects with mass M1 and M2 separated by a distance d. How would the gravitational force change if the distance between them increases to 3 d. How will it change in the distance in decreased to 0.1 d?

Discussion

Suppose a new planet is discovered out in the Kuiper belt. This planet has twice the mass of the Earth but is also twice the size. Is the surface gravity of this new planet greater than, less than or the same as the surface gravity of the Earth?

d

The distance to use is the distance between the two spheres centers.

Gravitational forces between spherical masses

Discussion

You dig a very deep mine shaft. As you get closer to the center of the Earth, does your weight increase or decrease? Why?

(Hint: consider what the force of gravity will be at the very center of the Earth.)

Escape Velocity

If an object is thrown up with a high enough velocity it will leave Earth forever. For Earth this velocity is about 11 km/sec.

If the Earth were the same mass but twice the radius, would the escape velocity be greater or less than 11 km/sec? Why?

Discussion

Where does it come from?

For a planet to orbit the Sun, it must constantly accelerate toward the Sun, otherwise it would fly off in a straight line at a constant velocity.

Discussion

If I drop two balls at exactly the same time and from exactly the same height, with each ball exactly same shape and size but very different masses, which ball hits the ground first?

Discussion

If I drop two balls at exactly the same time and from exactly the same height, with each ball exactly same shape and size but very different masses, which ball has the greater force acting on it?

Why proportional to the mass?

All objects, regardless of their mass, fall with the same acceleration. Because F = ma,

gravFa

m To keep the acceleration

constant, the force must vary proportional to the mass.

Discussion

If I swing a ball in a circle over my head with a short string and a long string with each ball moving at the same speed, which ball has the greater force acting on it? Explain why.

Why the square of the distance?

An inverse square central force law is required to get stable orbits that are conic sections, i.e. orbits that are elliptical.