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### Newton’s Law

Lecture 8

By reading this chapter, you will learn

4-5 How Galileo’s pioneering observations with a telescope supported a Sun-centered model

4-6 The ideas behind Newton’s laws, which govern the motion of all physical objects, including the planets

4-7 Why planets stay in their orbits and don’t fall into the Sun

4-8 What causes ocean tides on Earth

GelileoGalilei

- Galileo was one of the first people to use a telescope to observe the heavens.
- He discovered craters on the Moon, sunspots on the Sun, the phases of Venus, and four moons orbiting Jupiter.
- His observations strongly suggested that the Earth orbits the Sun, not vice versa.

Isaac Newton

Isaac Newton (1642–1727)

- Using mathematical techniques that he devised, Isaac Newton formulated the law of universal gravitation and demonstrated that the planets orbit the Sun according to simple mechanical rules.
- 1st Law : An object remains at rest, or moves in a straight line at a constant speed, unless acted upon by a net outside foce
- 2nd Law : A net outside force will result in an accelration. F=ma
- 3rd Law : Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

Newton’s Law of Gravitation

Two objects attach each other with a force that is directly proportional to the mass of each object and inversely proportional to the square of the distance between them.

Gravity and Orbits

If a ball is dropped from a great height above the Earth’s surface, it

falls straight down (A). If the ball is thrown with some horizontal speed, it

follows a curved path before hitting the ground (B, C). If thrown with just

the right speed (E), the ball goes into circular orbit; the ball’s path curves

but it never gets any closer to the Earth’s surface. If the ball is thrown

with a speed that is slightly less (D) or slightly more (F) than the speed for

a circular orbit, the ball’s orbit is an ellipse.

Different kinds of Orbits

A conic section is any one of a family of curves obtained by slicing a cone with a plane. The orbit of one object about another can be any one of these curves: a circle, an ellipse, a parabola, or a hyperbola.

Orbit cannot be changed in the 2-body system.

Newton’s Form of Kepler’s 3rd Law

For planets in the solar system,

m1 + m2 mass of the Sun.

So, the relation is simplified as

When we use years for P, and AU for a, the constant become unity.

However, if we apply this formula to an orbit around other object, we need to pay attention to the constant.

Origin of Tides

Imagine three identical billiard balls placed some distance from a planet and released.

The closer a ball is to the planet, the more gravitational force the planet exerts on it. Thus, a short time after the balls are released, the blue 2-ball has moved farther toward the planet than the yellow 1-ball, and the red 3-ball has moved farther still.

From the perspective of the 2-ball in the center, it appears that forces have pushed the 1-ball away from the planet and pulled the 3-ball toward the planet.

These forces are called tidal forces.

The Moon exerts different gravitational pulls at different locations on the Earth.

At any location, the tidal force equals the Moon’s gravitational pull at that location minus the gravitational pull of the Moon at the center of the Earth. These tidal forces tend to deform the Earth into a non-spherical shape.

Spring tide

So, strong tide happens at New and Full Moons.

Neap Tides

- Weak tides at quarter moons

Key Ideas

- Evidence for the Heliocentric Model: The invention of the telescope led Galileo to new discoveries that supported a heliocentric model. These included his observations of the phases of Venus and of the motions of four moons around Jupiter.
- Newton’s Laws of Motion: Isaac Newton developed three principles, called the laws of motion, that apply to the motions of objects on Earth as well as in space.

Key Ideas

- (1) the tendency of an object to maintain a constant velocity,
- (2) the relationship between the net outside force on an object and the object’s acceleration,
- and (3) the principle of action and reaction.
- These laws and Newton’s law of universal gravitation can be used to deduce Kepler’s laws. They lead to extremely accurate descriptions of planetary motions.
- The mass of an object is a measure of the amount of matter in the object. Its weight is a measure of the force with which the gravity of some other object pulls on it.

Key Ideas

- In general, the path of one object about another, such as that of a planet or comet about the Sun, is one of the curves called conic sections: circle, ellipse, parabola, or hyperbola.
- Tidal Forces: Tidal forces are caused by differences in the gravitational pull that one object exerts on different parts of a second object.
- The tidal forces of the Moon and Sun produce tides in the Earth’s oceans.
- The tidal forces of the Earth have locked the Moon into synchronous rotation.

In summary…

Important Concepts

Important Terms

Tidal force

- Phase of Venus
- Newton’s Law of Motion
- Newton’s Law of Gravitation
- Tides

- Chapter/sections covered in this lecture : sections 4-5 through 4-8

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