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
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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
Observation Log by Galilei
Isaac Newton (1642–1727)
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.
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.
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.
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.
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.
So, strong tide happens at New and Full Moons.