Explain why the Earth precesses and the consequences Explain why the Earth has seasons Explain the phases of Moon and how they differ from a lunar eclipse Kepler’s Laws Explain and apply Newton’s laws of motion

Discussion What are Kepler’s 3 laws of planetary motion?

Discussion What are Newton’s 3 laws of motion?

Newton’s laws of motion A body remains at rest or moves in a straight line at a constant speed unless acted on by a net external force. Force = mass  acceleration For any force there is always an equal and opposite reaction force.

Discussion Consider an object in uniform circular motion. That is, an object traveling in a circle with a constant speed. Is there a force acting on this object? Why or why not?

Discussion Consider an object in uniform circular motion. That is, an object traveling in a circle with a constant speed. How is the velocity of the object changing and how must the force on the object be directed to change its velocity in this way?

Discussion Is there a force acting on the Moon? How can you tell?

Discussion In firing a cannon, you want to be able to have the cannon ball reach as far as possible. How can you accomplish this?

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 in a circular orbit, describe how they would move.

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

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?

Gravitational forces between spherical masses d The distance to use is the distance between the two spheres centers.

Discussion You dig a very deep mine shaft. As you get closer to the center of the Earth, does your weight increase, decrease or remain the same? Why? (Hint: consider what the force of gravity will be at the very center of the Earth.)

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, 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.

Discussion A ball held on a string is coasting around in a large horizontal circle. The string is then pulled so the ball coasts in a smaller circle. When coasting the smaller circle its speed is Greater Less Unchanged

Newton’s form of Kepler’s 3rd law

Discussion Notice that we can only determine the sum of the masses using Newton’s from of Kepler’s 3rd law. In the case of the solar system this sum is dominated by the Sun. Why can’t we figure out the mass of a planet by observing its orbit? Can’t we get the force necessary to keep it in orbit and figure out the mass?

All objects fall in a gravitation field with the same acceleration regardless of mass. Because being in orbit is just falling, all objects will orbit the same regardless of their mass as long as the mass of the orbiting object is much less than that of the object it is orbiting.

Discussion The Moon’s mass (consider it all at the center of the Moon) attracts every atom on the Earth. If every atom has exactly the same mass, is the gravitational attraction of the Moon the same on each atom on the Earth? Explain.

Tidal Forces Different distances from a mass will experience different forces and therefore different accelerations.

Discussion Consider yourself sitting on the center ball, number 2 in the previous diagram. How will you perceive the motion of the other two balls relative to you?

Tidal Forces Tidal forces act to stretch things out along the direction of a gravitating source and squeeze them in the middle.

Discussion Does it matter that all the atoms on the earth have the same mass? Or that all three billiard balls have the same mass? Why or why not?