Review Question What is retrograde motion?

Review Question Explain why the phases of Venus proved to Galileo that Venus must orbit the Sun when the Moon also has phases and it orbits the Earth.

Review Question What are Kepler’s laws?

Review Question What are Newton’s laws?

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?

Speed and distance The faster you throw something, the farther it 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

Newton’s law of gravity

Discussion Consider the gravitational force between two objects with mass M 1 and M 2 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, 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.

The planets move in ellipses with the Sun at one focus. Conic section orbits are a natural outcome of the 1/d 2 nature of the gravitational force, in fact the only force law that gives stable orbits. Kepler’s 1 st law

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 a)Greater b)Less c)Unchanged

A line drawn from the planet to the Sun sweeps out equal areas in equal intervals of time. Just another way of saying angular momentum is conserved which comes from Newton’s 2 nd law of motion. Kepler’s 2 nd law

Conservation of angular momentum Any object that is spinning or orbiting has angular momentum which is equal to the mass × velocity × radius. In the absence of an external torque, or twisting force, the angular momentum will remain constant.

Discussion If angular momentum is conserved and I decrease the radius what happens?

Newton’s form of Kepler’s 3 rd law

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?

Spring Tides and Neap Tides The Sun also contributes to the Earth’s tides. When the Sun and Moon line up to produce higher tides, this is called spring tides. Neap tides occur when the Moon and Sun Partially cancel each other. What phases of the Moon do spring and neap tides occur?

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?

Tidal Friction

Discussion Due to tidal friction, what happens to the rotation rate of the Earth over time?

The Earth-Moon system The Moon exerts a force on the tidal bulges on Earth, trying to twist the tidal bugles back to face the Moon. This torque slows the rotation of the Earth.

Discussion The Moon is slowing the Earth’s rotation and the Earth is losing angular momentum. Where does that angular momentum go?

Orbit of the Moon Due to conservation of angular momentum, the slowing of Earth’s rotation requires the Moon to move faster in its orbit. Because the force of Earth’s gravity does not change, this means the Moon is getting farther away, by about 2 inches per year.

Discussion What do you think will be the ultimate fate of the Earth Moon system?

Fate of the Earth Moon System Over billions of years the length of the month and the length of the day will be the same, about 47 days. The Moon will stationary in the sky and will be too small for total solar eclipses.

Discussion Will the Moon still have phases?

Discussion What would happen to the Moon if its orbital period was less than the Earth’s day?