Q. 1 - 17 due Thursday, March 3, 6:00 pm. Homework #4 Q. 1 - 17 due Thursday, March 3, 6:00 pm. Q. 18 - 21 due now

Newton’s First Law of Motion A body in motion remains in motion and a body at rest remains at rest unless acted upon by an outside force. OR If the net force acting on an object is zero, then there is no change in the object’s motion.

Both p and v are vector quantities Momentum: p = mv Both p and v are vector quantities

Do not confuse mass and density Mass = amount of matter Density = amount of matter per volume Higher density means more matter packed into same volume

Law of Conservation of Momentum If the net force acting on an object is zero, then the total momentum of a system remains constant. This is the essence of Newton’s 1st Law of motion

What happens when there are forces?

F = ma = rate of change of momentum Newton’s Second Law of Motion The change in a body’s velocity a due to an applied force F is in the same direction as the force, and is proportional to the force, but is inversely proportional to the body’s mass m. a = F/m Or F = ma = rate of change of momentum

a = F / m Because force is a vector, forces only affect motion in the direction of the force. Motion perpendicular to the force is unchanged.

Newton’s Third Law of Motion “For every applied force, a force of equal size but opposite direction arises” or For every action there is an equal and opposite reaction

F = ma (= rate of change of momentum) Newton's Laws of Motion A body in motion remains in motion and a body a rest remains at rest unless acted upon by an outside force. F = ma (= rate of change of momentum) For every applied force, a force of equal size but opposite direction arises.

Major Conservation Laws Conservation of energy Conservation of momentum Conservation of angular momentum

Angular Momentum angular momentum – the momentum involved in spinning /circling = mass x velocity x radius torque – anything that can cause a change in an object’s angular momentum (twisting force)

Conservation of Angular Momentum In the absence of a net torque, the total angular momentum of a system remains constant.

Forces change momentum Torques change angular momentum

Gravity & Orbits Gravity provides this force. A planet is always changing its direction of motion. Newton’s second law therefore states that a force must be acting on the planet. Gravity provides this force.

Angular Momentum & Orbits The angular momentum of an orbiting planet is conserved, i.e., it is always the same. This provides yet another reason why planets move fastest at perihelion and slowest at aphelion.

Newton’s Law of Gravity

The Acceleration of Gravity (a force) As objects fall, they accelerate (a = g = Fgrav/m). We use the special symbol g to represent the acceleration due to the force of gravity. At sea level on the Earth, g = 9.8 m/s each second, or g = 9.8 m/s2. The higher you drop the ball, the greater its velocity will be at impact (force will be acting on it longer).

Weight is the force of gravity acting upon an object : W = Fg = mg

Galileo demonstrated that g is the same for all objects, regardless of their mass!

Is Mass the Same Thing as Weight? mass – the amount of matter in an object weight – a measurement of the force due to gravity acting upon an object W = mg (weight) F = ma When in free-fall, you still have weight! “weightless” is a misnomer

Objects do have weight in space Free-fall often confused with weightlessness

Tidal Forces Because the gravitational force decreases with (distance)2, the attractive force experienced by one object (e.g., the Earth) due to the gravitational field of a second object (e.g., the Moon) varies with position (closest parts attracted most strongly).  

  Now look at what happens when we measure the forces relative to the center of the Earth. 

Tidal Friction Tidal forces from the Moon produce a bulge in the Earth’s mass distribution. Rotation causes the bulge to be aligned slightly ahead of the Earth-Moon line.

Tidal Friction This fight between Moon’s pull & Earth’s rotation causes friction. Earth’s rotation slows down (1 sec every 50,000 yrs.) Conservation of angular momentum causes the Moon to move farther away from Earth (3.8 cm/yr).

Synchronous Rotation …is when the rotation period of a moon, planet, or star equals its orbital period about another object. Tidal friction on the Moon (caused by Earth) has slowed its rotation down to a period of one month. The Moon now rotates synchronously. We always see the same side of the Moon. Tidal friction on the Moon has ceased since its tidal bulges are always aligned with Earth.

Most of the large moons in the solar system are in synchronous rotation. Planets close to their parent star are tidally locked. Close binary stars are tidally locked

Now we are ready to examine the solar system!!

We want to understand how the solar system was formed and how it got to be in the state that it is today. Look for patterns and physical characteristics of the solar system.

What does any theory of the formation and evolution of the solar System have to account for?

The Sun: A fairly typical star Predominately H and He Most of the mass in the solar system. Rotates in same sense that planets orbit.

eight Nine planets Need to understanding the similarities and differences between the planets, moons, asteroids, & comets

People of earth. Help!!!!

Planetary orbits: 1) Prograde 2) approximately coplanar 3) approximately circular Rotation: 1) Mostly Prograde 2) Includes sun 3) Includes large moons

Two “flavors” of planets Terrestrial Jovian   Two “flavors” of planets

Terrestrial Planets Size – “smaller” Location – closer to Sun Venus Earth Terrestrial Planets Mercury Mars Size – “smaller” Location – closer to Sun Composition – rocky/metallic Temperature – hotter Rings – none Rotation rate – slow Surface – solid Atmosphere – “minimal”

Mercury No moons Venus No moons Earth One moon Mars Two moons

Jovian Planets Size – “larger” Location – farther from Sun Saturn Jupiter Jovian Planets Size – “larger” Location – farther from Sun Composition – gaseous (mostly H,He) Temperature – cold Rings – ubiquitous Rotation rate – fast Surface – not solid Atmosphere – substantial Uranus Neptune

Jupiter >61 moons Uranus > 27 moons Saturn > 31 moons Neptune > 13 moons