Answers to Home work 1 & 2 are now posted on the class website Multiple choice questions due Friday, February 10, 5:00 pm. Short answer questions due Monday, February 13, 2:30 pm Answers to Home work 1 & 2 are now posted on the class website Exam #1 Wednesday, February 15

The Doppler Shift: A shift in wavelength due to a wave emitter moving towards (shorter wavelength) or away (longer wavelength) from an observer.  v  c =  & c known  measured v calculated

Measuring Radial Velocity We can measure the Doppler shift of emission or absorption lines in the spectrum of an astronomical object. known observed  We can then calculate the velocity of the object in the direction either towards or away from Earth. (radial velocity) 1 Angstrom = 10-10 meters  v  c =

The Doppler Effect BLUESHIFT REDSHIFT Light waves coming from an object moving towards you will have their wavelength shortened. BLUESHIFT Light waves coming from an object moving away from you will have their wavelength lengthened. REDSHIFT Light waves from an object moving perpendicular to your line-of-sight will not change their wavelength.

Measuring Rotational Velocity

Measuring Rotational Velocity (2)

Universal Laws of Motion Forces and Newton’s Laws of Motion

Scalars & Vectors Scalar: a quantity described solely by its size (and units) Vector: a quantity described by its size AND direction

speed – rate at which an object moves [m/s; mi/hr]. A scalar quantity. velocity – an object’s speed AND direction, e.g. “10 m/s moving east”. A vector quantity. acceleration – a change in an object’s velocity, i.e., a change in speed or direction [m/s2]. A vector quantity.

This “acceleration” can be a change in in the direction of motion Forces change the motion of objects. This “acceleration” can be a change in speed OR in the direction of motion both

Force, momentum, and acceleration are all vectors Momentum (p) – the mass of an object times its velocity (p=mv) Force (f) – anything that can cause a change in an object’s momentum As long as the object’s mass does not change, the force causes a change in velocity, or an acceleration (a) Force, momentum, and acceleration are all vectors

Sir Isaac Newton (1642-1727) Invented calculus Invented the reflecting telescope Connected gravity and planetary forces Philosophiae naturalis principia mathematica

Newton’s Laws of Motion First Law A body in motion remains in motion and a body at rest remains at rest unless acted upon by an outside force.

What happens when there are forces? The First Law is essentially a statement that in the absence of forces there is no change in the motion. What happens when there are forces?

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

Acceleration is Inversely Proportional to Mass F = ma a = F / m

Because force is a vector, as is velocity, forces only affect motion in the direction of the force. Motion perpendicular to the force is unchanged.

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

Law of Conservation of Momentum In the absence of a net force, the total momentum of a system remains constant. If F = rate of change of momentum = 0 => No change in momentum

Third Law For every applied force, a force of equal size but opposite direction arises (For every action there is an equal and opposite reaction)

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.

One of the primary forces we will encounter over the rest of the semester arises from Gravity

Universal Law of Gravitation Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.

“Weight” is the force of gravity acting upon an object

Newton’s 3rd Law – For every applied force, a force of equal size but opposite direction arises. Consider the gravitational experienced by mass 2 due to the gravitational attraction of mass 1. Consider the gravitational experienced by mass 1 due to the gravitational attraction of mass 2.

The Acceleration of Gravity As objects fall, they accelerate. The acceleration due to Earth’s gravity is 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.

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 are “weightless” but you still have weight!

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

Got here

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

Major Conservation Laws Conservation of energy Conservation of (linear) 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

Orbital Paths from Law of Gravitation Extending Kepler’s Law #1, Newton found that ellipses were not the only orbital paths. All orbits are “conic sections” Orbital motion takes place around the center of mass Possible orbital paths ellipse (bound) parabola (unbound) hyperbola (unbound)

The Center of Mass In Kepler's Laws, the Sun is fixed at a point in space (a focus of an ellipse) and the planet revolves around it. Why is the Sun privileged? Kepler had mystical ideas about the Sun, endowing it with almost god-like qualities that justified its special place. Newton demonstrated that the the Sun does not occupy a privileged postion and in the process he modified Kepler's 3rd Law.

We may define a point called the center of mass between two objects through the equations m1d1 = m2d2 d1+ d2 = R where R is the total separation between the centers of the two objects.

The center of mass is familiar to anyone who has ever played on a see-saw. The fulcrum point at which the see-saw will exactly balance two people sitting on either end is the center of mass for the two persons. m1d1 = m2d2

Recall Kepler’s 3rd law: P2 / a3 = constant Because for every action there is an equal and opposite reaction, Newton realized that in the planet-Sun system the planet does not orbit around a stationary Sun. Instead, Newton proposed that both the planet and the Sun orbited around the common center of mass for the planet-Sun system. This led Newton to modify Kepler's 3rd Law. Recall Kepler’s 3rd law: P2 / a3 = constant

Newton’s Version of Kepler’s Third Law Newton’s modification of Kepler's 3rd Law reads: P2 = 42 a3 / G (m1 + m2) G is known as the universal gravitational constant.

P2 / a3 = 42 / G (m1 + m2) If you can measure the orbital period of two objects (P) and the distance between them (a), then you can calculate the sum of the masses of both objects (m1 + m2).

Changing Orbits orbital energy = kinetic energy + gravitational potential energy conservation of energy implies: orbits can’t change spontaneously An object can’t crash into a planet unless its orbit takes it there. An orbit can only change if it gains/loses energy from another object, such as a gravitational encounter: If an object gains enough energy so that its new orbit is unbound, we say that it has reached escape velocity.

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 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.

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 sufficiently close to their star will settle into synchronous rotation. Stars in close orbits about each other will settle into synchronous rotation.

If the wavelength of an electromagnetic wave increases, its velocity (red) Decreases (yellow) Increases (blue) Remains the same (green) Not enough information

If the wavelength of an electromagnetic wave increases, its velocity (red) Decreases (yellow) Increases (blue) Remains the same (green) Not enough information

If the wavelength of an electromagnetic wave increases, its frequency (red) Decreases (yellow) Increases (blue) Remains the same (green) Not enough information

If the wavelength of an electromagnetic wave increases, its frequency (red) Decreases (yellow) Increases (blue) Remains the same (green) Not enough information

If the wavelength of an electromagnetic wave increases, its energy (red) Decreases (yellow) Increases (blue) Remains the same (green) Not enough information

If the wavelength of an electromagnetic wave increases, its energy (red) Decreases (yellow) Increases (blue) Remains the same (green) Not enough information

Of the four fundamental forces of nature, the one that is inherently the weakest is the a) strong nuclear force. b) weak nuclear force. c) electromagnetic force. d) gravitational force.

Of the four fundamental forces of nature, the one that is inherently the weakest is the a) strong nuclear force. b) weak nuclear force. c) electromagnetic force. d) gravitational force.

Which of the four fundamental forces of nature has the largest effect on objects at astronomical distances from each other? a) strong nuclear force b) weak nuclear force c) electromagnetic force d) gravitational force

Which of the four fundamental forces of nature has the largest effect on objects at astronomical distances from each other? a) strong nuclear force b) weak nuclear force c) electromagnetic force d) gravitational force

For the strong nuclear force to hold together two protons, they must be a) moving slowly. b) moving rapidly. c) close together. d) of opposite charge.

For the strong nuclear force to hold together two protons, they must be a) moving slowly. b) moving rapidly. c) close together. d) of opposite charge.

Which situation(s) does NOT describe an acceleration: a) a car traveling with constant speed on a straight road. b) a car traveling with constant speed around a bend. c) a planet traveling in its orbit around the Sun. d) a car decreasing speed on a straight road. e) an electron traveling around a nucleus.

Which situation(s) does NOT describe an acceleration: a) a car traveling with constant speed on a straight road. b) a car traveling with constant speed around a bend. c) a planet traveling in its orbit around the Sun. d) a car decreasing speed on a straight road. e) an electron traveling around a nucleus.

a) throw the hammer at the space ship to get someone's attention. You are an astronaut taking a spacewalk to fix your spacecraft with a hammer. Your lifeline breaks and the jets on your back pack are out of fuel. To return safely to your spacecraft (without the help of someone else), you should a) throw the hammer at the space ship to get someone's attention. b) throw the hammer away from the space ship. c) use a swimming motion with your arms. d) kiss your ship good bye.

a) throw the hammer at the space ship to get someone's attention. You are an astronaut taking a spacewalk to fix your spacecraft with a hammer. Your lifeline breaks and the jets on your back pack are out of fuel. To return safely to your spacecraft (without the help of someone else), you should a) throw the hammer at the space ship to get someone's attention. b) throw the hammer away from the space ship. c) use a swimming motion with your arms. d) kiss your ship good bye.

A gram of lead has a greater ______ than a gram of feathers. a) mass. b) density. c) weight. d) volume.

A gram of lead has a greater ______ than a gram of feathers. a) mass. b) density. c) weight. d) volume.

Since angular momentum is conserved, the rotational speed of a collapsing gas cloud a) depends on its mass. b) increases. c) decreases. d) is independent of its initial rotation.

Since angular momentum is conserved, the rotational speed of a collapsing gas cloud a) depends on its mass. b) increases. c) decreases. d) is independent of its initial rotation.

Since angular momentum is conserved, the orbital speed of a planet at perihelion as compared to aphelion a) is larger. b) is smaller. c) is the same. d) approaches infinity.

Since angular momentum is conserved, the orbital speed of a planet at perihelion as compared to aphelion a) is larger. b) is smaller. c) is the same. d) approaches infinity.

Concept Test If you go to the moon, where the acceleration of gravity is weaker, your mass changes, but your weight stays the same your weight changes, but your mass stays the same your mass and weight both change your mass and weight both stay the same

Concept Test If you go to the moon, where the acceleration of gravity is weaker, your mass changes, but your weight stays the same your weight changes, but your mass stays the same your mass and weight both change your mass and weight both stay the same