The Motions of Celestial Bodies, and Newton’s Laws of

Motion

Announcements •  The results of Quiz 1 are posted in OWL •  Looking ahead:

–  Homework 1 is on-going, and is due on Thu, Sept. 29th;

–  Homework 2 will be available through SPARK/OWL starting on Thu. Sept 29th; it is due on Thu, Oct. 6th

–  The second in-class quiz will take place on Tue, Oct 4th

–  The First in-class Exam will take place on Thu, Oct 6th

Assigned Reading •  Units 13 and 14.

Section 2:

Tools of Astronomy

Section 2: Tools of Astronomy

They include: Ø  Understanding the Motions of Astronomical Bodies (gravity, inertia, mass, force, velocity, acceleration, etc.) Ø  Understanding matter, light, and their interactions Ø  Understanding the structure of the smallest of particles: atoms, and how they determine the appearance of some of the biggest of objects (stars, galaxies, etc.)

Today’s goals

•  Review the Laws of Planetary Motion •  Understand the concept of Inertia •  Introduce the concept of momentum •  Newton’s First Law of Motion

1  The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.

2  Planets move proportionally faster in their orbits when they are nearer the Sun (cover equal areas in equal time.

3  More distant planets take proportionally longer to orbit the Sun

Kepler’s Laws of Planetary Motion

Kepler’s Second Law of Orbits

2. As a planet moves around it’s orbit, it sweeps out equal areas in equal times.

1 month

Calculations Using Kepler's Third Law

The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semimajor axes. R3=P2 (R in AU; P in years)

As an example, the "radius" of the orbit of Mars (the length of the semimajor axis of the orbit) is: R=P2/3=(1.88)2/3=1.52 AU

Survey Question

A planet that is farther away from the Sun than the Earth, takes: an equal amount of time to orbit the Sun a smaller amount of time to orbit the Sun a larger amount of time to orbit the Sun

Survey Question

A planet that is farther away from the Sun than the Earth, takes: an equal amount of time to orbit the Sun a smaller amount of time to orbit the Sun a larger amount of time to orbit the Sun

P2 = R3

The Motions of Astronomical Bodies

•  Speed, velocity, acceleration, force •  Mass, momentum and inertia •  Newton’s three laws of motion •  The Force of Gravity

Survey Question •  `Common sense’: If the Earth spins on an axis, why don’t

objects fly off the spinning Earth? If the Earth revolves around the Sun, why

aren’t birds `left behind’? 1. Because of `superglue’ 2. Because of the pressure of the atmosphere 3. Because of gravity 4. Because we are at the center of the Universe

Survey Question •  `Common sense’: If the Earth spins on an axis, why don’t

objects fly off the spinning Earth? If the Earth revolves around the Sun, why

aren’t birds `left behind’? 1. Because of `superglue’ 2. Because of the pressure of the atmosphere 3. Because of gravity 4. Because we are at the center of the Universe

Describing Motion •  Motion is when the position of an object

changes in time •  If position does not change, the object is

at rest •  To describe motions we need to monitor

position and time •  The rate at which an objects covers a

given amount of space in a given amount of time is called speed Ø  v = s/t

Inertia

•  Inertia is the tendency of any physical objects to resist change in its state of motion (including rest)

Galileo and the Concept of Inertia Aristotle held that objects at rest remained

at rest unless a force acted on them, but that objects in motion did not remain in motion unless a force acted constantly on them: F = v (Incorrect).

Galileo concluded that an object in a state of motion possesses an ``inertia'' that causes it to remain in that state of motion unless an external force acts on it (Correct).

Inertia and Friction: think of Teflon

•  Teflon (polytetrafluoroethylene) : the most `slippery’ solid substance currently known

•  What would happen if our planet were

suddenly to change to teflon?

Inertia and Mass •  We measure Inertia by an object’s Mass,

which is the amount of material in the object.

•  Weight is the force exerted on the object by the gravity of another object, e.g. The force exerted by the planet Earth on you.

•  Thus, for an object, weight depends on the location of the object.

•  Your mass is the same on the moon, but your weight on the surface of the moon is smaller

Survey Question

The mass of an astronaut on the Moon is: smaller than his/her mass on the Earth the same as his/her mass on the Earth larger than his/her mass on the Earth

Survey Question

The mass of an astronaut on the Moon is: smaller than his/her mass on the Earth the same as his/her mass on the Earth larger than his/her mass on the Earth

Survey Question The weight of an astronaut on the Moon is

smaller than his/her weight on the Earth. True False

Survey Question The weight of an astronaut on the Moon is

smaller than his/her weight on the Earth. True False

The mass of the Moon is 100 times smaller than that of the Earth, thus its gravitational pull is smaller (smaller weights)

Sir Isaac Newton and the Unification of Physics & Astronomy

•  Newton was by many standards the most important figure in the development of modern science.

•  He demonstrated that the laws that govern the heavens are the same laws that govern the motion on the surface of the Earth.

•  Newton's Three Laws of Motion. •  Theory of Universal Gravitation

(1642-1727)

Vectors, or things with a direction

•  There are physical quantities in nature for which only one number, their intensity, tells the whole story: e.g. mass, temperature, luminosity, color

•  Other quantities need both an intensity and a direction to be fully described: e.g. velocity (speed with a direction), force, acceleration.

•  These quantities with a “direction” are called VECTORS

Law of Inertia (Newton’s First Law)

•  In the absence of a net force, an object moves with constant velocity, or it conserves its momentum (quantity of motion).

•  (paraphrased) If nothing acts on an object, the object will keep moving in a straight line and at a constant speed. If it was at rest (zero velocity), it will try to remain at rest.

•  Objects `resist’ change. Only a force can change the “quantity of motion” (momentum) of an object, either by changing its speed, or by changing its direction of motion, or both

Momentum •  Momentum is a quantitative way to

describe an object’s tendency to continue to do whatever it was previously doing.

•  An object’s momentum is simply its mass times its velocity. P = m·v

Don’t forget that velocity is a vector, so

momentum is a vector: the direction of motion is very important!

Survey Question You are driving your car and suddenly you

brake. What happens to the grocery bag on the passenger’s seat?

It stays where it is It tends to continue moving forward It tends to fall backward

Survey Question You are driving your car and suddenly you

brake. What happens to the grocery bag on the passenger’s seat?

It stays where it is It tends to continue moving forward It tends to fall backward

The grocery bag tends to keep its momentum constant.

Momentum is Conserved P = m·v

P1 = m1·v1 P2 = m2·v2

If two objects collide and stick together, the final momentum must be the same as the initial momentum.

Pfinal = P1 + P2

Linebacks and Fullbacks

P = m v; m in kg; and v in m/s

Momentum Conservation