Lecture 5Lecture 5

Modern AstronomyModern Astronomy

AnnouncementsAnnouncements

Test on Wednesday – Details to followTest on Wednesday – Details to follow

Homework 2 Due NowHomework 2 Due Now

Homework 3 Due next Monday, but it Homework 3 Due next Monday, but it is a good idea to finish before the Test is a good idea to finish before the Test Wednesday.Wednesday.

Test Information: MaterialsTest Information: Materials

RequiredRequired Pencil/penPencil/pen Equation sheetEquation sheet

RecommendedRecommended CalculatorCalculator Scratch paperScratch paper

Test CoverageTest Coverage Units 1, 2, 5, 6, 9, 11, 12Units 1, 2, 5, 6, 9, 11, 12

Test Information: MaterialsTest Information: Materials

ForbiddenForbidden Cell phone (Cell phone (not even for use as calculatornot even for use as calculator)) Communication with anyone other than meCommunication with anyone other than me Textbook or any other reference material not written Textbook or any other reference material not written

by you.by you. Equation SheetEquation Sheet

Single page (front and back) HAND WRITTEN notes, Single page (front and back) HAND WRITTEN notes, equations, or equations, or any informationany information you want to bring to you want to bring to the test.the test.

Max size 8.5 x 11 inches.Max size 8.5 x 11 inches. Will be turned in – counts Will be turned in – counts 10%10% of your test grade. of your test grade.

Test Information: FormatTest Information: Format

85 minutes Wednesday (5-6:25 pm)85 minutes Wednesday (5-6:25 pm)

Approximate Test Format:Approximate Test Format: 20 multiple-choice questions (2 points 20 multiple-choice questions (2 points

each)each) 10 True/False questions (2 points each)10 True/False questions (2 points each) 6 Short answer/problem questions (5 6 Short answer/problem questions (5

points each)points each) Equation sheet (10 points)Equation sheet (10 points)

ReviewReview 3000+ BC – Use Sun to predict seasons3000+ BC – Use Sun to predict seasons 1000 BC – Babylonian calendar, predict planet 1000 BC – Babylonian calendar, predict planet

motionmotion 700 BC – Start of classical revolution700 BC – Start of classical revolution 500 BC – Earth is a sphere500 BC – Earth is a sphere 360 BC – Plato Postulates Perfection360 BC – Plato Postulates Perfection 350 BC – Eudoxos/Aristotle – Geocentric system350 BC – Eudoxos/Aristotle – Geocentric system 310 BC – Aristarchus – Heliocentric (not accepted)310 BC – Aristarchus – Heliocentric (not accepted) 180 BC – Hipparchus – Star mapping180 BC – Hipparchus – Star mapping 185 AD – Ptolemy – Most advance Geocentric 185 AD – Ptolemy – Most advance Geocentric

modelmodel 1543 AD – Copernicus – Heliocentric model1543 AD – Copernicus – Heliocentric model 1577 AD – Tycho – Modified Geocentric model1577 AD – Tycho – Modified Geocentric model

Johannes Kepler (1571-1630)Johannes Kepler (1571-1630)

Student of Tycho Student of Tycho BraheBrahe

Uses Tycho’s Uses Tycho’s observations to observations to support Copernicus.support Copernicus.

Deduces three laws Deduces three laws that govern planetary that govern planetary motion.motion.

Explains planetary Explains planetary motion motion betterbetter than than Ptolemy’s model.Ptolemy’s model.

Kepler’s Big IdeaKepler’s Big Idea

Found a consistent description by Found a consistent description by abandoning bothabandoning both Circular motion andCircular motion and Uniform motion.Uniform motion.

Planets move around the sun on Planets move around the sun on elliptical paths, with non-uniform elliptical paths, with non-uniform velocities.velocities.

Kepler’s Three LawsKepler’s Three Laws

First LawFirst Law: All planets move around : All planets move around the sun in elliptical orbits, with the the sun in elliptical orbits, with the sun at one focus.sun at one focus.

Second LawSecond Law: All planets sweep out : All planets sweep out equal areas of their orbits in equal equal areas of their orbits in equal times.times.

Third LawThird Law: The square of a planet’s : The square of a planet’s orbital period is equal to the cube of orbital period is equal to the cube of its average distance from the sun.its average distance from the sun.

Kepler’s First LawKepler’s First Law

All planets move around the sun in All planets move around the sun in elliptical orbits, with the sun at one focus.elliptical orbits, with the sun at one focus.

In an ellipse:In an ellipse: a + b = a’ + b’a + b = a’ + b’

Eccentricities of EllipsesEccentricities of Ellipses

e = 0.02 e = 0.1 e = 0.2

e = 0.4 e = 0.6

1) 2) 3)

4) 5)

Eccentricities of Planetary OrbitsEccentricities of Planetary Orbits

Orbits of (major and minor) planets are virtually indistinguishable from circles:

Earth: e = 0.0167Most extreme example:

Pluto: e = 0.248

Kepler’s Second LawKepler’s Second Law

All planets sweep out equal areas of their All planets sweep out equal areas of their orbits in equal times.orbits in equal times.

Means the closer a planet is to the sun, the Means the closer a planet is to the sun, the faster it moves in its orbit.faster it moves in its orbit.

Conservation Of Angular MomentumConservation Of Angular Momentum

Kepler’s Third LawKepler’s Third Law

The square of a planet’s orbital period is The square of a planet’s orbital period is equal to the cube of its average distance equal to the cube of its average distance from the sun.from the sun.

Written Mathematically As:Written Mathematically As: PP22 = a = a33

P = orbital period of the planet in years.P = orbital period of the planet in years. a = average distance between the planet and a = average distance between the planet and

the sun in Astronomical Units (AU).the sun in Astronomical Units (AU). Giving something’s distance from the sun in AU is the Giving something’s distance from the sun in AU is the

same as giving its distance as “this many times further same as giving its distance as “this many times further from the sun than the Earth.”from the sun than the Earth.”

ExampleExample: Jupiter is 5.2 AU from the sun means Jupiter : Jupiter is 5.2 AU from the sun means Jupiter orbits the sun 5.2 times farther away than the Earth orbits the sun 5.2 times farther away than the Earth does.does.

The Beginning of the End:The Beginning of the End:Galileo Galilei (1564-1642)Galileo Galilei (1564-1642)

Contemporary with Contemporary with Kepler and an avid Kepler and an avid CopernicanCopernican

Contributions were Contributions were useful in helping to useful in helping to discredit Aristotelian discredit Aristotelian concepts of motion, and concepts of motion, and he was one of the first he was one of the first astronomers to record astronomers to record telescopic observations telescopic observations of the celestial objectsof the celestial objects

Promoted the modern Promoted the modern view of science: view of science: Transition from a faith-Transition from a faith-based “science” to an based “science” to an observation-based observation-based science. science.

Galileo’s Telescopic ObservationsGalileo’s Telescopic Observations

Craters on the Craters on the moon moon

Moons of JupiterMoons of Jupiter Saturn Saturn Phases of Venus Phases of Venus SunspotsSunspots Milky way Milky way Variable planet Variable planet

size size

Major Discoveries of GalileoMajor Discoveries of Galileo

• Moons of Jupiter Moons of Jupiter

(4 Galilean moons)(4 Galilean moons)

• Rings of SaturnRings of Saturn

(What he really saw)(What he really saw)

(What he really saw)(What he really saw)

Major Discoveries of GalileoMajor Discoveries of Galileo• Surface structures on the moon; first estimates Surface structures on the moon; first estimates

of the height of mountains on the moonof the height of mountains on the moon

Major Discoveries of GalileoMajor Discoveries of Galileo

• Sun spotsSun spots (proving (proving that the sun is not that the sun is not

perfect!)perfect!)

Major Discoveries of GalileoMajor Discoveries of Galileo• Phases of Venus (including “full Venus”), Phases of Venus (including “full Venus”), proving that Venus orbits the sun, not the Earth!proving that Venus orbits the sun, not the Earth!

Galileo’s Observations Conflict Galileo’s Observations Conflict With Catholic DogmaWith Catholic Dogma

Valleys and craters on moonValleys and craters on moon Sunspots on sunSunspots on sun ““Belts” on JupiterBelts” on Jupiter ““Ears” on SaturnEars” on Saturn All in conflict with the Catholic All in conflict with the Catholic

“perfect heavens.”“perfect heavens.”

Christiaan Huygens (1629-1695)Christiaan Huygens (1629-1695)

Good early telescope Good early telescope maker.maker.

““Discovered” Saturn’s Discovered” Saturn’s rings.rings.

Lots of contributions Lots of contributions to optics.to optics.

First estimate of First estimate of distance to another distance to another star (Sirius at 27,000 star (Sirius at 27,000 AU).AU).

Daily Grade 5 – Question 1Daily Grade 5 – Question 1

What is the difference between a What is the difference between a heliocentricheliocentric cosmology and a cosmology and a geocentric geocentric cosmology?cosmology?

Daily Grade 5 – Question 2Daily Grade 5 – Question 2

The seventh and eighth planets out The seventh and eighth planets out from the sun are Uranus and from the sun are Uranus and Neptune. Which one moves more Neptune. Which one moves more slowly in its orbit?slowly in its orbit?

The Birth of Modern Physics:The Birth of Modern Physics:Sir Isaac Newton (1643-1727)Sir Isaac Newton (1643-1727)

One of the most One of the most famous scientists of famous scientists of all time.all time.

Building on the Building on the work of Galileo and work of Galileo and Kepler, devised the Kepler, devised the Laws of motion and Laws of motion and Law of Universal Law of Universal Gravitation that Gravitation that provide the physics provide the physics behind the behind the heliocentric model.heliocentric model.

Other Major AccomplishmentsOther Major Accomplishments

Invented Calculus as a necessary tool to solve Invented Calculus as a necessary tool to solve mathematical problems related to motionmathematical problems related to motion

Major advances in optics and reflecting telescopesMajor advances in optics and reflecting telescopes

Newton’s LawsNewton’s Laws

Newton asked: When and Why do things Newton asked: When and Why do things move?move? Things move when you apply a force to them.Things move when you apply a force to them. A A forceforce is something that pushes or pulls on is something that pushes or pulls on

something else.something else. Can something be moving when no force is Can something be moving when no force is

being applied to it?being applied to it? Yes, it can.Yes, it can.

But, can something’s motion But, can something’s motion changechange when when no force is being applied to it?no force is being applied to it? No, it can’t!No, it can’t!

Newton’s First Law of MotionNewton’s First Law of Motion Newton’s First LawNewton’s First Law::

A body at rest tends to stay at rest unless acted A body at rest tends to stay at rest unless acted upon by an outside force.upon by an outside force.

A body in motion tends to stay in motion unless A body in motion tends to stay in motion unless acted upon by an outside force.acted upon by an outside force.

Consequences:Consequences: You need to apply a force to make a stationary You need to apply a force to make a stationary

object start moving.object start moving. You need to apply a force to stop a moving You need to apply a force to stop a moving

object.object. You need to apply a force to You need to apply a force to changechange the motion the motion

of an object:of an object: Speed it upSpeed it up Slow it downSlow it down Change it’s directionChange it’s direction

AccelerationAcceleration

We call We call anyany change in how an object moves change in how an object moves an an accelerationacceleration..

Examples of acceleration:Examples of acceleration: When your car speeds up after you hit the gas When your car speeds up after you hit the gas

pedal (your direction of motion is the same, but pedal (your direction of motion is the same, but you are going faster than before)you are going faster than before)

When your car slows down because you hit the When your car slows down because you hit the brakes (same direction of motion, less speed brakes (same direction of motion, less speed than before)than before)

Whenever your car turns, Whenever your car turns, even if it doesn’t even if it doesn’t speed up or slow downspeed up or slow down (your direction of (your direction of motion changes, but your speed stays the same).motion changes, but your speed stays the same).

Forces And AccelerationForces And Acceleration

Notice how in Notice how in all three all three examplesexamples you would you would feel a force…feel a force…

Car speeds up: you feel Car speeds up: you feel a force pressing you a force pressing you back into your seat.back into your seat.

Car slows down: you feel Car slows down: you feel a force pushing you a force pushing you forward toward the forward toward the windshield.windshield.

Car turns: you feel Car turns: you feel “pulled” toward the side “pulled” toward the side of the car.of the car.

Newton’s Second Law of MotionNewton’s Second Law of Motion

Describes the relationship between Describes the relationship between forceforce and and accelerationacceleration..

Newton’s Second Law:Newton’s Second Law: The acceleration of a body is directly The acceleration of a body is directly

proportional to the force applied to that proportional to the force applied to that body.body.

The acceleration of a body is inversely The acceleration of a body is inversely proportional to the mass of the body.proportional to the mass of the body.

Newton’s Second Law – The Newton’s Second Law – The Equation!Equation!

You can write Newton’s Second Law as a You can write Newton’s Second Law as a mathematical equation:mathematical equation:

F = m × aF = m × aIn this equation:In this equation:F = the force, measured in a unit called F = the force, measured in a unit called Newtons (N)Newtons (N)m = the mass, measured in kilograms (kg)m = the mass, measured in kilograms (kg)a = the acceleration, measured in m/sa = the acceleration, measured in m/s22

Let’s say I wanted to give an object an acceleration of 10 m/s2 (free-fall).

The more massive the object, the more force I’d have to apply to get that acceleration.

A 0.1 kg object, like an apple, would require a “push” of only 1 N:

0.1 kg × 10 m/s2 = 1 N

A 4 kg object, like a gallon jug of milk, would require a “push” of 40 N:

4 kg × 10 m/s2 = 40 N

A 1,000 kg object, like a car, would require a “push” of 10,000 N!

1,000 kg × 10 m/s2 = 10,000 N

More mass means I need more force to get the same effect. Mass is an object’s resistance to a change in its motion.

Acceleration of GravityAcceleration of Gravity

Acceleration of Acceleration of gravity is gravity is independent of the independent of the mass (weight) of the mass (weight) of the falling object!falling object!

Newton’s second law Newton’s second law still applies! Since still applies! Since the acceleration is the acceleration is the same and the the same and the mass is different, mass is different, the force is more for the force is more for the heavier object.the heavier object.

Acceleration of GravityAcceleration of Gravity Light objects (like Light objects (like

feathers) appear feathers) appear to fall slower on to fall slower on Earth due to air Earth due to air resistance.resistance.

In a vacuum In a vacuum (such as on the (such as on the moon), a hammer moon), a hammer and a feather fall and a feather fall at the same rate.at the same rate.

Daily Grade 5 – Question 3Daily Grade 5 – Question 3

If we drop a feather and a hammer at the If we drop a feather and a hammer at the same moment and from the same height, same moment and from the same height, we see the hammer strike the ground first, we see the hammer strike the ground first, whereas on the moon both strike the whereas on the moon both strike the ground at the same time. Why?ground at the same time. Why?

A.A. The surface gravity of Earth is stronger than The surface gravity of Earth is stronger than the gravity of the moon.the gravity of the moon.

B.B. In strong gravity fields heavier objects fall In strong gravity fields heavier objects fall faster.faster.

C.C. The is no air resistance effect on the moon.The is no air resistance effect on the moon.D.D. Feathers are made mostly of air.Feathers are made mostly of air.

And Now, On To The Most Famous And Now, On To The Most Famous Of Newton’s Laws… The Law For Of Newton’s Laws… The Law For

Rocket Science!Rocket Science!

Newton’s Third LawNewton’s Third Law

The Action-Reaction Law:The Action-Reaction Law: For every action there is an equal and For every action there is an equal and

opposite reaction.opposite reaction. Examples:Examples:

If you punch a wall, you will exert a force on the If you punch a wall, you will exert a force on the wall. The wall will exert an equal and opposite wall. The wall will exert an equal and opposite force back on your hand (which is why it hurts)!force back on your hand (which is why it hurts)!

In a rocket engine, the engine “pushes” In a rocket engine, the engine “pushes” superheated gas superheated gas downdown out of the bottom of the out of the bottom of the rocket. The gas exerts an equal and opposite rocket. The gas exerts an equal and opposite force force upup on the rocket, “pushing” the rocket on the rocket, “pushing” the rocket upward.upward.

Newton’s Third LawNewton’s Third Law

Newton’s Third Law means forces Newton’s Third Law means forces always come in opposing pairs: equal always come in opposing pairs: equal in strength and opposite in direction.in strength and opposite in direction.

Newton’s LawsNewton’s Laws

Newton’s three laws of motion Newton’s three laws of motion explain how everything in the explain how everything in the universe moves, from cars …universe moves, from cars …

……to colliding galaxies!to colliding galaxies!

Newton’s Law of GravitationNewton’s Law of Gravitation

After devising his three laws of motion, Newton After devising his three laws of motion, Newton became interested in studying the actual force became interested in studying the actual force that caused objects to fall.that caused objects to fall.

Newton realized that according to his laws of Newton realized that according to his laws of motion, some force must be keeping the moon motion, some force must be keeping the moon in orbit around the Earth, and the Earth in orbit in orbit around the Earth, and the Earth in orbit around the Sun.around the Sun.

In a flash of insight, Newton In a flash of insight, Newton hypothesized hypothesized that the force that held the moon in its orbit that the force that held the moon in its orbit was the was the same forcesame force that caused apples to fall that caused apples to fall to the ground, to the ground, gravitygravity..

Newton’s Law of GravitationNewton’s Law of Gravitation

Newton knew gravity could reach the Newton knew gravity could reach the tallest mountain, but could it reach all tallest mountain, but could it reach all the way to the moon?the way to the moon?

Newton made a few assumptions about Newton made a few assumptions about how gravity worked:how gravity worked: Gravity should get weaker the farther away Gravity should get weaker the farther away

you got from the Earth’s center.you got from the Earth’s center. That it got weaker at a rate that was That it got weaker at a rate that was

proportional to the proportional to the distance squareddistance squared from from the Earth’s center.the Earth’s center.

The Inverse Square LawThe Inverse Square Law Gravity’s strength getting weaker at a rate Gravity’s strength getting weaker at a rate

proportional to the distance squared is an proportional to the distance squared is an example of an example of an inverse square lawinverse square law..

At the Earth’s surface, you are 6,370 km from At the Earth’s surface, you are 6,370 km from the Earth’s center. At Earth’s surface, gravity the Earth’s center. At Earth’s surface, gravity accelerates you downward at 9.8 m/saccelerates you downward at 9.8 m/s22..

If you move to 6,370 km If you move to 6,370 km aboveabove Earth’s Earth’s surface, you have surface, you have doubleddoubled your distance your distance from the Earth’s center. So gravity should from the Earth’s center. So gravity should get weaker by a factor of 2get weaker by a factor of 222 = 4. At 6,370 = 4. At 6,370 km km aboveabove Earth’s surface, gravity should Earth’s surface, gravity should accelerate you downward ataccelerate you downward at

9.8 / 4 = 2.45 m/s9.8 / 4 = 2.45 m/s22

Can Gravity Hold The Moon In Can Gravity Hold The Moon In Orbit?Orbit?

Newton wondered: Was gravity strong enough Newton wondered: Was gravity strong enough to hold the moon in orbit?to hold the moon in orbit?

He calculated that the moon would have to be He calculated that the moon would have to be accelerated at a rate of 0.0027 m/saccelerated at a rate of 0.0027 m/s22 to stay in to stay in an orbit around the Earth.an orbit around the Earth.

It was already known that the moon is 60 It was already known that the moon is 60 times farther from the Earth’s center than the times farther from the Earth’s center than the Earth’s surface is.Earth’s surface is.

So the force of gravity at the moon should be So the force of gravity at the moon should be 606022 = 3600 times weaker than at the Earth’s = 3600 times weaker than at the Earth’s surface.surface.

9.8 / 3600 = 0.0027 m/s9.8 / 3600 = 0.0027 m/s22

So Newton determined that gravity So Newton determined that gravity was indeed what held the moon in was indeed what held the moon in

orbit around the Earth!orbit around the Earth!

Daily Grade 5 – Question 4Daily Grade 5 – Question 4

Why did Newton conclude that some Why did Newton conclude that some force had to pull the moon toward force had to pull the moon toward Earth?Earth?

A.A. The moon's motion is a straight line away The moon's motion is a straight line away from Earth.from Earth.

B.B. Some force causes the moon to change Some force causes the moon to change its phases.its phases.

C.C. The moon does not seem to go anywhere.The moon does not seem to go anywhere.D.D. The moon follows a curved path around The moon follows a curved path around

Earth.Earth.

GravityGravity

Newton also realized that, according to his Newton also realized that, according to his third law, gravity had to be third law, gravity had to be mutualmutual – if the – if the Earth pulls on the moon, the moon pulls on Earth pulls on the moon, the moon pulls on the Earth with an equal and opposite force.the Earth with an equal and opposite force.

Also, larger objects seem to be able to pull Also, larger objects seem to be able to pull with much more force: the Sun pulls on the with much more force: the Sun pulls on the Earth harder than Earth pulls on the Moon.Earth harder than Earth pulls on the Moon.

So gravity’s strength must also depend on So gravity’s strength must also depend on massmass!!

GravityGravity

If gravity is If gravity is mutualmutual, its strength must , its strength must depend on the masses of both objects.depend on the masses of both objects.

Gravity increases proportionally with Gravity increases proportionally with mass.mass.

Gravity decreases proportionally with Gravity decreases proportionally with distance squared.distance squared.

Led Newton to his famous equation for Led Newton to his famous equation for the the Law of Gravity:Law of Gravity:

F = GMm/rF = GMm/r22

The Universal Law of GravitationThe Universal Law of Gravitation

In this equation:In this equation:

F = GMm/rF = GMm/r22

M = the mass of the more massive object (kg).M = the mass of the more massive object (kg).

m = the mass of the less massive object (kg).m = the mass of the less massive object (kg).

r = the distance between the r = the distance between the centerscenters of each of each object (m)object (m)

G = the gravitational constant (6.67 × 10G = the gravitational constant (6.67 × 10-11-11))

F = the force with which gravity pulls on the two F = the force with which gravity pulls on the two objects (N).objects (N).

How To Use It?How To Use It?

1.1. Using your calculator, first multiply the Using your calculator, first multiply the masses of the two object together. Then masses of the two object together. Then multiply the answer by 6.67 × 10multiply the answer by 6.67 × 10-11-11. . Write down the resulting number.Write down the resulting number.

2.2. Next, use your xNext, use your x22 or x or xyy button to get the button to get the square of the distance between the square of the distance between the centers of the two objects.centers of the two objects.

3.3. Finally, take your result from 1 and Finally, take your result from 1 and divide it by your result from 2. That’s the divide it by your result from 2. That’s the force of gravity between the two objects.force of gravity between the two objects.

The Universal Law of GravitationThe Universal Law of Gravitation

Is the culmination of the Copernican Is the culmination of the Copernican revolutionrevolution

United terrestrial & celestial mechanicsUnited terrestrial & celestial mechanics Balancing the force (called “centripetal Balancing the force (called “centripetal

force”) necessary to keep an object in force”) necessary to keep an object in circular motion with the gravitational circular motion with the gravitational force = an expression equivalent to force = an expression equivalent to Kepler’s third lawKepler’s third law

Gravitation And OrbitsGravitation And Orbits

If an object moves fast enough, its path will If an object moves fast enough, its path will match the curvature of the Earth, and it match the curvature of the Earth, and it will never hit the ground - it goes into orbit. will never hit the ground - it goes into orbit.

Circular Circular orbital velocityorbital velocity for a low Earth orbit for a low Earth orbit is about 5 miles per second. is about 5 miles per second.

If the object's velocity is greater than 5 If the object's velocity is greater than 5 miles/sec but less than 7 miles/sec, its orbit miles/sec but less than 7 miles/sec, its orbit will be an ellipse. will be an ellipse.

Velocities greater than 7 miles/sec reach Velocities greater than 7 miles/sec reach escape velocityescape velocity, and the object moves in a , and the object moves in a curved path that does not return to Earth.curved path that does not return to Earth.

Orbital MotionOrbital MotionIn order to stay on a closed orbit, an object has to be within a certain range of velocities:

Too slow => Object falls back down to Earth

Too fast => Object escapes Earth’s gravity

Orbital MotionOrbital Motion

Geosynchronous Orbits

For Next TimeFor Next Time

Test on WednesdayTest on Wednesday

Read Units 22 and 28 for next MondayRead Units 22 and 28 for next Monday Students may also find the following Students may also find the following

sections useful:sections useful: Unit 21.1Unit 21.1 Unit 26.1Unit 26.1 Unit 27.2Unit 27.2 Unit 29.2Unit 29.2 Unit 30.1Unit 30.1