ScheduleSchedule

• Today: Gravity• Thursday: Light• Tuesday, Feb 5: More light• Thursday, Feb 7: Test 1

• Today: Gravity• Thursday: Light• Tuesday, Feb 5: More light• Thursday, Feb 7: Test 1

The Road to a Sun-Centered Solar System

The Road to a Sun-Centered Solar System

• Ptolemy (90-168)- Almagest published ~150

• Copernicus (1473-1543)- Published in 1544

• Tycho Brahe (1546-1601)- Never published

• Johannes Kepler (1571-1630)- Published his Laws of Motion starting in

1609

• Galileo (1564-1642)- Published “Dialogue of the Two Chief

World Systems” in 1632

• Ptolemy (90-168)- Almagest published ~150

• Copernicus (1473-1543)- Published in 1544

• Tycho Brahe (1546-1601)- Never published

• Johannes Kepler (1571-1630)- Published his Laws of Motion starting in

1609

• Galileo (1564-1642)- Published “Dialogue of the Two Chief

World Systems” in 1632

The Acceleration of Gravity (g)The Acceleration of Gravity (g)

• Galileo showed that g is the same for all falling objects, regardless of their mass.

• Galileo showed that g is the same for all falling objects, regardless of their mass.

NewtonNewton• Newton was born about a year after Galileo died

• He nailed the foundation of the physics of our ordinary reality. He dominated Physics until Einstein.

• He was a bit of a misanthrope.‒ Did poorly in school.

Reports described him as 'idle' and 'inattentive'.

‒ He went to college at Cambridge when he was 18.

‒ Even then he was thought of as an average student.

• Newton was born about a year after Galileo died

• He nailed the foundation of the physics of our ordinary reality. He dominated Physics until Einstein.

• He was a bit of a misanthrope.‒ Did poorly in school.

Reports described him as 'idle' and 'inattentive'.

‒ He went to college at Cambridge when he was 18.

‒ Even then he was thought of as an average student.

NewtonNewton• But at 20 (1663) math caught his fancy- In two years he ran through all of

humankind’s mathematical knowledge and then proceeded to significantly advance it….

• The plague closed the University between 1665-1667, sending Newton back home to a bit of enforced reflection.

• It was during this period that he puzzled-out most of his major contributions - Invention of calculus- Theory of gravity- The Laws of Motion- The inverse square law

• But at 20 (1663) math caught his fancy- In two years he ran through all of

humankind’s mathematical knowledge and then proceeded to significantly advance it….

• The plague closed the University between 1665-1667, sending Newton back home to a bit of enforced reflection.

• It was during this period that he puzzled-out most of his major contributions - Invention of calculus- Theory of gravity- The Laws of Motion- The inverse square law

NewtonNewton• At 27 he became the Lucasian Professor of Mathematics at Cambridge

• In later life he held a number of major positions- Member of Parliament- Master of the Mint- President of the Royal Society- The first scientist to be knighted

• He was still very much a misanthrope- His response to any criticism was a

bit extreme- He suffered two nervous breakdowns

• He could be a pretty nasty guy. - Take his dispute with Leibniz

• At 27 he became the Lucasian Professor of Mathematics at Cambridge

• In later life he held a number of major positions- Member of Parliament- Master of the Mint- President of the Royal Society- The first scientist to be knighted

• He was still very much a misanthrope- His response to any criticism was a

bit extreme- He suffered two nervous breakdowns

• He could be a pretty nasty guy. - Take his dispute with Leibniz

GravityGravity• Take a look around you….in our everyday

experience we see gravity acting on all objects.• Take a look around you….in our everyday

experience we see gravity acting on all objects.

• Newton made some simple observations based on his understanding of motion. - “A body remains stationary or moves in a

straight line unless a force acts on it”- If a pen drops out of your hand, there HAS TO

BE a force acting on that pen.

• Newton made some simple observations based on his understanding of motion. - “A body remains stationary or moves in a

straight line unless a force acts on it”- If a pen drops out of your hand, there HAS TO

BE a force acting on that pen.

• Newton watched the Moon orbiting the Earth.- It is in orbit- it is moving in (essentially) a

circle- Therefore…. force HAS TO

BE acting on it to deflect it from a straight line.

• If you know the force HAS TO EXIST, then you can calculate what its strength has to be….- About 1/3600 of the force of

gravity on the Earth’s surface.

- Other fact: Moon was about 60 times farther from the CENTER OF THE EARTH than the Earth’s surface

• Newton watched the Moon orbiting the Earth.- It is in orbit- it is moving in (essentially) a

circle- Therefore…. force HAS TO

BE acting on it to deflect it from a straight line.

• If you know the force HAS TO EXIST, then you can calculate what its strength has to be….- About 1/3600 of the force of

gravity on the Earth’s surface.

- Other fact: Moon was about 60 times farther from the CENTER OF THE EARTH than the Earth’s surface

• So the force on the Moon was 1/3600 as strong as the force acting on you at the surface of the Earth…..- He concluded that the force

of the Earth’s gravity decreases by 1/r2. The inverse square of distance

- That is how gravity (and other fundamental forces) work, their intensity decreases by the inverse square of distance.

• This is called the INVERSE SQUARE LAWINVERSE SQUARE LAW

• So the force on the Moon was 1/3600 as strong as the force acting on you at the surface of the Earth…..- He concluded that the force

of the Earth’s gravity decreases by 1/r2. The inverse square of distance

- That is how gravity (and other fundamental forces) work, their intensity decreases by the inverse square of distance.

• This is called the INVERSE SQUARE LAWINVERSE SQUARE LAW

How does this work?

How does this work?

• ALL matter produces a gravitation force!

• Why???

• The force changes by 1/r2

• The inverse square law applies to ALL Forces….gravity, magnetism, electrical fields, light….!

• ALL matter produces a gravitation force!

• Why???

• The force changes by 1/r2

• The inverse square law applies to ALL Forces….gravity, magnetism, electrical fields, light….!

Gravity

Light

• What is the difference in terms of gravity between these pictures?

• What is the difference in terms of gravity between these pictures?

GravityGravity

• Remember gravity is measured from the center of an object- We are 6378 km from

the center of the Earth- Space shuttle

astronauts in space are only 200 km farther away…..

- In inverse square terms that is 1.03 times

• Remember gravity is measured from the center of an object- We are 6378 km from

the center of the Earth- Space shuttle

astronauts in space are only 200 km farther away…..

- In inverse square terms that is 1.03 times

GravityGravity

• Work it out- If the distance is

1.03 times the distance at the Earth’s surface….

- R2 = 1.06- 1/R2 x G = 9.2 m/s2

- The force of gravity is only 6% less in low Earth orbit

• Work it out- If the distance is

1.03 times the distance at the Earth’s surface….

- R2 = 1.06- 1/R2 x G = 9.2 m/s2

- The force of gravity is only 6% less in low Earth orbit

• The reason astronauts are “weightless” in orbit is because they are in FREEFALL!

• The reason astronauts are “weightless” in orbit is because they are in FREEFALL!

Remember: We live on a sphereRemember: We live on a sphere

• When you drop something it heads toward the center of the Earth

• IF you put a bit of horizontal velocity on that something….

• When you drop something it heads toward the center of the Earth

• IF you put a bit of horizontal velocity on that something….

Newton’s three laws of motionNewton’s three laws of motionNewton’s first law of motion: An object moves

at constant velocity unless a net force acts to change its speed or direction.

Newton’s first law of motion: An object moves at constant velocity unless a net force acts to change its speed or direction.

Newton’s second law of motion:Newton’s second law of motion:

Force = mass accelerationForce = mass acceleration

Newton’s third law of motion:

Newton’s third law of motion:

For every force, there is always an equal and opposite reaction force.

For every force, there is always an equal and opposite reaction force.

How do gravity and energy together explain orbits?

How do gravity and energy together explain orbits?

• Orbits cannot change spontaneously.• An object’s orbit can only change if it

somehow gains or loses orbital energy =

kinetic energy + gravitational potential energy

(due to orbit).

• Orbits cannot change spontaneously.• An object’s orbit can only change if it

somehow gains or loses orbital energy =

kinetic energy + gravitational potential energy

(due to orbit).

So what can make an object gain or lose orbital energy?

• Friction or atmospheric drag

• A gravitational encounter.

• Rockets….

So what can make an object gain or lose orbital energy?

• Friction or atmospheric drag

• A gravitational encounter.

• Rockets….

Center of massCenter of mass

• Objects attracted by gravity orbit around their center of mass

• Objects attracted by gravity orbit around their center of mass

Why Does Gravity Work?Why Does Gravity Work?• Einstein’s Relativity• Quantum Gravity (String theory, Loop quantum gravity,

Causal Dynamical Triangulation……and many more)• Brans–Dicke theory of gravity• Induced gravity• In the modified Newtonian dynamics (MOND)• The self-creation cosmology theory of gravity• Nonsymmetric gravitational theory (NGT)• Tensor–vector–scalar gravity (TeVeS)• Gravity as an entropic force• Superfluid vacuum theory

• Einstein’s Relativity• Quantum Gravity (String theory, Loop quantum gravity,

Causal Dynamical Triangulation……and many more)• Brans–Dicke theory of gravity• Induced gravity• In the modified Newtonian dynamics (MOND)• The self-creation cosmology theory of gravity• Nonsymmetric gravitational theory (NGT)• Tensor–vector–scalar gravity (TeVeS)• Gravity as an entropic force• Superfluid vacuum theory

Why are there Tides?Why are there Tides?• Take the Bay of Fundy in Nova

Scotia- Tides there can range 50 feet

between high and low• High (and low) tides happen

basically twice a day

• Take the Bay of Fundy in Nova Scotia- Tides there can range 50 feet

between high and low• High (and low) tides happen

basically twice a day

Tidal Bores in the Severn EstuaryTidal Bores in the Severn Estuary

TidesTides

Gravitational force decreases with (distance)2

The Moon’s pull on Earth is strongest on the side facing the Moon, and weakest on the opposite side.

The Earth gets stretched along the Earth-Moon line. The oceans rise relative to land at these points.

Gravitational force decreases with (distance)2

The Moon’s pull on Earth is strongest on the side facing the Moon, and weakest on the opposite side.

The Earth gets stretched along the Earth-Moon line. The oceans rise relative to land at these points.

TidesTides

• Every place on Earth passes through high tides twice per day as the Earth rotates.

• High tides occur every 12 hours 25minutes• remember, the Moon moves!

• The Sun’s tidal effect on Earth is not as strong. Remember the inverse square law….the Sun is a long way away.

• Every place on Earth passes through high tides twice per day as the Earth rotates.

• High tides occur every 12 hours 25minutes• remember, the Moon moves!

• The Sun’s tidal effect on Earth is not as strong. Remember the inverse square law….the Sun is a long way away.

TidesTides

• Tides are strongest when the Sun & Moon pull in the same direction (new & full phases)– high tide is higher than usual

(spring)

• Weakest when the Sun & Moon pull at right angles (first & last quarter phases)– high tide is lower than usual (neap)

Spring and Neap Tides

Spring and Neap Tides

Tidal FrictionTidal 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.- The Moon is moving away from

Earth at of 38 mm per year!

• 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.- The Moon is moving away from

Earth at of 38 mm per year!

Tidal FrictionTidal Friction

- It adds up! 4 billion years ago 1 day may have only been 5 or 6 hours long.

- The moon may have been 1/10 the distance: 22 Earth radii away instead of 221

- How big would the tides be if the Moon was 110 Earth radii away?

- It adds up! 4 billion years ago 1 day may have only been 5 or 6 hours long.

- The moon may have been 1/10 the distance: 22 Earth radii away instead of 221

- How big would the tides be if the Moon was 110 Earth radii away?