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Conservation of Momentum

•  Newton’s first law •  The total momentum

of interacting objects cannot change unless an external force is acting on them

•  Interacting objects exchange momentum through equal and opposite forces

Conservation of Angular Momentum

•  The angular momentum of an object cannot change unless an external twisting force (torque) is acting on it

•  Earth experiences no twisting force as it orbits the Sun, so its rotation and orbit will continue indefinitely

angular momentum = mass x velocity x radius

Conservation of Angular Momentum

•  Angular momentum = m × v × r •  Orbital – Kepler’s 2nd law

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Conservation of Energy

•  Energy can be neither created nor destroyed. •  It can change form or be exchanged between

objects. •  The total energy content of the Universe was

determined in the Big Bang and remains the same today.

Where do objects get their energy?

•  Energy makes matter move.

•  Energy is conserved, but it can: – Transfer from one object to another – Change in form

Basic Types of Energy

•  Kinetic (motion) •  Radiative (light) •  Stored or potential

Energy can change type but cannot be destroyed.

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Thermal Energy: the collective kinetic energy of many particles

(for example, in a rock, in air, in water) Thermal energy is related to temperature but it is NOT the same. Temperature is the average kinetic energy of the many particles in a substance.

Temperature Scales

Thermal energy is a measure of the total kinetic energy of all the particles in a substance. It therefore depends both on temperature AND density Example:

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Gravitational Potential Energy

•  On Earth, depends on: –  object’s mass (m) –  strength of gravity (g) –  distance object could

potentially fall

Gravitational Potential Energy •  In space, an object or gas cloud has more gravitational

energy when it is spread out than when it contracts. ⇒ A contracting cloud converts gravitational potential

energy to thermal energy.

Mass-Energy •  Mass itself is a form of potential energy

•  A small amount of mass can release a great deal of energy •  Concentrated energy can spontaneously turn into particles (for example, in particle accelerators)

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A force must pull the Moon toward Earth’s center

•  According to Newton’s 1st Law, the Moon should follow a straight line and leave Earth

•  But, for every 1020m is moves eastward, it falls 1.6mm toward Earth

•  So, there must be a force acting on it The Moon can orbit the Earth

only if a force is acting on it

Newton’s Great Insight

•  The same force makes things fall down on Earth and keeps the planets in their orbits

•  GRAVITY

Gravity makes apples fall from trees and keeps the Moon orbiting the Earth

The Universal Law of Gravitation •  Every mass attracts every other mass •  Attraction is directly proportional to the product

of their masses •  Attraction is inversely proportional to the square

of the distance between their centers

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The Universal Law of Gravitation

Strength of gravity vs. distance

What does it mean to be “inversely

proportional to the square of the

distance between their centers”?

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Newton’s Law and Gravitation

•  Projectile motion

Force

Velocity

Acceleration

Imagine that you throw a ball directly upward. Which of the following statements best describes how Newton’s second law accounts for the motion of the ball when it reaches its maximum height? a) The ball has a velocity that is zero and an

acceleration that is zero. b) The ball has a velocity that is upward and an

acceleration that is downward. c) The ball has a net force that is downward and a

velocity that is downward. d) The ball has a net force that is downward and an

acceleration of zero. e) The ball has a net force that is downward and an

acceleration that is downward.

In-class Activities: Gravity and Newton’s Laws

•  Work with a partner! •  Read the instructions and questions carefully. •  Discuss the concepts and your answers with one

another. Take time to understand it now!!!! •  Come to a consensus answer you both agree on. •  If you get stuck or are not sure of your answer, ask

another group. •  If you get really stuck or don’t understand what the

question is asking, ask me.

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Note that position B is at the midpoint between the Moon and Earth.

At which location would the net force be least?

Earth A B

Moon C

Note that position B is at the midpoint between the Moon and Earth.

If a spaceship is traveling from Earth to the Moon,

At which position would the acceleration of the ship be greatest?

At which position would the acceleration of the ship be least?

Earth A B

Moon C

Note that position #2 is at the midpoint between the Moon and Earth.

If a spaceship was coasting very fast toward the Moon when at position #2, which direction would

the acceleration of the ship point?

A. toward the moon B. Toward Earth C. the acceleration would be zero

Earth 1 2

Moon 3

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Which of the following correctly describes how the gravitational force exerted by asteroid A on its “partner” asteroid compares to the gravitational force exerted by asteroid B on its “partner” asteroid.

a) A > B b) B > A c) A = B

Acceleration of Gravity

•  The acceleration of a falling object •  g = 9.8 m/s on earth

How is mass different from weight?

•  Mass – the amount of matter in an object •  Weight – the force that acts upon an object

You are weightless in free-fall!

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In which scenario is the weight of the person the greatest?

a)  Elevator stationary b)  Elevator moving at a constant velocity c)  Elevator accelerating upward d)  Elevator accelerating downward e)  Elevator in free-fall

Mass vs. Weight

On Earth, 1 kg of bananas weighs 9.8

Newtons of force

On the Moon, 1 kg of bananas weighs 1.7

Newtons of force

On the Moon:

A.  My weight is the same, my mass is less. B.  My weight is less, my mass is the same. C.  My weight is more, my mass is the same. D.  My weight is more, my mass is less.

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Orbiting Bodies are Falling Bodies

•  An object orbiting Earth is actually falling (being accelerated) toward Earth’s center

•  An object in a stable orbit continuously misses Earth because of its orbital velocity

•  There is gravity in space •  Weightlessness is due to a constant state of free-fall

Why are astronauts weightless in space?

http://www.youtube.com/watch?v=QnB6uYNPia0

Astronauts feel weightless because they are in free-fall!

•  Remember, an astronaut is “falling around” the Earth

•  So is the spaceship! •  Both are in free-fall

together •  No force holding the

astronaut to the wall of the spaceship

•  So, they feel weightless! Having fun in Zero-G

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Extending Kepler’s Laws with Newton’s Law

•  Ellipses are not the only orbital paths

•  Orbits can be: –  Closed (ellipses or circles) –  Open (parabolas or

hyperbolas) •  NASA uses unbound

orbits to “slingshot” spacecraft to the outer planets

Center of Mass •  Objects orbiting each

other actually revolve around their mutual center of mass

•  Objects of equal mass orbit a point halfway between them

•  Objects of unequal mass orbit a point closer to larger object

Newton’s Version of Kepler’s 3rd Law

•  Remember Kepler's 3rd Law: •  Newton’s found a general version with his Law of

Gravity

•  (P in years, a in AUs, M in solar masses) •  Kepler's Law works because the mass of the Sun

is much larger than the mass of any planet –  MEarth = 0.000003 MSun, MJup = 0.00096 MSun –  MSun + MPlanet ≈ MSun = 1

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Use Kepler’s 3rd Law (modified) to find mass!

•  If we know a moon’s orbit around its planet, we can find the planet’s mass!

How do gravity and energy together allow us to understand orbits?

•  Total orbital energy (gravitational + kinetic) stays constant if there is no external force

•  Orbits cannot change spontaneously.

More gravitational energy; Less kinetic energy

Less gravitational energy; More kinetic energy

Total orbital energy stays constant

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

•  Friction or atmospheric drag

•  A gravitational encounter.

Changing an Orbit

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Escape Velocity •  If you want to leave

Earth never to return, you must give your spaceship a high enough velocity so it will follow an open orbit

•  This velocity is called the escape velocity

At Earth’s surface, the escape velocity is 11 km/s

(40,000 km/hr)

A Triumph of Newton’s Laws •  Sir Edmund Halley used

Newton’s Laws to predict that a comet observed in 1682 would return in 1758

•  We call the comet Halley’s Comet today

•  Has a 76 year orbit •  Last around in 1986,

next appearance 2061!

Halley’s Comet, 1986

Another Triumph - The Discovery of Neptune

•  In 1781, Uranus was discovered by chance, by William & Caroline Herschel

•  Irregularities in Uranus’ orbit could not all be accounted for by gravitational “nudges” from Jupiter & Saturn

•  Two astronomers, Adams & Le Verrier, each used Newton’s laws to predict the existence of a new planet

•  Neptune was found on Sept. 23rd, 1846 by Galle in Berlin

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Tides

•  Everywhere along the seacoast, the oceans periodically rise and fall

•  Let’s explore what causes tides and what effects they have on the Earth

How does the Moon’s gravity cause tides?

•  Moon’s gravity pulls more on near side of Earth than on far side

•  Difference in Moon’s pull from one side of Earth to the other creates tidal bulges

Not All Tides Are Equal

Neap Tide Neap

Tide Neap Tide

Spring Tide

Spring Tide

Spring Tide

1st Quarter

Moon Full

Moon

3rd Quarter

Moon

New Moon

1st Quarter

Moon

Full Moon

High Tide

Low Tide

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Tides and Phases

Size of tides depends on phase of Moon

Spring Tides

•  Spring tides occur when the Sun and Moon are aligned

•  Both new moon and full moon!

•  Sun's tides and Moon's tides combine to make extreme tides

Neap Tides •  Neap tides occur

when the Sun and Moon are at a right angle

•  1st and 3rd quarter moon phases

•  Sun's tides partially cancel the Moon's tides

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Tides are a drag...

Gravity of the bulge pulls the Moon ahead, increasing the size of its orbit!

The Moon’s rotation: Tidally locked

•  Tidal forces on the Moon from the Earth have also slowed the Moon’s rotation

•  Lunar day equals a lunar orbit (about 1 month)!

•  We call this tidal locking