Where do objects get their energy?

• Energy makes matter move.

• Energy is always 'conserved'

Conservation of Energy

• Energy can neither be created nor destroyed

• The total energy content of the universe was determined at the Big Bang and remains constant to this day

• Energy can change form or can transfer between objects

Basic Types of Energy

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

Energy can change type but cannot be destroyed.

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

E = mcE = mc22

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

Gravitational Potential Energy(a form of Stored 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.

What have we learned?• Where do objects get their energy?

– Conservation of energy: energy cannot be created or destroyed but only transformed from one type to another.

– Energy comes in three basic types: kinetic, potential, radiative.

– One type of kinetic energy is Thermal Energy (the movement of particles)

– One type of potential (or stored) energy is Gravitational Energy

The Universal Law of Gravitation

Our goals for learning:• What determines the strength of gravity?

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

•How does Newton’s law of gravity extend Kepler’s laws?

•Why do all objects fall at the same rate?

What determines the strength of gravity? 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.

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 stored gravitational energy;Less kinetic energy

Less stored gravitational energy;More kinetic energy

Total orbital energy stays constant

Center of Mass

• Orbiting objects actually orbit around a common center of mass.

• The location of that center depends on where most of the mass is located.

How does Newton’s law of gravity extend Kepler’s laws?

Newton's relationship between the orbital period and average orbital distance of a system tells us the total mass of the system.

Examples:• Earth’s orbital period (1 year) and average distance (1 AU) tell us the Sun’s mass.• Orbital period and distance of a satellite from Earth tell us Earth’s mass.• Orbital period and distance of a moon of Jupiter tell us Jupiter’s mass.

Newton’s Version of Kepler’s Third Law

p = orbital perioda=average orbital distance (between centers)(M1 + M2) = sum of object masses

The result:• The masses of any orbiting bodies can be

calculated from the size or period of their orbit (measureable quantities!)

p2=4p2

GM1+M2a3OR M1+M2=

4p2

Ga3

p2

highlighted.

l This technique is used to calculate the mass of distant objects which we cannot measure, by using motions that we can measure.

l The mass of the Sun and all the planets was derived this way. Binary stars and extra-solar planet properties are derivied this way.

What have we learned?• What determines the strength of gravity?

– Directly proportional to the product of the masses (M x m)

– Inversely proportional to the square of the separation

• How does Newton’s law of gravity allow us to extend Kepler’s laws?– Applies to other objects, not just planets.– Can be used to measure mass of orbiting

systems.

Tides and Gravity

Our goals for learning:•How does gravity cause tides?

•How does the competing gravity from the Sun and the Moon affect tide height?

•How does the Moon's gravity affect the Earth's rotation?

Gravity Force of the Moon on the Earth

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

• The difference in the Moon’s gravitational pull, stretches Earth (called the 'tidal force')

• Similar to pulling on 1 end of a rubberband

Tidal Bulge of Earth

High Tide

High Tide

Low Tide

Low Tide

High Tide

High Tide

Low Tide

Low Tide

•Earth rotates under the bulge•Your location moves from under the high water, into the low water and out again.•You see two tides/day

Tidal range of 2-4m, (6-12 feet)

Bay of Fundy, Nova Scotia

Tides of

40-52 feet

Tides and PhasesSize of tides depends on the phase of Moon

Sun & Moon’s gravities acting together = Large tides

Sun & Moon’s gravities acting at odds = weakened tides

Tidal Friction

As a Result:

• The Earth’s rotation slows down (days get longer)

• The Moon accelerates (it moves further away from us)

The tidal bulge points toward the Moon and drags on the Earth as Earth rotates under it.

What have we learned?• How does gravity cause tides?

– Moon’s gravity stretches Earth and its oceans• How does the competing gravity from the Sun

and the Moon affect tide height?– When the Sun and Moon are along on the

same line their gravities combine and tides are higher.

• How does the Moon's gravity affect the Earth's rotation?– The Moon pulls the tidal bulge back, which

slows the Earth (called tidal friction)