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)