Transcript 8._energy_and_Gravity

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 =
• A small amount of mass
can release a great deal of
energy
• Concentrated energy can
spontaneously turn into
particles (for example, in
particle accelerators)
2
mc
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?
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?
More stored gravitational energy;
Less kinetic energy
• Total orbital
energy
(gravitational +
kinetic) stays
constant if there
is no external
force
• Orbits cannot
Less stored gravitational energy; change
More kinetic energy
spontaneously.
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
2
2
3
4p
4p
a
2
3
p =
a OR M 1 +M 2=
G M 1 +M 2
G p2
p = orbital period
a=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!)


This technique is used to calculate the mass
of distant objects which we cannot measure,
by using motions that we can measure.
The mass of the Sun and all the planets was
derived this way. Binary stars and extra-solar
planet properties are derivied this way.
highlighted.
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
Low Tide
High
Tide
High
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
Low Tide
High
Tide
High
Tide
Low Tide
Tidal range of 2-4m,
(6-12 feet)
Bay of Fundy, Nova
Scotia
Tides
of
40-52
feet
Tides and Phases
Size 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
The tidal bulge points toward the Moon and drags
on the Earth as Earth rotates under it.
As a Result:
• The Earth’s rotation slows down (days get
longer)
• The Moon accelerates (it moves further away
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)