Download Astro 110-01 Lecture 11 Newton`s laws

Astro 110-01 Lecture 11
Newton’s laws
Twin Sungrazing
comets
11/02/09
Habbal Astro110-01 Lecture 11
http://umbra.nascom.nasa.gov/comets/movies/SOHO_LASCO_C2.mpg
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Understanding Newton’s 3rd law
Weight = force that acts upon an object due to acceleration of gravity
Let R = reaction force = - ma (a= acceleration of elevator)
F = force on scale inside elevator
F = mg + R
F(elev) = ma
F = mg
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R=0
R = ma
R = -ma
R = -mg
F = mg
F = mg + ma
F = mg - ma
F = mg – mg = 0
Habbal Astro110-01 Lecture 11
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Conservation Laws in Astronomy
[Section 4.3]
Our goals for learning:
• What keeps a planet rotating and
orbiting the Sun?
• Where do objects get their energy?
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1. Conservation of Momentum:
Linear momentum
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.
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1. Conservation of Momentum:
Linear momentum (cont’d)
• Newton’s 2nd law:
– Object 1 exerts a force that will change the
momentum of object 2
• Newton’s 3rd law:
– Object 2 exerts an equal and opposite force on
object 1
momentum(1) = - momentum(2)
Total momentum of colliding objects is conserved
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Conservation of Angular Momentum
m x v x r = constant
or What keeps a planet rotating and
orbiting the Sun?
r greater so
v is smaller
r smaller so
v is greater
v = velocity v
r = average distance from the Sun
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Angular momentum conservation also explains why objects
rotate faster as they shrink in radius
Extending arms means
larger radius, so smaller
velocity of rotation
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Habbal Astro110-01 Lecture 11
Bringing arms in reduces
the radius, so increases
rotational velocity
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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 rate and orbit must stay about the
same
– But Earth is very gradually transferring some of its rotational
angular momentum to the Moon, and is gradually slowing
down
• Clouds of gas, spinning disks orbiting young stars:
They will start to spin faster as gravity makes them
shrink in size
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Habbal Astro110-01 Lecture 11
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2. Conservation of Energy
• Energy cannot appear out of nowhere or
disappear into nothingness.
• Objects can gain or lose energy only by
exchanging energy with other objects
– All actions in the universe involve exchanges of
energy or the conversion of energy from one form
to another
• The total energy content of the universe was
determined in the Big Bang and remains the
same today.
 Energy can change type but cannot be destroyed.
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Basic Types of Energy
• Kinetic (motion):
– Moving objects
– Thermal energy
• Radiative energy:
– carried by light
• Potential or Stored
energy:
– Gravitational potential
energy
– Mass energy
– Chemical energy
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Thermal Energy, a form of Kinetic
Energy
the collective/total kinetic energy of many particles
moving randomly within a substance, like a rock,
the air or the gas within a distant star
Thermal energy is related to temperature but it is NOT the
same.
Temperature is a measure of the average kinetic energy of
the many particles in a substance.
 particles, on
average have
a higher kinetic
energy, move
faster
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Thermal energy is a measure of the total kinetic energy of all
the particles in a substance.
 It therefore depends on both temperature AND density.
But water in the
pot contains more
thermal energy
because of its
much higher
density
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Air in oven at
400 F is hotter
than the boiling
water (212 F)
in the pot
Habbal Astro110-01 Lecture 11
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Common Temperature Scales

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Absolute zero Kelvin is when all motion stops
Habbal Astro110-01 Lecture 11
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Energy due to movement of
object
• Example of kinetic energy due to motion
Ek = ½ m v2
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Exercise
Compare kinetic energy of a car traveling
at 100 km/hr with one traveling at 50
km/hr
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Gravitational Potential Energy
Eg = m × g × h
• On Earth, it depends
on…
— an object’s mass (m).
— the strength of gravity
(g).
— the distance an object
could potentially fall.
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Gravitational Potential Energy
Eg = m × g × h
• In space, an object or gas cloud has more gravitational
potential energy when it is spread out than when it
contracts.
 A contracting cloud converts gravitational potential energy
to thermal energy.
o
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h
Habbal Astro110-01 Lecture 11
h’
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Mass-Energy
• Mass itself is a form of potential energy.
E =
2
mc
• 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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Energy comparisons
Energy of sunlight at Earth
(per square meter per second)
Energy from metabolism of 1 candy bar
Energy needed to walk for 1 hour
Daily food energy need of average adult
Energy released by fission of 1 kg of U235
Energy released by 1 megaton H-bomb
Energy released by major (magnitude 8) earthquake
Energy released by a supernova
1046
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Habbal Astro110-01 Lecture 11
1.3 x 103 joules
1 x 106
1 x 106
1 x 107
5.6 x 1013
5 x 1015
2.5 1016
1044 -
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What have we learned?
• What keeps a planet rotating and orbiting the
Sun?
— Conservation of angular momentum
• 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.
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The Force of Gravity
[Section 4.4 ]
Our goals for learning:
• What determines the strength of
gravity?
• How does Newton’s law of gravity
extend Kepler’s laws?
• How do gravity and energy together
allow us to understand orbits?
• How does gravity cause tides?
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What determines the strength of gravity?
The Universal Law of Gravitation:
1. Every mass attracts every other mass.
2. Attraction is directly proportional to the product
of their masses.
3. Attraction is inversely proportional to the
square of the distance between their centers.
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Exercise
• Compare the strength of gravity
between Earth and Sun to that between
Earth and Moon
M(Sun) = 1.99 1030 kg
M(Moon) = 7.35 1022 kg
d(Earth-Sun) = 1.5x108 km
d(Earth-Moon) = 3.84 105 km
G = 6.67 10-11 m3/kg s2
179
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g = 9.8 m/s2
http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html
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