How did Newton change our view of the Universe?

How did Newton change our view of the Universe?
• Discovered laws of motion
and gravity
• Studied the nature of light.
• Developed the first reflecting
telescope
• Invented calculus
Sir Isaac Newton
(1642-1727)
“If I have seen farther than
others, it is because I have
stood on the shoulders of
giants.”
How did Newton change our view of the Universe?
• Aristotle: the Earth and the
heavens are distinct.
• Newton: realized the same
physical laws that operate
on Earth also operate in the
heavens
⇒ one universe
Sir Isaac Newton
(1642-1727)
• 1687: Principia published.
Contained the laws of motion & gravity.
Likely the most influential physics book
ever written.
Newton’s first law of motion:
An object moves at constant velocity unless a
net force acts to change its speed or direction.
INTERTIA
• An object will move forever in a straight line unless an
external force acts on it.
– Astronomical objects do not need any fuel to travel
through the Universe.
– Spacecraft continually travel through outer space
without any fuel.
• Aristotle asserted that the natural state of an object
was at rest. This was wrong. In fact, the natural state
is to maintain its motion.
Newton’s second law of motion:
When a force acts on an object, it produces an
acceleration equal to the force divided
by the mass, or Force = mass x acceleration:
F = ma
m = mass of the object
a = acceleration
F = force
•
For the same amount of force, you produce less acceleration for a more
massive object. (You can throw a wad of paper farther than a rock.)
•
For an object of a given mass, the larger force produces more
acceleration. (The Sun has more influence on comets than the Earth.)
Newton’s third law of motion:
For every force, there is always an
equal and opposite reaction force.
• Examples
– Rocket launches: to balance the force of the gas
leaving the back of the rocket, an equal and opposite
force propels the rocket forward.
– Recoil from a gun.
– If you were floating motionless in outer space, you
could propel yourself by throwing something in the
opposite direction.
QUESTION: A compact car and a Mack truck have a headon collision. Are the following true or false? (Think about a
limiting case – what about a truck and a flying insect?)
1. The force of the car on the truck is equal and
opposite to the force of the truck on the car.
2. The momentum transferred from the truck to
the car is equal and opposite to the momentum
transferred from the car to the truck.
3. The change of velocity of the car is the same
as the change of velocity of the truck.
QUESTION: A compact car and a Mack truck have a headon collision. Are the following true or false? (Think about a
limiting case – what about a truck and a flying insect?)
1. The force of the car on the truck is equal and
opposite to the force of the truck on the car. TRUE
2. The momentum transferred from the truck to
the car is equal and opposite to the momentum
transferred from the car to the truck. TRUE
3. The change of velocity of the car is the same
as the change of velocity of the truck. FALSE
Conservation Laws
Important conservation laws in physics:
• Conservation of momentum (linear momentum and
angular momentum)
• Conservation of energy
Fundamental laws of nature &
critical to understanding how the Universe works!
Conservation Laws
• The conservation laws are embodied in Newton’s
laws, but offer a different and sometimes more
powerful way to consider motion of objects.
• Conservation of momentum is reflected in
Newton’s Second & Third Laws.
• For example, when 2 objects collide:
• Object 1 exerts a force Object 2 and changes its momentum
(Newton’s Second Law).
• However, Object 2 exerts an equal and opposite change in
the momentum of Object 1 (Newton’s Third Law).
• Overall, the total momentum of the 2 objects is unchanged.
•
Linear momentum =
an object’s tendency to move in a straight line
linear momentum = mass x velocity
p = mv
•
Angular momentum =
an object’s tendency to spin
angular momentum = mass x velocity x radius
L = mvr
where “radius” is object’s distance from its center of rotation.
Conservation of Angular Momentum
• Objects rotate
faster as they
“shrink” in
radius.
• Important effect
in the formation
of planets, stars
and galaxies.
What keeps a planet rotating and orbiting the Sun?
--> Conservation of Angular Momentum
Explains Kepler’s Second Law
(equal areas in equal times: object move faster when closer to the Sun)
Conservation of Energy
• Energy = the ability to move matter.
• Energy is conserved, but it can:
– Transfer from one object to another
– Change in form
• All actions in the universe involve
transfers or changes of energy.
Basic Types of Energy
1. Kinetic (motion)
2. Radiative (light)
3. Stored or potential
Energy can be changed
from one form to another,
but it cannot be destroyed.
Joule (J) = metric unit of energy
(1 food Calorie ≈ 4200 Joules)
Thermal energy:
the collective kinetic energy of many particles
(for example, in a rock, in air, in water)
• Temperature is the average kinetic energy of the many
particles in a substance.
• Thermal energy is related to temperature but NOT the same.
Cold
Hot
Thermal energy:
the collective kinetic energy of many particles
(for example, in a rock, in air, in water)
• 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.
Which one would you
stick your hand in?
Different temperature scales
gravitational potential energy:
the stored (untapped) kinetic energy of an
object under the influence of gravity
• Depends on:
– Object’s mass (m)
– Strength of gravity (g)
– Height that an
object could
potentially fall (h)
gravitational potential energy:
the stored (untapped) kinetic energy of an
object under the influence of gravity
•
In space, an object or
gas cloud has more
gravitational potential
energy when it is
spread out than when it
contracts.
•
A contracting gas cloud
converts gravitational
potential energy into
thermal energy.
Mass-energy potential energy:
mass itself is a form of potential energy
E = mc2
•
A small amount of mass can
release a great deal of energy.
– One megaton H-bomb gets its
energy by converting about 0.1 kg
(3 oz) of mass into energy.
• Concentrated energy can
spontaneously turn into
particles (e.g. the Big Bang).
Recap: 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.
4.4 The Force of Gravity
• 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?
Newton: Universal Law of Gravitation
1.
2.
3.
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.
Fg = G M1M2 / d2
M
M
M
d
d
M
Force, F
2M
Force, 2F
2d
M
Force, 1/4F
QUESTION: Given two planets, if the mass
of one planet doubles, then the gravitational
attraction between them becomes:
a.
b.
c.
d.
2x as strong
4x as strong
1/2 as strong
1/4 as strong
QUESTION: Given two planets, if the mass
of one planet doubles, then the gravitational
attraction between them becomes:
a.
b.
c.
d.
2x as strong
4x as strong
1/2 as strong
1/4 as strong
QUESTION: If the distance between two
planets doubles, the gravitational attraction
between them becomes:
a.
b.
c.
d.
2x as strong
4x as strong
1/2 as strong
1/4 as strong
QUESTION: If the distance between two
planets doubles, the gravitational attraction
between them becomes:
a.
b.
c.
d.
2x as strong
4x as strong
1/2 as strong
1/4 as strong
QUESTION: Given two planets, if the
masses of both planets are doubled, then
the gravitational attraction between them
becomes:
a.
b.
c.
d.
2x as strong
4x as strong
1/2 as strong
1/4 as strong
QUESTION: Given two planets, if the mass
of both planets are doubled, then the
gravitational attraction between them
becomes:
a.
b.
c.
d.
2x as strong
4x as strong
1/2 as strong
1/4 as strong
Kepler’s Laws of Planetary Motion
1. The orbit of each planet is an ellipse with
the Sun at one focus.
2. As a planet orbits, it sweeps out equal areas
in equal time.
3. More distant planets orbit at slower speeds:
P2 = a3 (with P in years and a in AU)
•
•
However, no explanation of WHY these laws were true.
They result from Universal Law of Gravitation
+ Conservation of Energy
+ Conservation of Angular Momentum
Newton’s law of gravity extends
Kepler’s laws
• Kepler’s first two laws
apply to all orbiting
objects, not just planets.
• Newton showed that
ellipses are not the only
types of orbits. Orbits can
be either:
– bound (ellipses)
– unbound
• parabola
• hyperbola
Newton’s law of gravity extends
Kepler’s laws
• Newton’s version of Kepler’s Third Law:
p2 =
⎛
⎞
2
⎜ 4π ⎟
⎜
⎟
⎜ G ⎟
⎜
⎟
⎝
⎠
3
a
(M +M )
1
2
p = orbital period
a = average orbital distance (between centers of objects)
(M1 + M2) = sum of object masses
(4π/G) = numerical constant
Newton’s law of gravity extends
Kepler’s laws
• Newton’s version of Kepler’s Third Law:
p2 =
⎛
⎞
2
⎜ 4π ⎟
⎜
⎟
⎜ G ⎟
⎜
⎟
⎝
⎠
3
a
(M +M )
1
2
p = orbital period
a = average orbital distance (between centers of objects)
(M1 + M2) = sum of object masses
(4π/G) = numerical constant
• VERY POWERFUL: If a small object orbits a larger one, by
measuring the orbiting object’s orbital period AND average
orbital distance, can find mass of the larger object.
Newton’s law of gravity extends
Kepler’s laws
• Newton’s version of Kepler’s Third Law:
p2 =
⎛
⎞
2
⎜ 4π ⎟
⎜
⎟
⎜ G ⎟
⎜
⎟
⎝
⎠
3
a
(M +M )
1
2
• VERY POWERFUL: If a small object orbits a larger one, by
measuring the orbiting object’s orbital period AND average
orbital distance, can find the mass of the larger object.
– Calculate the mass of Sun from Earth’s orbital period (1 year) and average
distance (1 AU).
– Calculate mass of Earth from orbital period and distance of a satellite.
– Calculate mass of Jupiter from orbital period and distance of one of its
moons.
Energy + gravity explains orbital motion
• An orbiting object has 2 forms of energy:
orbital energy = kinetic energy +
gravitational potential energy
Energy + gravity explains orbital motion
• An orbiting object has 2 forms of energy:
orbital energy = kinetic energy +
gravitational potential energy
• An orbit cannot change spontaneously, because
energy must be conserved.
• Hence, an object must gain or lose energy for
its orbit to change.
– Friction or atmospheric drag.
– Propulsion.
– Gravitational encounter.
Energy + gravity explains orbital motion
• If an object gains
enough orbital
energy, it can
escape: changes
from a bound to
unbound orbit.
• Escape velocity
from Earth
≈ 11 km/s from
sea level (about
40,000 km/hr),
independent of an
object’s mass.
How does gravity cause tides?
• Gravitational force depends on (distance)2,
so Moon’s pull on the Earth is strongest on the side
facing the Moon, weakest on the opposite side.
• There are 2 tides each day.
• Tides affect both land and water.
Tides vary with the
phase of the Moon
• Spring & neap tides.
• Tide due to the Sun about
1/3 as strong as Moon’s
tides.
Why does the Moon always show the
same face to Earth?
• Synchronous rotation = the Moon rotates in
the same amount of time that it orbits.
• WHY? Tidal forces.
Tidal friction caused Moon’s synchronous rotation
• Tidal friction due to the Moon slows Earth’s rotation.
• Earth’s lost angular momentum is transferred to the Moon,
leading to an increased orbital distance.
• Likewise, Moon once orbited faster. Tidal friction due to the
Earth caused it to “lock” in synchronous rotation.