Chapter 4
Making Sense of the Universe Understanding
Motion, Energy, and Gravity
4.1 Describing Motion: Everyday
Life Examples
How do we describe motion?
How is mass different from weight?
How do we describe motion?
• Speed: Rate at which object moves
•speed of 10 meters/second = 10 m/s
•speed of 22 miles/hour = 22 mph
• Velocity: Speed and direction
• 10 m/s, due east
• 22 mph down Hesperian Blvd.
How do we describe motion?
• Velocity: Speed and direction
example: 10 m/s, due east
• Acceleration: Any change in velocity; either in
direction, magnitude, or both
The Acceleration of Gravity
 As objects fall, they
move faster & faster.
 They accelerate.
The Acceleration of Gravity
 Acceleration near Earth’s
surface from gravity
means falling speed
increases by
10 meters/second
each second
The Acceleration of Gravity
 Falling from rest…
 after 1 second, moving
10 m/s (about 22 mph)
 after 2 seconds, moving
20 m/s (about 44 mph)
The Acceleration of Gravity
 Higher you drop a ball,
greater its velocity will
be at impact…
 …unless other forces
act!
The Acceleration of Gravity (g)
 Galileo demonstrated that g is
the same for all objects,
regardless of their mass!
 Heavier objects (with more
mass) must be pulled more to
accelerate at the same rate.
And Gravity indeed pulls more
on heavier objects!
The Acceleration of Gravity (g)
 Confirmed by Apollo astronauts on the
Moon, where there is no air resistance.
How is mass different from weight?
Mass—the amount of
matter in an object
(protons, neutrons,
electrons)
Weight—the force from
graivty that acts upon an
object from other mass
Question: On the Moon….?
•
your weight is the same, your
mass is less.
•
your weight is less, your mass
is the same.
•
your weight is more, your mass
is the same.
•
your weight is more, your mass
is less.
Question: On the Moon….
•
your weight is the same,
your mass is less.
•
your weight is less, your
mass is the same.
•
your weight is more, your
mass is the same.
•
your weight is more, your
mass is less.
Why are astronauts
weightless in space?
• There is no gravity in space.
• The force of gravity is much less.
• The moon is pulling astronauts in the
other direction.
• The Earth’s magnetic field holds
them up.
• They are massless.
Why are astronauts
weightless in space?
• There is no gravity in space.
• The force of gravity is much less.
• The moon is pulling astronauts in
the other direction.
• The Earth’s magnetic field holds
them up.
• They are massless.
Why are astronauts
weightless in space?
•
•
•
•
•
There is no gravity in space.
The force of gravity is much less.
The moon is pulling astronauts in the other direction.
The Earth’s magnetic field holds them up.
They are massless.
Gravity IS pulling them towards Earth.
They ARE falling!
Why are astronauts
weightless in space?
• There is gravity in space.
• Weightlessness is due to a
constant state of free-fall.
How can they ORBIT?
How can they ORBIT?
• As spacecraft fall, they also move sideways fast
• At 300 miles above Earth:
•Falling towards Earth continuously, but…
•Moving at 17,000 miles per hour SIDEWAYS
• Orbits are continuous falling “around” Earth!
Sir Isaac Newton
Invented reflecting
telescope
Invented calculus
Connected gravity &
planetary forces
Philosophiae naturalis
principia mathematica
Universal Laws of Motion
“If I have seen farther than others, it
is because I have stood on the
shoulders of giants.”
Sir Isaac Newton
(1642 – 1727)
Physicist
Newton’s Laws of Motion
1
A body at rest or in motion at a
constant speed
along a straight line
remains in that state of rest or
motion
unless acted upon by an outside
force.
Newton’s 1st Law
Planets orbit stars stay in motion, but are
continually being pulled in their orbit by the
star.
Rockets heading to the moon or Mars,
once launched, can coast along a straight
line.
Newton’s 2nd Law of Motion
Newton’s 2nd Law
The change in a body’s velocity due to an applied
force is in the same direction as the force and
proportional to it, but is inversely proportional to the
body’s mass.
F=ma
Launch a rocket – as fuel is used up, mass decreases,
and rocket accelerates even faster!
“Staging” rockets is even smarter!
Thought Question
Is there a net force for each of the following?
•
•
•
•
•
A car coming to a stop.
A bus speeding up.
An elevator moving up at constant
speed.
A bicycle going around a curve.
A moon orbiting Jupiter.
Thought Question
Is there a net force for each of the following?
•
•
•
•
•
A car coming to a stop. Yes
A bus speeding up. Yes
An elevator moving up at constant
speed. No
A bicycle going around a curve. Yes
A moon orbiting Jupiter. Yes
Newton’s 3rd Law of Motion
Newton’s 3rd Law
For every applied force, a force of equal size but
opposite direction arises.
As rocket exhaust pushes backwards, the rocket itself
moves forwards
 As Earth pulls on the Moon, the Moon pulls on Earth
Universal Law of Gravitation
Between every two objects there is an attractive
force, the magnitude of which is directly
proportional to the mass of each object and
inversely proportional to the square of the
distance between the centers of the objects.
Universal Law of Gravitation
Between every two objects there is an attractive force,
the magnitude of which is directly proportional to the
mass of each object and inversely proportional to the
square of the distance between the centers of the
objects.
Law of Gravity
Between every two objects there is an attractive force,
the magnitude of which is directly proportional to the
mass of each object and inversely proportional to the
square of the distance between the centers of the
objects.
Gravity is ONLY attractive!
There is no “anti-gravity”
Gravity
Between every two objects there is an attractive force,
the magnitude of which is directly proportional to the
mass of each object and inversely proportional to the
square of the distance between the centers of the
objects.
What kind of Mass?
It doesn’t matter !
What shape, size, temperature, state?
It doesn’t matter!!
Illustrating Gravity with Tides
• Why are there two high tides each day?
• Why are tides on Earth caused primarily by
the Moon rather than by the Sun?
• Why is Earth’s rotation gradually slowing
down?
• Why does the Moon always show the same
face to Earth?
Tides
 Gravitational force decreases with (distance)2,
Tides
 Since gravitational force decreases with
(distance)2, the Moon’s pull on Earth is
strongest on the side closer to the Moon, and
weakest on the opposite side.
Tides
 Since gravitational force decreases with
(distance)2, the Moon’s pull on Earth is
strongest on the side closer to the Moon, and
weakest on the opposite side.
Tides
 The Earth gets stretched along the Earth-Moon
line.
 The oceans rise relative to land at these points.
Tides - Observations
 Every place on Earth passes through these points,
called high tides, twice per day as the Earth rotates.
 SF Bay Tide Tables
Tides - Observations
 High tides occur every 12 hours… plus!
 Average difference between high tides
= 12 hours and 25 minutes
 remember, the Moon moves!
Tides - Observations
 Tides are tied to the phases of the moon
Tides - Observations
 High tides occur every 12 hours 25minutes
 remember, the Moon moves!
 The Sun’s tidal effect on Earth is not as strong
 About ½ as large as the Moon
 But when BOTH stretch in the same direction,
even larger tides!
Tides - Observations
 Tides are tied to the phases of the moon
Tides
When Sun & Moon pull in the same
direction (new & full phases)
 high tide is HIGHER than usual
Tides
When Sun & Moon pull
at right angles
(first & last quarter
phases)
high tide is LOWER
than usual
Tidal Friction
 Reaction between Moon’s pull & Earth’s rotation.
 Earth’s rotation slows down (1 sec every 50,000 yrs.)
 Moon moves farther away from Earth.
Where’s the PROOF? Stromatolites!
Earth’s rotation slows down
Synchronous Rotation
 When rotation period of a moon, planet, or star
equals its orbital period about another object.
 Tidal friction on the Moon (caused by Earth)
has slowed its rotation down to 1 month.
 The Moon now rotates synchronously.
 We always see the same side of the Moon.
Orbital Paths
 Extending Kepler’s Law #1,
Newton found that ellipses
were not the only orbital paths.
 possible orbital paths
 ellipse (bound)
 parabola (unbound)
 hyperbola (unbound)
Newton’s Version of Kepler’s Third Law
Using calculus, Newton was able to derive
Kepler’s Third Law from his own Law of Gravity.
In its most general form:
2
2
3
P = 4 a / G (m1 + m2)
If you can measure the orbital period of two
objects (P) and the distance between them (a),
then you can calculate the sum of the masses
of both objects (m1 + m2).
Changing Orbits
orbital energy = kinetic energy +
gravitational potential energy
conservation of energy implies
orbits can’t change
spontaneously
An object can’t crash into a planet
unless its orbit takes it there.
Changing Orbits
An orbit can only change if it
gains/loses energy from
another object, such as a
gravitational encounter
If an object gains enough
energy so that its new orbit is
“unbound” it has reached
escape velocity.
Changing Orbits
We can use the gravitational
pull of planets to “slingshot”
spacecraft to other parts of
the solar system!
“Gravitational Assist” cuts travel
time to outer solar system by
years!