Transcript Unit 1

Units 17, 18, 19, 20
Homework 3 is on the website of the course
http://www.astro.wisc.edu/~lazarian/ast103_2014/
Acceleration of a body is its rate of change of
A. Mass
B. Weight
C. Velocity
D. Positions
An object orbiting the sun in a circle can be said to be
A. Weightless
B. Always accelerating
C. Moving at a constant velocity
D. Moving under equal and opposite forces
An accelerating body must at all times
A. Have a changing direction of motion
B. Have an increasing velocity
C. Be moving
D. Have a changing velocity
Which of the following statements about an asteroid
moving in a circular orbit around the Sun is untrue?
A. It is moving on a flat plane
B. It is moving with constant velocity
C. It is accelerating
D. It is moving with constant speed
Orbits
• As we saw in Unit 17, we can
find the mass of a large object
by measuring the velocity of a
smaller object orbiting it, and
the distance between the two
bodies.
d ´V 2
M=
G
• We can re-arrange this
expression to get something
very useful:
Vcirc
GM
=
d
We can use this expression to determine
the orbital velocity (V) of a small mass orbiting
a distance d from the center of a much larger
mass (M)
Calculating Escape Velocity
• From Newton’s laws of
motion and gravity, we can
calculate the velocity
necessary for an object to
have in order to escape from
a planet, called the escape
velocity
Vesc
2GM
=
R
What Escape Velocity Means
• If an object, say a rocket, is
launched with a velocity less than
the escape velocity, it will
eventually return to Earth
• If the rocket achieves a speed
higher than the escape velocity, it
will leave the Earth, and will not
return!
Escape Velocity is for more
than just Rockets!
• The concept of escape velocity is useful
for more than just rockets!
• It helps determine which planets have an
atmosphere, and which don’t
– Object with a smaller mass (such as the
Moon, or Mercury) have a low escape
velocity. Gas particles near the planet can
escape easily, so these bodies don’t have
much of an atmosphere.
– Planets with a high mass, such as Jupiter,
have very high escape velocities, so gas
particles have a difficult time escaping.
Massive planets tend to have thick
atmospheres.
Konstantin Tsiolkovsky, pioneer of space exploration
Werner Von Braun --Dark Genius of Rocket Science
Centripetal Force
•
•
FC =
m ´V 2
d
•
•
If we tie a mass to a string and
swing the mass around in a circle,
some force is required to keep the
mass from flying off in a straight
line
This is a centripetal force, a force
directed towards the center of the
system
The tension in the string provides
this force.
Newton determined that this force
can be described by the following
equation:
m ´V 2
FC =
d
Masses from Orbital Speeds
• We know that for planets, the
centripetal force that keeps the
planets moving on an elliptical
path is the gravitational force.
• We can set FG and FC equal to
each other, and solve for M!
d ´V 2
M=
G
• Now, if we know the orbital speed
of a small object orbiting a much
larger one, and we know the
distance between the two objects,
we can calculate the larger
object’s mass!
Newton’s Modification of Kepler’s 3rd Law
• Newton applied his ideas to
Kepler’s 3rd Law, and
developed a version that works
for any two massive bodies, not
just the Sun and its planets!
a 3AU
MA + MB = 2
PYR
• Here, MA and MB are the two
object’s masses expressed in
units of the Sun’s mass.
• This expression is useful for
calculating the mass of binary
star systems, and other
astronomical phenomena
The Origin of Tides
• The Moon exerts a
gravitational force
on the Earth,
stretching it!
– Water responds to
this pull by
flowing towards
the source of the
force, creating
tidal bulges both
beneath the Moon
and on the
opposite side of
the Earth
High and Low Tides
As the Earth rotates beneath
the Moon, the surface of the
Earth experiences high
and low tides
The Sun creates tides, too!
•
•
The Sun is much more massive than the
Moon, so one might think it would create
far larger tides!
The Sun is much farther away, so its tidal
forces are smaller, but still noticeable!
•
•
When the Sun and the Moon line up,
higher tides, call “spring tides” are formed
When the Sun and the Moon are at right
angles to each other, their tidal forces work
against each other, and smaller “neap
tides” result.
The Conservation of Energy
• The energy in a closed system may change
form, but the total amount of energy does not
change as a result of any process
Kinetic Energy
• Kinetic Energy is simply the energy of
motion
• Both mass (m) and velocity (V) contribute
to kinetic energy
1
2
EK = m ´ V
2
• Imagine catching a thrown ball.
– If the ball is thrown gently, it hits your hand
with very little pain
– If the ball is thrown very hard, it hurts to
catch!
Thermal Energy
• Thermal energy is the energy
associated with heat
• It is the energy of the random motion
of individual atoms within an object.
• What you perceive as heat on a
stovetop is the energy of the individual
atoms in the heating element striking
your finger
Potential Energy
• You can think of potential
energy as stored energy,
energy ready to be converted
into another form
• Gravitational potential energy
is the energy stored as a result
of an object being lifted
upwards against the pull of
gravity
• Potential energy is released
when the object is put into
motion, or allowed to fall.
Definition of Angular Momentum
• Angular momentum is the rotational equivalent of
inertia
• Can be expressed mathematically as the product of the
objects mass, rotational velocity, and radius
• If no external forces are acting on an object, then its
angular momentum is conserved, or a constant:
L = m ´V ´ r = constant
Conservation of Angular Momentum
• Since angular momentum is
conserved, if either the mass,
size or speed of a spinning
object changes, the other
values must change to
maintain the same value of
momentum
– As a spinning figure skater
pulls her arms inward, she
changes her value of r in
angular momentum.
– Mass cannot increase, so her
rotational speed must increase
to maintain a constant angular
momentum
• Works for stars, planets
orbiting the Sun, and satellites
orbiting the Earth, too!