Transcript Week 6

For Wednesday, February 25
No new reading assignment
QUIZ #2 FRIDAY (BRING A CALCULATOR)
Assignments: Homework #3 (due today)
Measuring Planet Orbits
Can measure size of planet’s
orbit (a) if:
PLANET’S
FORCE ON
STAR
• measure P from star’s wobble
• determine M for star from its light
(and as long as Mplanet << Mstar)
STAR’S
FORCE ON
PLANET
4p
3
P =
A
GM total
2
2
Example: planet orbiting star HD189733
æ P ö æ M Sun öæ A ö3
֍
÷
ç
÷ =ç
è 1 yr ø è M øè 1 AU ø
2
Thought Question:
A new planet is discovered orbiting a star that is 4
times as massive as the Sun. Astronomers find
that it takes 0.5 yr to make one orbit. What does
this say about the planet’s orbit?
A. The planet orbits 1 AU from its star.
B. The planet orbits more than 1 AU from its star.
C. The planet orbits less than 1 AU from its star.
D. It isn’t possible to tell how big the planet’s orbit is.
Thought Question:
A planet is discovered orbiting another star.
Astronomers find that its average distance from
its star is 1 AU, but it takes 3 years to make one
orbit. What does this say about the star?
A. The host star is more massive than the Sun.
B. The host star is less massive than the Sun.
C. The host star is the same mass as the Sun.
D. It isn’t possible to tell what the star’s mass is.
Impacts
JUPITER
- 1994
Energy
The ability to do work: move a distance against an
opposing force…
FORCE
(GRAVITY)
DISTANCE


FORCE (FRICTION)
• Metric unit: Joule (J)
kg × m
1 J =1 N × m = 1 2
s
• English unit: Calorie
1 Cal = 4184 J
2
DISTANCE
Energy
The ability to do work …
• Metric unit: Joule (J)
kg × m
1 J =1 N × m = 1 2
s
2
• English unit: Calorie
1 Cal = 4184 J




energy to pick a burger off floor (move it up by 1 m): 1 J
energy from eating candy bar: 106 J
energy released by H bomb: 5  1015 J
energy released by Sun each second: 4  1026 J
Types of Energy: Kinetic Energy
• kinetic energy: energy of motion

FORCE
(GRAVITY)
1
E K = mv 2
2
o gain kinetic energy by moving with a force
• thermal energy: kinetic energy involving random
motions of atoms and other particles
higher temperature 
more thermal energy
EXAMPLE: GAS IN A BOX
Tunguska
Event
SIBERIA - 1908
7:14 am (local)
Chelyabinsk
Meteor
RUSSIA – 2013
9:20 am (local)
Thought Question:
How fast does a 1010 kg asteroid have to be traveling to
have a kinetic energy equal to an H bomb (5  1015 J)?
v
A. 1 m / s
B. 1 km / s
C. 103 km / s
D. 106 km / s
Meteors
• meteors tend to hit
on the leading side
of Earth
• impact speed is
usually at least
Earth’s orbit speed
(~30 km/s)
For Friday, Feb. 27
QUIZ #2
Types of Energy: Potential Energy
• potential energy: energy of position –
a kind of “stored” energy
Gm1m2
EP = d
• increases as distance between objects increases
• defined to be 0 at infinite separation (d=∞)
POTENTIAL ENERGY
DECREASES AS IT
ROLLS DOWN…
BECOMING KINETIC ENERGY
Thought Question:
A spacecraft is moving away from the Sun
without firing its engines. What will happen
to the spacecraft’s…
USA
 kinetic energy?
 potential energy?
Answer:
A. increases
B: decreases
C: stays the same
(Enter the two letters and hit send.)
USA
CONSERVATION OF ENERGY: energy can be
transferred from object to object, or converted
from one form to another, but never destroyed
E K,initial + E P,initial = E total = E K, final + E P, final
Jupiter’s
Moon Io
total energy : E = E K + E P
1
GM Io m
E = mv 2 at surface
2
RIo
GM Iom
E =0at top of plume
d
Example: Io volcanic eruption
If you shoot
cannonballs into
space at greater
and greater
speeds, what will
happen?
Newton’s Thought Experiment
Fire cannonballs
from tall mountain
at different speeds:
low speed: crash
into surface
medium speed:
circular orbit
high speed: ellipse
orbit (cannonball
gets farther from
Earth)
Escape Velocity
ON PLANET’S
SURFACE
Rplanet
IN SPACE
USA
v
d
USA
total energy : E = E K + E P
1 2 GM planet m
E = mv at surface
2
Rplanet
GM planet m
E =0at maximum height
d
If ship escapes, it must get far enough away
that gravity can’t pull it back:
d = ¥ so
E =0
Escape Velocity
v esc
2GM
=
d
Bound and Unbound Orbits
miniature golf analogy: imagine the Sun at bottom of a valley,
and object rolling along the sides
• BOUND ORBIT – object does not have
enough kinetic energy to escape:
E total < 0
• UNBOUND ORBIT – object can eventually
reach d = ∞
E total > 0
Bound and Unbound Orbits
• BOUND ORBIT (ellipse or circle)
— gravity able to hold object
• UNBOUND ORBIT (parabola or
hyperbola) — object does not
return after closest approach
Review Question:
Two of the orbits in the diagram below have
the same orbit period. Which one doesn’t?
Enter the letters of the two answers and hit send.
Review Question:
In the diagram below, the larger of the two
orbiting objects has 4 times as much mass
as the other. Where is the center of mass?
0
1
2
3
4
5
6
Enter the number of the position.
7
8
9
10
Review Question:
If you need to calculate the speed of Earth
orbiting the Sun, what mass and distance
do you need to use?
A.
Earth’s mass
Earth-Sun distance
B.
Sun’s mass
Earth’s radius
C.
Earth’s mass
Earth’s radius
D.
Sun’s mass
Earth-Sun distance
Review Question:
For the Dawn spacecraft going into orbit around
the dwarf planet Ceres, which of the following do
you need to know to calculate the spacecraft’s
orbit period? (Enter all letters you need.)
A.Ceres’ radius
B.Ceres’ semi-major axis
C.Dawn’s semi-major axis
D.Sun’s mass
E.Ceres’ mass
F.Dawn’s mass