Download Lecture 7 Phys 1810

Lecture 5 Phys 1810
MONDAY!
1.Tutorial/Office hour 3:00
pm Allen 514.
Syllabus at
http://www.physics.umanit
oba.ca/~english/2014fallph
ys1810/
(Google “Jayanne English teach”)
along supplemental
material.
REVISE DATE IS
Wed. Sept 15
(Do Honours rather than
General Science 3yr degree)
• Read BEFORE coming to class:
– Electromagnetic Radiation 3.1 to
3.4
• Energy
• Thermal Radiation Box 3-2
• Flux and Luminosity
(L equation in Box 17-2)
– Spectra 4.1, 4.2
• Kirkhhoff’s Laws
– Radio Emission 18.4
– Doppler shift: 3.5, Box 3-3, 4.5
Examples of the Effects of Gravity: Tides
Tides at the Bay of Fundy
Effect of the Moon on Earth
Gravity (
)  Tidal Forces:
== Distortion of an object by the gravitational pull of another
object.
-- nearby (e.g. Earth & Moon)
OR
-- very massive (e.g. Earth & Sun)
Tidal Force Examples:
Asteroid Belt –tidal force of Jupiter prevented formation of planet
between Mars & Jupiter.
Tidal Force Examples: The tidal force of Jupiter (and Europa)
cause
- deformation of Io’s interior
-> heat
- volcanism
Split apart
Comet
Shoemaker-Levy
q
Saturn raises tides on its moons.
Gravity  orbits of material in rings.
Peculiar Galaxies
Tidal Tail
Tides
summary
Recall column
• Make note of your prediction.
• There is a difference in the
gravitational force on each side of an
object. Splitting the object into 3
parts, which is going to feel the most
force?
a) The red (closest) ball?
b) The blue (middle) ball?
c) The yellow (furthest) ball?
summary
Tides
Recall column
• Make note of your prediction.
• Which ball moves the least?
a) The red (closest) ball?
b) The blue (middle) ball?
c) The yellow (furthest) ball?
summary
Tides:
Recall column
• Movie about motion of the balls.
• Note perspective from someone
sitting on centre ball
summary
Tides
Recall column
• Difference in
object.
on each side of an
Tides
summary
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• On centre ball: appears other 2 balls have
moved in opposite directions. These 2
opposing forces == tidal forces.
• Tidal forces: cause distortion of an object
by pull of another object.
• Can occur when
– Objects close (e.g. Earth & Moon)
– 1 object is very massive (e.g. Jupiter &
Io; Sun & Earth.)
Tides
summary
Recall column
• Moon pulls on Earth & tides effect
water more than land.
• Make a prediction about how Earth’s
ocean is distributed due to moon.
summary
Tides
Recall column
• Note 2 tidal bulges at one time!
Apply what we know:
Recall column
summary
• If the Earth had no Moon, then the
tides would occur twice a day but
would not be as strong.
(Think of the objects in the Solar
System.)
Tidal Locking:
summary
Tidal Drag
Recall column
Why does the moon always show the
same face to us?
Synchronous Orbit:
P == Period
Tidal Locking:
What happens to Earth
summary
Tidal Drag
Recall column
Misalignment due to friction between ocean &
crust  crust drags ocean
Moon pulls back on tidal bulge  Earth’s spin
slows down.
100’s of billions of yrs  tidal locking
Tidal Locking:
summary
Tidal Drag
Recall column
Moon’s tidal bulge formed when moon
solidified & Earth’s tidal pull on
moon’s bulge is larger  tidal
locking faster for moon.
P == Period
summary
Tidal Locking:
Recall column
• Summary – Examples:
Tidal forces cause
1) Synchronous Orbits
2) Fragmenting
Comets
3) Structures in Interacting Galaxies
Note: there is structure on each side of an individual galaxy – the bridge and the tail.
2.7 Newton’s Laws
Gravity
Kepler’s Laws of
Planetary Motion
from Newton’s perspective.
Description of Ellipse
Objects orbit a common centre of mass.
Centre of mass == average position of all matter making up the 2 bodies.
Equal mass
1 object more massive
1 object very massive
Notice “wobble” of sun!
 large planets around stars are
easier to detect because they cause
star to “wobble”.
• Kepler’s 1st Law : Kepler I
• Orbit of a planet around the sun is an ellipse
with the center of mass of the planet-sun
system at one focus
• Note: r = radius of circle = distance. O.k. since r == average distance,
which equals semi-major axis a
• Kepler II
An imaginary line connecting the sun to any
planet sweeps out equal areas of an ellipse in
equal intervals of time.
•
•
•
Area of A, B, and C are the same.
Note Arc of A, Arc of C and Arc of B
v = distance/time and time remains constant. Therefore planet travels a
different speeds when at different distances from the sun.
• Kepler III
The square of the planet’s orbital period (P) is
proportional to the cube of its semi-major axis (a)
divided by the combined mass in the system
(Mtotal)
Solar mass = 99.85% of Mtotal
Note proportionality. If distance from sun
increases so does time to go around sun.
Relationship is NOT 1-to-1.
Note
P in earth years
A in AU
M in solar masses
Example: Planet A and
Planet B. Distance between
star and B is twice that of A.
Long does it take for B to
orbit compared to A?
Example: Planet A and
Planet B. Distance between
star and B is twice that of A.
Long does it take for B to
orbit compared to A?
Compare planets’ velocities  Keplerian Rotation Curve
And since
Works for:
• Earth’s satellites
• Jupiter’s moons
• planets
Plot Velocity Equation for planets the Solar
System:
summary
Recall column
a
1
25
36
64
100
v
1
1/5
1/6
1/8
1/10
Keperlian motion
 Keplerian rotation curve.
Important when we study Dark Matter.
summary
Derive v using Newton’s Laws
Recall column
Notice how m of
smaller object cancels
out. So hammer and
feather have same
acceleration!
For Earth’s gravity: accel = g
Derive v using Newton’s Laws
Recall column
Kepler’s v is empirical with no
reason for formula.
Newton’s version provides
reason – Forces in balance for
an object to be in orbit.
Since r = semi-major axes “a” and G & M are constant:
summary
•
•
•
v to little, fall back
v enough, go into orbit
v to much, unbound ==escape
Escape Velocity
• Let’s weigh the sun!
– Re-arrange the velocity equation and substitute.
– Exercise – weigh the Earth using the moon.(Look
relevant values in textbook.)
Weighing the sun
Recall column
summary
Weighing the sun
Recall column
Many ways to calculate
co-efficients.
How does this compare with the Earth’s mass?
What else can we “weigh” with this equation?
summary