Download Keplar_s Laws and Universal Gravitation

Do Now (on a new sheet please):

What net force must act on a 5 kg mass
that is moving at a constant speed of 4
m/s around a circle with a radius of 2 m?
Objective/Homework
Objective:
 Homework:

◦
◦
◦
◦
◦
Circular Motion – due Tuesday 12/14
Quiz: Circular Motion – Tuesday 12/14
Lab: Circular Motion – Friday 12/17
Kepler’s Laws Worksheet: Monday 12/20
Test: 2-D Motion – Tuesday December 12/21
What
are some
things you know
about the
universe?
Keplar’s Laws and Universal
Gravitation
12/13/10
Do Now (12/19):
What are the three views of
the universe that changed
over time?
2. Who are the men who
developed each?
3. Which is our current view?
1.
History of Views of the Universe
Aristotle: Geocentric (everything
rotates around the Earth in perfect
circles)
 Patterns of stars in the sky never change
 Planets drift with respect to background
stars
History of Views of the Universe
Nicolas Copernicus: Heliocentric
(everything rotates around the sun in
perfect circles)
 Accurately predicts the rising and setting
Sun, moon, and stars
 Accounts for retrograde motion of Mars,
Jupiter, and Saturn
History of Views of the Universe
Johannes Keplar: Heliocentric
 Used the accurate recorded observations
of Tyco Brahe to develop a new planetary
model and three laws
 Planets rotate around the sun in ellipses
with the sun at one focus
Keplar’s Laws

First law: The path of each planet about
the sun is an ellipse with the sun at one
focus
Keplar’s Laws
Second Law: Each planet moves so that
the planet sweeps out equal areas in
equal periods of time
 http://www.physicsclassroom.com/mmedi
a/circmot/ksl.cfm

Keplar’s Laws

Third Law: The ratio of the squares of the
periods (time of rotation: T) of any two
planets revolving around the sun is equal
to the ratio of the cubes of their radius R
from the sun
2
1
3
1
2
2
3
2
T
T

or
r
r
2
T
K 3
r
Variables and constants:
T=period of orbit
 R or r= radius of orbit
 G=universal gravitational ; G= 6.67x10-11
Nm2/kg2
 m=mass
 F= force
 K=Kepler’s constant

Newton’s Law of Universal
Gravitation




Fg = force of gravity
G = 6.67x10-11 Nm2/kg2
r = distance between two objects
m = mass 1 or 2
Gm1m2
Fg 
2
r
Equations:
Gm1m2
Fg 
2
r
Gm
v
r
Practice/Review:
 Please
use the rest of class
to work on “Kepler’s Laws
and Universal
Gravitation.” Make sure
your test trial results are
in by the end of the day!!!
Example:

A 3 kg mass and a 2 kg mass are placed
with their centers 5 m apart. What is the
force of attraction between them?
Do Now:
A 5 kg mass and a 6 kg mass are placed
with their centers 0.5 m apart. What is
the force of attraction between them?
 Turn in your Circular Motion worksheet
and your Do Now’s from last week
(starting with 12/6)

Quiz:

Clear your desks except for a piece of
paper and a writing utensil
Quiz:

A 9800 N car is driven on a circular track
with a diameter of 600 m at 30 m/s.
Calculate the car’s centripetal
acceleration & its centripetal force.
Do Now (12/20):
A
5 kg mass and a 6 kg
mass are placed with
their centers 0.5 m apart.
What is the force of
gravitational attraction
between them?
Law of Universal Gravitation:
The gravitational force between two
objects
Gm1m2
Fg 
2
r
Period of a planet orbiting the sun
•ms: the mass of the sun (constant)
•r: radius of orbit
3
r
T  2
Gms
Speed of a satellite orbiting earth
me= mass of the earth
 r=radius of orbit

Gme
v
r
Period of a satellite orbiting the earth

r=radius of orbit
3
r
T  2
Gme
Practice/Review:
 Please
use the rest of class
to work on “2-D Forces
Review.” Make sure your
test trial results are in!!!
Once you finish, you may
work on your notecard for
tomorrow’s test.
Do Now:

What is the speed of the planet Jupiter
around the sun?
◦ hint – look on page 178 of your classroom
textbooks
◦ Hint – look for the radius of the ORBIT not
the radius of the planet
Do Now:

What is the period of the planet Neptune
around the sun?
◦ hint – look on page 178 of your classroom
textbooks