Download notebook- Universal Gravitation

Instructions for PowerPoint
 Copy into your notebook (or if you
don’t have that with you on a
separate sheet of paper)
the stuff in BLUE
Circular Motion
Universal Gravitation
What we know…
 What is uniform
circular motion?
 How do you define
centripetal
acceleration?
 What is the
difference between
a centripetal and
centrifugal force
What we want to know…
 What is Newton’s Law of Universal
Gravitation?
 How does distance affect gravitational
force between two objects?
 What is weight and how can
something appear weightless?
 What are Kepler’s Laws of Planetary
Motion?
Gravity
 The force that causes an apple to fall
to the ground is the same force that
holds the planets in orbit.
Projectile Motion
 Gravity causes an object to
fall
 Orbit occurs when velocity is
such that the projectile’s path
is parallel to the surface
 This is true when centripetal
force equals the force of
gravity…
2
v
mg  m
r
 However, the force of gravity
is not the same everywhere
Tides
 Gravity from moon cause high and
low tides.
Pull of moon’s gravity stronger.
Water pools. High tide.
Water pulled
away. Low tide
M
A
Earth
B
Pull of Earth’s gravity stronger.
Water pools. High tide.
Flow of water
Water pulled
away. Low tide
Tides
High Tide
Low Tide
Newton’s Law of Universal Gravitation
 Gravitational Force
 depends on the
distance between two
masses
 depends on the mass of
the objects
d
M1
m2
 Mathematically…
G= the gravitational constant
= 6.67 x 10-11 Nm2/kg2
r = distance between the
center of each mass.
M 1m2
Fg  G 2
r
Gravity
 All objects that have mass have gravity.
 Small dense
objects can
have as much
or more
gravity than
larger hollow
objects.
*Black holes can have a size 4 times the size of our
sun but a pull of gravity millions times stronger
Gravity
 Gravity follows the inverse square law..
 Force of gravity is inversely related to the
square of the distance
Gravity has no
range limitcopy down
graph to the
left
Weight
 Weight is the measure of the force of
gravity.
 Weight = mass x acceleration of gravity
 Weight varies depending on location
 Apparent Weight
 Depending on the forces acting on an
object, the perceived weight of the
object may change.
 “How heavy an object appears to be”
G force
 People have
experienced
various levels of
“g-forces”.
 1 g is normal
weight. 3 g’s
means a person
feels they weigh 3
times their
normal weight.
Fun Facts (around town)
 Desperado (at
Buffalo Bill’s- near
CA state line)
reaches 4 Gs
 El Loco (at Circus
Circus) reaches a
1.5 Gs
 Canyon Blaster (at
Adventure Dome)
reaches 3.5 Gs
 Astronauts feel
3.5 Gs in space
during take-off
 Most people pass
out above 5 Gs!
Planetary Motion
 Originally believed that the Earth was
the center of the Universe. Everything
including the planets and sun revolved
around us.
 Copernicus (1473-1543): proposed that
the Earth and other planets revolved
around the Sun in perfect circles
(heliocentric)
 Did not match up with the new precise
observations made by Tycho Brahe (15461601).
Kepler’s Laws of Planetary Motion
 Johannes Kepler (1571-1630):
reconciled the Copernican model with
Brahe’s observations. Developed 3
laws of planetary motion.
Kepler’s 1st Law
 Planets travel in an elliptical orbit
around the sun, and the sun is at one
of the focal points.
Sun
Kepler’s 2nd Law
 An imaginary line drawn from the sun
to any planet sweeps out equal areas
in equal time intervals.
Δt1
Sun
A1
A2
Δt2
 Planets travel faster when they are
closer to the sun.
 Practice worksheet
Try this…in your notebook
 Given G = 6.67 x 10-11 Nm2/kg2, the
mass of the earth is 5.98 x 1024 kg, and
the radius of the earth is 6.37 x 106 m,
what is the force of gravity between the
Earth and a 9 kg apple?
 Remember… the gravitational force is
actually the object’s weight.
 Fg= Weight = mg
 “g” only equals 9.81 on Earth
M1m2
_____
Fg = G r²
Gravity on the Moon
 What is the acceleration of gravity on
the moon, given the Moon’s mass is
7.35 x 1022 kg and the radius of the
moon is 1.74 x 106 m?
ag = gmoon
M1m2
_____
mag = G r²
M1
___
ag = G r²
Kepler’s 3rd Law
 The square of a planet’s orbital period
is proportional to the cube of the
average distance between the planet
and the sun.
T² is proportional to r³
4π²
T² =
r³
Gm
Try it (in your notebook)
Gravity on Mars
 Lance Fortnight has a total mass of
140 kg when he lands on Mars. Mars
has a mass of 6.42x1023 kg, and a
mean radius of 3.40x106 m.
 Find Mars’ acceleration of gravity. (gM)
 Find the force of gravity between Lance
and Mars. (Fg)
Try it…in your notebook
 Lance Fortnight has a total mass of
140 kg when he lands on Mars. Mars
has a mass of 6.42x1023 kg, and a
mean radius of 3.40x106 m.
 Find Mars’ acceleration of gravity. (gM)
 Find the force of gravity between Lance
and Mars. (Fg)
 Buzz Miles has a mass of 140 kg too, but
an apparent weight of 480 N. How far
from Mars’ center is he?