Download Universal Law - Nassau BOCES

Week of 11/ 06
/2006
The Newtonian Synthesis
Nicolaus Copernicus
1473 – 1543
• Frame of Reference
Tycho Brahe 1546- 1601
• Accurate Data
Johannes Kepler
1571-1630
• Emperical Laws
Isaac Newton 1642 – 1727
• Universal Law
Kepler’s Laws of Planetary Motion
Law of Ellipses
• Each planet orbits the sun on an elliptical path with the
sun at one focus.
Law of Equal Areas
• The radius vector drawn from the sun to each planet
sweeps out equal areas during equal time intervals.
Harmonic Law
• The period of a planetary orbit is directly proportiopnal
to the cube of its semimajor axis.
Newton’s Universal Law of
Gravitation
Every body in the universe attracts every
other body with a force directly proportional
to the product of their masses and inversely
proportional to the square of their
separation
F=
G M1M2
r2
F = Gravitational Force (N)
F
m1 = Mass of body 1 (kg)
m2 = Mass of a body 2 (kg)
Gm1 m2
d
2
G =Universal Gravitational Constant
d = Distance between the centers of the objects (m)
G  6.67 x10
11
N m
2
kg
2
60 kg Katie and 80 kg Evan are sitting at opposite ends of the
Physics classroom 6 meters apart.
a. Find the gravitational force that one exerts on the other.
b. Who is attracted to the other more?
Physics
F = ma
The Force is:
1. Directly proportional to the product of the masses.
2. Inversely proportional to the square of the distance
F
Gm1 m2
d
2
F
Gm1 m2
d2
Hyperbolic
Intensity of force diminishes as 1/d2
Forces are equal in magnitude
and opposite in direction
FAE
FEA
Earth pulls apple down and
apple pulls earth up
Find the Gravitational force of attraction between the following
Mass 1 (kg) Mass 2 (kg) Distance (m) Force (N)
1.
Football Player
100
Earth
5.98 x 10 24
6.37 x 10 6
?
2.
Physics Student
70
Moon
7.34 x 10 22
1.71 x 10 6
?
F
Gm1 m2
d
Where
2
G  6.67 x1011
N  m2
2
kg
Two objects attract each other with a force of 16 N, what
is the new force if:
1. The distance is doubled?
2. The distance is tripled
3. The distance is quadrupled
4. The distance is reduced in half
5. The mass of one is doubled
6. The mass of both is doubled
7. The mass of one is halved
8. The mass of both is halved
9. The mass of both is tripled
10.One mass is doubled the other halved
F
Gm1 m2
d2
Tougher Ones:
F
10.The mass of both is doubled, and the distance is doubled
11.The mass of both is tripled, and if the distance is doubled
12.The mass of one is doubled, and if the distance is tripled
Gm1 m2
d2
Our solar system is in the Milky Way galaxy. The nearest galaxy is
Andromeda, 2 x 1022 m away. The masses of the Milky Way and
Andromeda galaxies are 7 x 1011 and 6 x 1011 kg respectively. Find
the magnitude of the gravitational force exerted on the Milky Way
by the Andromeda galaxy.
Using an apple to weigh the earth!
The gravitational force on an apple:
Gma M E
F 

m
a
a
2
r
G = Universal gravity constant
= 6.67 x 10 -11 N m2 / kg2
M = mass of earth = (?)
R = radius of earth = 6.4 x 10 6 m
Weighing the Earth Solve
equation for M
GM E
F  2  a
r
gR 2 (9.81m / s 2 )(6.4 x106 m)2
ME 

11
2
2
G
6.67 x10 N  m / kg
M E  6.4 x1024 kg
To find the Mass of a planet, you have to know:
1. “g” on the planet
2. Radius of planet
Conversely:
Finding “g”
Gma M E
F 
 ma a
2
r
GM P
a  "g" 
RP 2
To find the acceleration due to gravity on a planet in the above
equation you have to know:
1. Mass of planet
2. Radius of planet
Earth’s Gravitational field diminishes as 1/r2
Summary:
The forces are equal in
magnitude and opposite
in direction
The gravitational force due to the Earth on a 1 kg mass at one
Earth radius above the surface of the Earth is equal to_______
the force on the same mass on the surface of the Earth.
a.
b.
c.
d.
1/2 of
1/4 of
1/8 of
1/16 of