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```Newton’s Law of
Universal
Gravitation
 Any two objects exert a
gravitational force of
attraction on each other. The
magnitude of the force is
proportional to the product of
the gravitational masses of the
objects, and inversely
proportional to the square of
the distance between them.
Gm1m2
Fg 
2
r
G=6.67X10-11 N m2/kg2
BASIC PROBLEM
Find the gravitational force between
a baseball (m=0.3kg) and a billiard
ball (m=0.4kg) if the distance
between their centers is 0.3m.
 The gravitational force
between two electrons 1.00m
apart is 5.42X10-71N.
Calculate the mass of an
electron.
 What is the electrical force
between these two electrons?
A STELLAR PROBLEM
We can consider the sun to be a satellite
of our galaxy, the Milky Way. The sun,
mass 2.0X1030kg, revolves around the
center of the galaxy with a radius of
2.2X1020 m. The period of one rotation is
8.2X1016.
a. Find the approximate mass of the galaxy.
b. Assume the average star in the galaxy has
the mass of the sun, find the number of
stars in the galaxy.
Acceleration due to gravity
 Find the acceleration due to
gravity on Earth’s surface.
 Find the acceleration due to
gravity on the surface of the
asteroid in Armageddon. r =
2.35x105 m, m = 4.28x1020 kg.
International Space Station
 The International Space
Station has an orbital
height of 370 km, what
is its speed as orbits
the earth?
 Earth mass –
5.97x1024kg
6.38x106m
 In minutes, how long
does it take the ISS to
rotate once around the
Earth?
Kepler’s laws
Kepler’s laws
Kepler’s 1st law
The paths of the planets
around the sun are ellipses
with the sun at one focus
point
Kepler’s 2nd law
 An imaginary line drawn from a planet to the
sun sweeps out equal areas in equal amounts
of time as the planet travels along its
elliptical path.
Kepler’s 2nd law
 An imaginary line drawn from a planet to the
sun sweeps out equal areas in equal amounts
of time as the planet travels along its
elliptical path.
A1
A2
Kepler’s 2nd law
If A1 = A2, then t1 = t2
t1
A1
A2
t2
Kepler’s 3rd law
The ratio of the squares of the periods of
any two planets is equal to the ratio of
the cubes of the planets average
distances from the sun.
2
A
2
B
T
T
3
A
3
B
r

r
Problem- A Geosynchronous
satellite
What is the orbital radius of a
geosynchronous satellite?
(______________________)
How far up from the surface of
the earth is this satellite?
Satellite problem
Uranus requires 84 years to
circle the sun. Find the
distance from the sun to
Uranus.
Kepler’s Third Law Problems
1. Comet Halley returns every 74 years. Find the average
distance from Halley to the sun.
2. Find the orbital radius of a Geosynchronous satellite. How
far from the surface of the earth is the satellite located?
3. Mars has a period around the sun of 686 days. What is its
average distance from the sun?
4. An asteroid revolves around the sun with an average orbital
radius twice that of Earth’s. Predict the period of the asteroid in
Earth years.
5. What is the period of a satellite that orbits the Earth at
6.7X106 m measured from the Earth’s center?
```
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