Download Newton`s Law of Universal Gravitation

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.
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 thee galaxy with a radius of
2.2X1020 m. The period of one rotation is
2.6X108 years.
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.
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 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
Satellite problem
Uranus requires 84 years to
circle the sun. Find the
distance from the sun to
Uranus.
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?