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Newton's Law of Universal Gravitation
Where G is the Universal Gravitational Constant, m and M are the masses of the two objects, and r is the center-to-center distance.
Lord Henry Cavendish was one of the first to calculate G. His apparatus was a torsion pendulum below.
Example 10 A man takes his dog for a walk on a deserted beach. Treating people and dogs as point objects for the moment, find the force of gravity between the 105 kg mand and his 11.2 kg dog when they are separated by a distance of (a) 1.00 m and (b) 10.0 m.
Example 11 The figure shows
an arrangement of three particles, particle 1 having mass
Example 12 As part of a daring
rescue attempt, the Millennium Falcon passes between a pair of twin
asteroids, as shown. If the mass of the spaceship is
Example 13 The figure shows
an arrangement of five particles, with masses
Absolute gravitational acceleration at the Earth's surface is:
Acceleration due to gravity for an object above the Earth's surface:
To calculate the orbital speed we set the gravitational force and the centripetal force equal and solve. This leads to the following equation for orbital speed:
Example 14 If you climb to the top of Mt. Everest, you will be about 5.50 mi above sea level. What is the acceleration due to gravity at this altitude?
Example 15 (a) Find the acceleration of gravity on the surface of the Moon. (b) The lunar
rover had a mass of 225 kg. What was its weight on the Earth and on
the Moon? (Mass of Moon
Example 16 Find the mass
of Mars, given that its radius is
Kepler's Laws of Orbital Motion Kepler's
First Law Kepler's
Second Law
Kepler's
Third Law
Using Newton's Universal Law of Gravitation and algebra we can find a relationship for the period.
Example 17 The Earth revolves
around the Sun once a year at an average distance of
Example 18 Find the altitude
above the Earth's surface where a satellite orbits with a period of
one day
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and
particles 2 and 3 having mass 
and
with distance a = 2.0 cm. What is the net gravitational force 
that
acts on particle 1 due to the other particles?
and
the mass of each asteroid is 
,
find the net gravitational force exerted on the Millennium Falcon (a)
when it is at location A and (b) when it is at location B. Treat the
spaceship and the asteroids as if they were point objects.
, 
,
and with a = 2.0 cm and 
.
What is the net gravitational force 
on
particle 1 due to the other particles?
and
its radius is 
)
,
and that the acceleration of gravity on its surface is 
.
.
(a) Use this information to calculate the mass of the Sun. (b) Find
the period of revolution for the planet Mercury, whose average distance
from the Sun is 
.
, 
, 
)