Download Newton`s Law of Gravitation

Newton’s Law
of Gravitation
 Newton concluded that gravity was a force that acts
through even great distances
 Newton did calculations on the ar of the moon and its
Fr
 Found the Fr inversely proportional to the square of
the radius of orbit
 Since Fr is caused by gravity, the force of gravity is
inversely proportional to square of radius
 Newton also realized that the force of gravity
depends on the mass – directly proportional to the
mass of the two objects being attracted
Law of Universal Gravitation
 Every part in the universe attracts every other part
with a force that is proportional to the product of
their masses and inversely proportional to the square
of the distance between them.
Equation

FG = Gm1m2/ r2

G = universal constant
= 6.67 x 10-11 N m2/kg2
Example 1
 A 50 kg person and a 75 kg person are sitting on a
bench so that their centers are about 50 cm apart.
How much gravitational force is there between
them?
Example 2
 What is the force of gravity acting on a 2000 kg
spacecraft when it orbits two Earth radii from the
Earth’s surface?
Radius = 6380 km
Mass of earth = 5.98 x 1024 kg
Acceleration Due to Gravity






FG = Gm1m2/ r2
On the earth m2 is the mass of the earth and m1 the
mass of the object
FG = mg
mg = Gm1m2/ r2
m1 cancels (this is the mass of the object)
g = Gm2/ r2
Example 3
 What is the acceleration due to gravity on the moon
which has a mass of 7.4 x 1022 kg and a radius of
1750 km?
Example
 What is the acceleration due to gravity acting on a
satellite orbiting at a distance of two earth’s radii
from the earth’s surface?
 The velocity of a satellite keeps it in orbit
 Even when moving, the satellite is actually
accelerating toward the Earth (this is what
keeps it in its circular path)
 Its acceleration results in a curved path which
is the same as the curve of the Earth
 Gravity is providing the centripetal force
Perception of Weightlessness
 There is still gravity acting in a satellite (about 8.9
m/s2), so why do we feel weightless?
 In an free falling elevator, if the FA is equal to the FG,
there is no FN
 No force is felt feel weightless – called apparent
weightlessness
 Weightlessness that you feel in a satellite is like
the weightlessness in an elevator
 The satellite and everything on it are all
accelerating toward the earth at the same rate