Transcript Universal Gravitation

Newton’s Law of
Universal Gravitation
Who Found It?
Universal Law of Gravitation
Universal Law of Gravitation
Universal Law of Gravitation
Universal Law of Gravitation
Universal Law of Gravitation
Universal Law of Gravitation
Universal Law of Gravitation
Universal Law of Gravitation
Cavendish
The Statement
of the Law

Magnitude: Every particle in the universe
attracts every other particle with a force that is
proportional to the product of their masses and
inversely proportional to the square of the
distance between them.
F G

m1m2
r2
G  6.67 1011 N  m2 / kg 2
Direction: This force acts along the line joining
the two particles.
Gravity Near the Earth’s Surface
m1m2
mE m

G
 mg
2
2
r
rE
m
g  G 2E
rE
grE2
mE 
 5.98 1024 kg
G
F G
Moon:
Special Satellite
22
Mass
:
7.35

10
kg


Dis tan ce :1.5 108 km

Period : 29.5306days
Earth: the Satellite of the sun
Kepler’s Laws
Johannes Kepler discovered 3 laws
from the motion of the planets as
mapped by Tycho Brahe
1.
2.
3.
Planetary orbits are elliptical not circular
Orbits sweep out equal areas in equal times
T2 /r3 = k where k = “constant”
The orbits of the planets are
ellipses, with the sun at one
focus.
(Law of Ellipses)
The closer the planets are to one
another,
the more circular the orbit.
Kepler’s 2nd Law
An imaginary line drawn from
the center of the sun to the
center of the planet will
sweep out equal areas in equal
intervals of time.
(Law of Equal Areas) Deals with
speed…
faster when closer to the sun.
Kepler’s 2nd Law
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 their average
distances from the sun.
(Law of Harmonies)
(TA /TB)2= (rA /rB)3
Satellite Motion

If a projectile moves fast enough, it falls at the
same rate that the Earth curves
Satellites


What keeps a satellite up?
Its high speed
How they move?
2
msat mE
vsat
G 2 m
r
r
How fast are satellites moving?
Weightlessness
What is gravity in outer
space?
Where space shuttle
orbits…g = 8.7m/s
How come astronauts
are “floating” then?
g = F/m