Transcript Universal Gravitation

Universal Gravitation
ISAAC NEWTON (1642 –
1727)
• The rate of acceleration due to gravity
at the Earth’s surface was proportional
to the Earth’s gravitational force on the
Moon.
• The Earth’s gravitational force on the
moon was inversely proportional to the
square of the Earth’s distance from the
moon.
Fg  1/r2
LAW OF UNIVERSAL
GRAVITATION
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Fg = G (m1 m2) / r2
m1 and m2 = masses of the 2 objects
(kg)
r = center-to-center distance between
the objects
G = universal gravitational constant
G = 6.67 x 10 -11 Nm2 / kg 2
HENRY CAVENDISH (17311810)
• 1798: Using a
torsion balance,
Cavendish measured
the gravitational
attraction between
small objects, and
calculated the value
of the Universal
Gravitational
Constant.
Gravity Near Earth’s Surface
• The force of gravity is the weight of the
object. Near Earth’s surface,
Fg = G (m mE) / rE 2 = mg
G (mE) / rE 2 = g
• The mass of the Earth can be
calculated from this:
mE = g rE 2/ G
Gravity Near Earth’s Surface
• The value of g on Earth can vary due to:
– Elevation and latitude (distance from
center of Earth)
– Variations in densities of rock. This may
indicate the presence of mineral or oil
deposits.
• These variations are small, but can be
measured with a gravimeter
Satellites
• Satellites are placed in orbit by “throwing”
them with enough velocity that they fall
around the earth.
– If you give it enough speed, a satellite will
escape, never to return (escape speed).
TYCHO BRAHE (1546 1601)
• Danish astronomer.
• Became astronomer to the King of
Denmark, and made highly detailed
observations of planetary
movements for over 20 years.
JOHANN KEPLER (1571 1630)
• German mathematician
• 1609: Kepler publishes a book
which describes the motion of the
planets.
– Kepler’s 1st Law: Planets move
around the sun in elliptical orbits,
with the sun at one focus.
JOHANN KEPLER (1571 1630)
• Kepler’s 2nd
Law: A straight
line connecting
the sun and a
planet sweeps out
equal areas in
equal time
intervals.
JOHANN KEPLER (1571 1630)
• Kepler’s 3rd Law: The ratio of the
squares of the periods T of any two
planets revolving around the Sun is
equal to the ratio of the cubes of their
mean distances s from the Sun.
(T1/T2)2 = (s1/s2)3
• Kepler’s 3rd law applies to any two
bodies orbiting a common center.
Kepler’s Laws and Newton’s
Synthesis
• Newton was able to show that:
– Kepler’s Laws could be derived from
universal gravitation and the laws of
motion
– Only an inverse-square relationship for
gravitation would explain Kepler’s laws.
• Deviations in the orbits predicted by
Kepler’s laws (perturbations) can be
used to locate undiscovered planets.
Types of Forces in Nature
• Four fundamental forces:
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Gravitational
Electromagnetic
Strong nuclear
Weak nuclear
• Physicists have unified the electromagnetic
and the weak nuclear forces (electroweak
force), but still seek a Grand Unified Theory
• Everyday forces are due to electromagnetic
and gravitational forces.