Transcript Universal Gravitation

Universal Gravitation
Circular Orbits

The moon moves in a nearly circular path around the
Earth.
• The path is called an orbit
• The period is about 28 days


The Earth and planets move in nearly circular paths
around the sun.
The moon and planets have a centripetal
acceleration.
• A centripetal force - the law of action
Central Force

There is no normal or
tension force affecting the
planets.

Like falling bodies that
accelerate, the moon
accelerates toward the earth.

Gravity is a central force.
orbital
velocity
centripetal
acceleration
Moon
Earth
Inverse Square Distance

The Earth’s radius is about
rE = 6400 km.

The distance from the Earth
to the Moon is about
380,000 km = 60 rE .

The centripetal acceleration
is a constant.

The centripetal acceleration
of the moon is known from
the period.
• g = 9.8 m/s2.
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• a = v2 / r = (4p2 / T2) r
• a = 0.0027 m/s2 = g / 3600
If a falling object and the moon are acted on by the same force,
the force gets weaker as the square of the distance.
This is an inverse square law: a = C / r2.
Mass Dependence

Newton’s law of action applies
to orbits.
• Centripetal acceleration times
mass is the force of gravity
FEM
• FEM = mM a = mM C / r2
Moon
a
Earth
Equal and Opposite

Newton’s law of reaction
also applies to the forces.
• The forces are equal and
opposite
• FME = FEM
• mE K / r2 = mM C / r2
FME
Earth
FEM
Moon
Gravitational Constant

To make these equations agree Newton made the
equation depend on the two masses.
• FEM = G mE mM / r2


Other planets also obey the same law.
The gravitational force is universal.
• F = G m1 m2 / r2

The gravitational constant, G = 6.67 x 10-11 Nm2/kg2.
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