Transcript on ellipses and orbits

Gravity and Orbits

Newton’s Law of Gravitation

The attractive force of gravity between two particles
r

G = 6.67 x 10-11 Nm2/kg2
m1
• Why is this important?
m2
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Gravity and Orbits

Earth’s composition and g
The value of g = 9.8 m/s2 is an average value
for objects near the Earth’s surface

Variations are due to altitude, the shape of the
Earth and its local density

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Gravity and Orbits

Tides
Caused by differences
in the force of gravity
across an object

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Gravity and Orbits

Tides
The Sun’s tidal effect is
smaller than the Moon’s even
though it has a larger
gravitational pull on the Earth.

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Gravity and Orbits

Newton’s Cannon
A thought experiment that related the motion of
the Moon around the Earth and a falling object

How fast would you need to travel to orbit the
Earth?

• v ~ 8000 m/s ~ 17,600 mi/h
• Why does this only happen when in outer space?
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Gravity and Orbits

Circular Orbits
Satellites travel at a constant speed depending
on their distance from the central body

The mass of the satellite does not affect its
orbital speed

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Gravity and Orbits

Kepler’s First Law

Planets orbit the Sun in elliptical paths
• Tycho Brahe – observations of Mars
• Johannus Kepler – mathematical explanation of orbits
planet
Sun
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Gravity and Orbits

More on ellipses and orbits
Semimajor axis (a) and eccentricity (e) define the
shape of an orbit

d
a
Sun
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Gravity and Orbits

Kepler’s Second Law

Planets sweep out equal areas in equal times
Sun
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Gravity and Orbits

Kepler’s Third Law
Relationship between the orbital period and the
semimajor axis: T2 ~ a3

• Assumes that m1 >> m2
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