Gravity and OrbitsGravity and Orbits

Newton’s Law of Gravitation

The attractive force of gravity between two particles

G = 6.67 x 10-11 Nm2/kg2

• Why is this important?

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m1

m2

r

Gravity and OrbitsGravity 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 OrbitsGravity and Orbits

Tides

Caused by differences in the force of gravity across an object

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Gravity and OrbitsGravity 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 OrbitsGravity 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

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Gravity and OrbitsGravity 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 OrbitsGravity and Orbits

Kepler’s First Law

Planets orbit the Sun in elliptical paths

• Tycho Brahe – observations of Mars• Johannus Kepler – mathematical

explanation of orbits

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Sun

planet

Gravity and OrbitsGravity and Orbits

More on ellipses and orbits

Semimajor axis (a) and eccentricity (e) define the shape of an orbit

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Sun

ad

Gravity and OrbitsGravity and Orbits

Kepler’s Second Law

Planets sweep out equal areas in equal times

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Sun

Gravity and OrbitsGravity 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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