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GRAVITATION AND PLANETARY MECHANICS(PHYSICS 12 – NELSON)

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Earth’s Gravitational Field

g is also called the gravitational field strength

Units: N/kg

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History of Planetary Mechanics

Geocentric Model:Ptolemy

Heliocentric Model:Copernicus

Tychonic Model:Tycho Brahe

Kepler’s Elliptical Model

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Kepler’s Third Law

and Newton’s

Law of Universal

Gravitation

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http://www.youtube.com/watch?v=d__hN6nqi-k

http://www.youtube.com/watch?v=mbDQSxUXefk

http://www.youtube.com/watch?v=54MSV2B399o&feature=related

Space Flight: Applications of Orbital Mechanics

How do Satellites Work?

Satellites 101

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Gravitational Potential Energy in General

Near Earth’s surface:

However, a few hundred kilometers above the surface of Earth, why does this equation become inaccurate?

the ‘g’ value starts decreasing

Therefore, a general way of determining the Eg must be found out

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Remember, the law of universal gravitation:

In order to increase the separation between two masses such as these, work must be done

The force required to increase the separation between these two masses looks like this:

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How are force, distance, and work related? How can work be found from this Force-Distance graph?

Area under the graph (N.m)

Rearrange the equation:

Therefore: E2 =

Therefore: E1 =

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Illustration of Earth’s Potential Well

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Gravitation Potential Energy atEarth’s Surface

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Escape from Earth’s Gravitational Field

Rocket at rest on Earth: ET = Eg

Rocket in flight ET = Ek+Eg

Rocket reaches zero velocity at maximum heightET = Eg

Therefore, ET<0 and it is earth-bound

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Escape velocity from Earth

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Binding Energy

On Earth’s surface In Earth’s Orbit

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In Earth’s OrbitOn Earth’s surface

IS EQUAL TO