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9.4. Planetary Motion and Orbits
Famous Astronomers, 1473-1726
• Nicolaus Copernicus (1473-1543), Polish – formulated a testable heliocentric model
• Tycho Brahe (1546-1601), Danish – made accurate astronomical observations
• Galileo Galilei (1564-1622), Italian – defended the heliocentric model with data
• Johannes Kepler (1571-1630), German – stated Three Laws of Planetary Motion
• Isaac Newton (1642-1726), English – explained planetary motion as due to gravity
Kepler’s Three Laws
Kepler deduced three Laws that all the planets, including Earth, follow. He was not quite sure why they obeyed these Laws, just that the data showed that they did. (This is regarded as a great example of the Scientific Method.)
Kepler’s First Law: The planets follow elliptical orbits---not circles---with the Sun at one at one focus of the ellipse.
Ellipses
Kepler’s Second Law
Kepler’s Second Law: As a planet moves in its orbit, it sweeps out an equal amount of area in an equal amount of time.
Kepler’s Third Law
Kepler’s Third Law: The orbital period of a planet (the time it takes to complete one orbit) increases as its distance from the Sun raised to the 3/2 power.
Newton’s Synthesis of Kepler’s Laws
Newton’s Synthesis: The Moon is Accelerating Toward Earth!
Though it never gets any closer…
The Moon is in “free fall”.
Alternative Views
The Moon is continually falling, but the Earth curves from underneath it.
The Moon is Accelerating Toward Earth!
An object in orbit is weightless.
The Moon is Accelerating Toward Earth!
1. An object in closer orbit needs a higher velocity. 2. This velocity does not depend on the object’s mass.
To have a circular orbit, an object needs a specific tangential velocity:
Orbital Motion
Newton considered an object thrown horizontally from a high mountain. The greater its initial velocity the farther away it would land---and if the velocity were great enough, the object would achieve orbit.
My Solar System
http://phet.colorado.edu/en/simulation/my-solar-system
mass x y x y
body 1 2000 0 0 0 0
body 2 .006 150 0 0
body 2 Velocity y
0
100
250
365
450
730
Result
Crashes.
Crashes.
Elliptical orbit around far focus.
Circular orbit.
Elliptical orbit around near focus.
Escapes.
Newton’s Synthesis
Example 9.11
Earth’s orbit is slightly elliptical. Earth is closer to the Sun in January (1.47×1011 m) than in July (1.52×1011 m). Is the speed of the Earth in January greater than, less than, or equal to its speed in July?
Greater than, according to Kepler’s Second Law.
Discovery of Neptune
The existence of Neptune was inferred from deviations in the orbit of Uranus. Newton’s law was used to predict its location, and Neptune was found on the first night of observations.
Tides
Tides are caused by the gravitational force of the Moon and Sun.
Tides
Tides may be a reliable source of
renewable energy.
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