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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