The Solar System

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Slide 25

Parameters of an elliptical orbit (a,e)

► Semi-major axis = a = one half the largest diameter

► Eccentricity = e = ratio of the distance between the focal points to the major diameter

For example, this ellipse has a = 1 and e = 0.5.

Perihelion = r2 = 0.5 Aphelion = r1 = 1.5

► Perihelion and aphelion

Slide 26

Example.

Determine a, e, r1, r2.

Slide 27

Isaac Newton

Slide 28

The observed solar system at the time of Newton

Sun

Mercury

Venus

Earth

Mars

Jupiter

Saturn

(all except Earth are named after Roman gods, because astrology was practiced in ancient Rome)

Three outer planets discovered later…

Uranus (1781, Wm Herschel)

Neptune (1846 Adams; LeVerrier)

Pluto (1930, Tombaugh)

Slide 29

To explain the motion of the planets, Newton developed three ideas:

The laws of motion

The theory of universal gravitation

Calculus, a new branch of mathematics

Newton solved the premier scientific problem of his time --- to explain the motion of the planets.

Isaac Newton

“If I have been able to see farther than others it is because I stood on the shoulders of giants.”

--- Newton’s letter to Robert Hooke,

perhaps referring to Galileo and Kepler

Slide 30

Newton’s Theory of Universal Gravitation

Newton and the Apple

(The apple never fell on his head, but sometimes a stupid person will say that, trying to be funny.)

Newton asked good questions  the key to his success.

Observing Earth’s gravity acting on an apple, and seeing the moon, Newton asked whether the Earth’s gravity extends as far as the moon.