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Models of the solar system (Ch.29.1)

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1 st model of the solar system Aristotle (300’s BC) said solar system was geocentric

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1 st model of the solar system Aristotle (300’s BC) said solar system was geocentric, meaning that the earth is center.

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1 st model of the solar system Aristotle (300’s BC) said solar system was geocentric, meaning that the earth is center. This model did not make sense because some planets seem to sometimes move backward (retrograde motion)

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New model of the solar system Copernicus (Poland 1500’s): Established heliocentric model What does this mean? Galileo (Italian) got in trouble with the Roman Catholic Church for popularizing Copernican model

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Kepler’s 3Laws of Planetary Motion Kepler (Denmark): Reinforced Copernicus with laws of physics

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Law 1: Law of Ellipses Planets orbit in an ellipse an ellipse is an oval shape determined by two center points called foci (focus is singular) One of our foci is the sun

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Law 1: Law of Ellipses perihelion: the closest point of Earth to the sun in an orbit aphelion: the farthest point from the sun in an orbit When is Earth at perihelion? Does that make sense?

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Law 2: Law of Equal Areas Distance unit in our solar system See diagram below The average distance between the Earth and Sun is 1 AU (or astronomical unit)

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Illustration of Kepler's second law. The planet moves faster near the Sun, so the same area is swept out in a given time as at larger distances, where the planet moves more slowly. The green arrow represents the planet's velocity, and the purple arrows represents the force on the planet.

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Law 3: Law of Periods Describes the relationship between the average distance of a planet from the sun and the orbit period of the planet. for Earth, r³ = p² (where r = avg radius and p = orbit period). Unlike Kepler's first and second laws that describe the motion characteristics of a single planet, the third law makes a comparison between the motion characteristics of different planets. The comparison being made is that the ratio of the squares of the periods to the cubes of their average distances from the sun is the same for every one of the planets.

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Amazingly, every planet has the same p 2 /r 3 ratio. Planet Orbit Period (yr) Avg. Distance (AU) p 2 /r 3 (yr 2 /AU 3 ) Mercury0.2410.390.98 Venus.6150.721.01 Earth1.00 Mars1.881.521.01 Jupiter11.85.200.99 Saturn29.59.541.00 Uranus84.019.181.00 Neptune16530.061.00 Pluto24839.441.00 Amazingly, every planet has the same T 2 /R 3 ratio.

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Kepler and Newton Newton’s laws of motion reinforce Kepler’s Laws of Planetary Motion. For example: and object in motion wants to stay in motion unless acted upon by an outside force. What is the force that keeps planets from going off in a straight line?

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Since the planets move on ellipses (Kepler's 1st Law), they are continually accelerating, as we have noted above. This implies a force acting continuously on the planets. Because the planet-Sun line sweeps out equal areas in equal times (Kepler's 2nd Law), it is possible to show that the force must be directed toward the Sun from the planet. From Kepler's 1st Law the orbit is an ellipse with the Sun at one focus; from Newton's laws it can be shown that this means that the magnitude of the force must vary as one over the square of the distance between the planet and the Sun. Kepler's 3rd Law and Newton's 3rd Law imply that the force must be proportional to the product of the masses for the planet and the Sun. Newton's Laws reinforce Kepler's Laws mathemati cally

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