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## Physics…

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### Physics…

How Copernicus, Tycho, Kepler, and Newton revolutionized astronomy

Aristotle and the Greek Philosophers

- Thales (c. 624 – 546 BC)
- Anaximander (c. 612 – 546 BC)
- Pythagoras (c. 560 – 480 BC)
- Eudoxus (c. 400 – 347 BC)
- Aristotle (384 – 322 BC)

Claudius Ptolemy

- c. 90 – 168 AD
- Almagest (c. 150 AD)
- Epicycles upon epicycles in a geocentric universe

Nicholas Copernicus

- 1473 – 1543 AD
- De Revolutionibus Orbium Coelestium (1543)

Tycho Brahe

- 1546 – 1601 AD
- 20+ years of observations at observatories he designed himself with instruments he designed himself

Johannes Kepler

- From

to three “Laws of Planetary Motion” in 10 years and thousands of pages of calculations

- Conclusion:

COPERNICUS WAS CORRECT.

http://www.pafko.com/tycho/observe.html

- 1571 – 1630 AD

Kepler’s First Law

- Orbits are ellipses with the Sun at one focus.

- Orbits are …

http://www.daviddarling.info/encyclopedia/E/ellipse.html

http://www.math.rutgers.edu/courses/251/maple_new/maple3.html

Eccentricity Simulator

Earth’s elliptical orbit

- The Earth’s orbit is slightly elliptical: at its perihelion it is approximately 147 million km from the Sun, and at aphelion it is approximately 152 million km from the Sun. Which of the following is a result of the Earth’s elliptical orbit?

a. It is summertime at perihelion and

wintertime at aphelion.

b. The Earth moves faster in its orbit at

perihelion and slower at aphelion.

c. Days are longer at aphelion and shorter

at perihelion.

d. The Earth spins faster at perihelion and

slower at aphelion.

Kepler’s Second Law

- “Equal areas in equal times”: An imaginary straight line between a planet and the Sun sweeps out equal areas in equal times as the planet moves around the Sun.

http://observe.arc.nasa.gov/nasa/education/reference/orbits/orbit2.html

Simulation of Kepler’s 2nd Law

http://astro.unl.edu/naap/pos/pos_background1.html

A different solar system

- Consider two planets, Starsky and Hutch, orbiting a distant star. Starsky orbits twice as far from the star as Hutch does. How does Starsky’s orbital period compare to Hutch’s?

a. half as long

b. the same

c. twice as long

d. more than twice as long

Kepler’s Third Law

- The square of a planet’s orbital period is proportional to the cube of its semimajor axis.

http://jersey.uoregon.edu/kepler/Kepler.html

Simulation of Kepler’s 3rd Law

Additional Kepler’s 3rd Law Simulation

Isaac Newton

- 1642 – 1727 AD

Traveling out into space…

- Suppose that you are in a spaceship traveling past two different planets. You pass a blue planet that has twice the mass of the Earth at a distance of 1 AU, then you pass a red planet that has the same mass as the Earth, also at a distance of 1 AU. From which planet will you feel the greater gravitational pull?

a. the blue planet

b. the red planet

c. neither – the gravitational pull from

each planet will be equal

Still traveling…

- Suppose that you are in a spaceship traveling past two different planets. You pass a blue planet that has the same mass as the Earth at a distance of 1 AU, then you pass a red planet that also has the same mass as the Earth, but at a distance of 2 AU. From which planet will you feel the greater gravitational pull?

a. the blue planet

b. the red planet

c. neither – the gravitational pull from

each planet will be equal

Almost home…

- Compared to your mass here on Earth, your mass out in space between the stars would be

a. zero.

b. negligibly small.

c. the same.

d. unknown.

Make a distinction:

- Gravitational pull of an object
- Surface gravity of an object
- For example…

Guiding Questions

- How did astronomers/astrologers/philosophers view the universe before Copernicus?
- What did Copernicus propose, and why was it heretical?
- How did Kepler show that Copernicus was correct?
- Describe what Kepler’s Laws tell us about the motions of planets in our solar system.
- What makes an ellipse different from a random oval?
- Explain how Kepler’s 2nd and 3rd Laws are different.
- What quantities determine the force of gravity between two objects?
- Using Newton’s Law of Gravity, describe how the force of gravity varies based on objects’ masses and distance from one another.
- How does gravity explain Kepler’s 2nd and 3rd Laws?
- What is surface gravity?

Sample questions

1. a. Draw an ellipse with an eccentricity of 0.

b. Draw an ellipse with high eccentricity. Assuming this ellipse is the orbit of a comet around the Sun, show where within the orbit the Sun is located.

c. Show where the comet would move the fastest, and where it would move the slowest.

d. Halley's Comet has an elliptical orbit with a period of 76 years. Why does this comet only spend a small fraction of that 76-year period close enough to Earth and the Sun for us to see it? (Note: there are two reasons…)

2. If you were able to stand on Saturn (you couldn't really, because it is made mostly of gas), you would weigh about the same as you weigh on Earth (this means the force of gravity on you from the Earth is roughly the same as the force of gravity on you from Saturn). How is this possible – Saturn's mass is 95 times the mass of the Earth! (You do not need to do any calculations, just explain how the correct equation works…)

3. Despite the fact that Saturn’s SURFACE GRAVITY is similar to the Earth’s, its gravitational pull on its moons is much larger than the Earth’s pull on our Moon. Consider Saturn’s moon Dione, located approximately the same distance from Saturn’s center as the Moon is from the Earth’s center. For this question, assume the distances are equal.

a. WHY does Dione feel more gravitational pull than the Moon?

b. What would you expect Dione’s orbital period to be – the same as the Moon’s, larger, or smaller? Explain why.

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