Astronomy

Day One

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Ptolemy

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Copernicus

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Galileo

He found the four large moons of Jupiter with his large telescope.

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Brahe

Made great measurements of the skies.

Fake nose that he lost in a duel

Assistant was Kepler

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KeplerDetermined what Brachs work was good for.

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1st law, orbits are ellipses not circles.

2nd, for similar time periods, the areas in the triangles is the same.

3rd law, T2/R3

T is time

R is distance from Sun, or other gravitationally attractive point.

Examples of Kepler's 3rd Law

Taken from The physics classroom tutorial

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Newton put these together with the three laws of motion.

a. Velocity will not change unless there is an unbalanced force.

b. Force, Mass and Acceleration are related. Force = Mass x Acceleration

c. Every action has an equal and opposite reaction.

Our understanding of the elliptical motion of planets about the Sun spanned several years and included contributions from many scientists.

a. Which scientist is credited with the collection of the data necessary to support the planet's elliptical motion?

b. b. Which scientist is credited with the long and difficult task of analyzing the data?

c. c. Which scientist is credited with the accurate explanation of the data?

Tycho Brahe gathered the data. Johannes Kepler analyzed the data. Isaac Newton explained the data

Galileo is often credited with the early discovery of four of Jupiter's many moons. The moons orbiting Jupiter follow the same laws of motion as the planets orbiting the sun. One of the moons is called Io - it's distance from Jupiter's center is 4.2 units and it orbits Jupiter in 1.8 Earth-days. Another moon is called Ganymede; it is 10.7 units from Jupiter's center. Make a prediction of the period of Ganymede using Kepler's law of harmonies.

Answer: T = 7.32 days

Given:Io: Rio = 4.2 and Tio = 1.8

Ganymede: Rg = 10.7 Tg=???

Use Kepler's 3rd law to solve.

(Tio)2/(Rio)3 = 0.04373;so (Tg)2 / (Rg)3 = 0.04373

Proper algebra would yield (Tg)2 = 0.04373 ･ (Rg)3(Tg)2 = 53.57 so Tg = SQRT(53.57) = 7.32 days

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