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Johannes Kepler (1571 – 1630)Used the precise

observational tables ofTycho Brahe to study

planetary motionmathematically.

1. Circular motion and

• Planets move around the sun on elliptical paths,with non-uniform velocities.

Found a consistentdescription by

abandoning both:

2. Uniform motion.

Kepler’s Laws ofPlanetary Motion

1. The orbits of the planets are ellipses with thesun at one focus.

c

Eccentricity e = c/a

Eccentricities of planetary orbitsOrbits of planets are virtually indistinguishable from circles:

Earth: e = 0.0167Most extreme example:

Pluto: e = 0.248

But their centersmay be

significantly offsetfrom the sun.

3. A planet’s orbital period (P) squared isproportional to its average distance from thesun (a) cubed:

Py2 = aAU

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2. A line from a planet to the sun sweeps overequal areas in equal intervals of time.

(Py = period in years; aAU = distance in AU)

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Galileo Galilei(1594 – 1642)

•Introduced the modern view ofscience:

•Transition from a faith-based“science” to an observation-based science.

•Greatly improved on the newlyinvented telescope technology.

•Galileo did NOT invent thetelescope!

• Was the first to meticulously reporttelescope observations of the sky tosupport the Copernican model ofthe universe.

Major discoveriesof Galileo (I):

• Moons of Jupiter (4 Galilean moons)

• Rings of Saturn

(What he really saw)

Major discoveries of Galileo (II):

• sunspots (proving that the sun is not perfect!)

• Phases of Venus (including “full Venus”), provingthat Venus orbits the sun, not Earth!

Major discoveries of Galileo (III):

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Historical Overview Isaac Newton (1643 - 1727)

• Building on the results of Galileo and Kepler

Major achievements:1. Invented calculus as a necessary tool to solve

mathematical problems related to motion

• Adding physics interpretations to the mathematicaldescriptions of astronomy by Copernicus, Galileo and Kepler

2. Discovered the three laws of motion3. Discovered the universal law of mutual gravitation

The Universal Law of Gravity

• Any two bodies are attracting eachother through gravitation, with a forceproportional to the product of theirmasses and inversely proportional tothe square of their distance:

F = - G Mmr2

(G is the gravitational constant.)

Orbital Motion (II)In order to stay on a closed

orbit, an object has to be withina certain range of velocities:

Too slow : Object falls backdown to Earth

Too fast : Object escapesthe Earth’s gravity