MAPPING THE SOLAR

SYSTEMThe Tycho Brahe, Johanes Kepler

Connection

MAPPING THE SOLAR SYSTEM

1. Tycho Brahe

2. Johannes Kepler

3. Keplers Laws

4. Sample Problems

Tycho Brahe

Born 1546 in Denmark

At age 15 went to Leipzig at to study law,

secretly studied astronomy.

Spent several years at European universities

studying astronomy

Tycho Brahe

The king of Denmark and Norway gave Tycho a

prodigious quantity of cash ($5 billion in today's

money, by one estimate) and his own island.

Tycho Brahe Accomplishments

observed one of the first

supernovae to be seen with the

naked eye (new star)

He proved that comets are not

objects in the atmosphere.

He showed irregularities in the

moons orbit.

He made an instrument out of

brass and wood that could measure

the altitude of the sun and planets

to 1/6 of a minute of arc.

Tycho believed that the earth was

fixed in the center of the world.

Around the earth circulated the

moon and the sun.

Around the sun orbited the rest of

the planets

Tycho Brahe other “ Accomplishments ”

At age 20-year-old Tycho was studying at the University of Rostock in Germany. Attending a dance at a professor's house.

He got into a quarrel with one Manderup Parsbjerg, like himself a member of the Danish gentry.

Over a woman? No!, the two were fighting over some fine point of mathematics. (Fermat's Next-to-Last Theorem, which posits that 2 + 2 = 5 for very large values of 2.)

They got into it again at a Christmas party a couple weeks later and decided to take it outside in the form of a duel.

The duel was conducted in pitch darkness with swords. Parsbjerg, a little quicker off the dime, succeeded in slicing off the bridge of Tycho's nose.

Tycho Brahe other “Accomplishments ”

Had an artificial nose made, not from wax, but from an alloy of gold and silver

Carried a small box with a paste or glue, with which he often would put on the nose.

Never married the mother of his eight children,

Employed a dwarf as a jester,

Kept a pet elk (which died after breaking a leg while going downstairs drunk),

Tyrannized the local peasantry.

Managed to tick off everyone in Denmark,

Eventually found it wise to leave the country.

Relocated to Prague

Rumor: died after drinking heavily at a dinner.

Johannes Kepler

Born Dec. 27 1571.

He studied astronomy at the University of

Tubingen.

Died Nov. 15 1630.

Johannes Kepler

Accomplishments

First to investigate the formation of pictures with a pin hole camera;

First to explain the process of vision by refraction within the eye;

First to formulate eyeglass designing for nearsightedness and farsightedness;

First to explain the use of both eyes for depth perception.

First to describe: real, virtual, upright and inverted images and magnification;

First to explain the principles of how a telescope works;

First to discover and describe the properties of total internal reflection

Johannes KeplerTycho Brahe’s Assistant

1600. Johannes Kepler is employed as an assistant.

Kepler and Brahe did not get along well.

Unlike Brahe, Kepler believed firmly in the Copernican system. (Sun at Center of Universe)

Brahe feared that his bright young assistant might eclipse him as the premiere astonomer of his day.

He let Kepler see only part of his voluminous data.

Two days after Tycho's death, Kepler was appointed his successor as imperial mathematician.

He inherited Tycho's observations as well as the responsibility to complete his unfinished work.

Keplers Solar System

Keplers Laws of Planetary

Motion

1st Law: Planets move in ellipses with the

Sun at one focus.

Keplers Laws of Planetary

Motion

2nd Law: The radius vector describes equal areas

in equal times

Keplers Laws of Planetary

Motion

3rd Law: The ratio of the squares of the

revolutionary periods for two planets is

equal to the ratio of the cubes of their

semimajor axes.

T2/T2 =r3/r3

Or

The Period of the Planet are proportional to the

3/2 power of the major axis length of the orbit.

T=2πr3/2/(√Gm)

T=2 πr√(r/Gm)

r=length of semi major axis

=length of major axis divided by 2

Sample Problems

Planet Period of Orbit Average

Orbital Radius

Mercury 88 days

Earth 1 year 1 A.U.

Mars 2.125 A.U.

Saturn 29 years

Sample Problems

The average radius of the moons orbit around

the earth is 384 748 km and has a period of 27.3

days. A Direct TV satellite has a period of

exactly one day.

What is the radius of the satellites orbit?

How far is the satellite above the Earths surface?