Tycho, Kepler and Newton

Great Astronomers

Tycho Brahe - An Observer

• Tycho Brahe was a prominent scholar and aristocrat in Denmark in the mid-late 1500's

• He made a huge number of observations of the stars and planets, all with the naked eye– Even without a telescope, he was

very accurate in his measurements

• Also recorded the appearance of comets and supernovae– The Tycho supernova remnant is still

visible today

Tycho (1546-1601)

Johannes Kepler - A Theorist

• Shortly before his death, Tycho began working with another scientist named Kepler

• Kepler was put to the task of creating a model to fit all of Tycho's planetary data

• Kepler spent the remainder of his life formulating a set of laws that explained the motion of the planets

Kepler (1571 - 1630)

Kepler's First Law• Kepler first noted that the orbital

path of a planet around the Sun is an ellipse, not a perfect circle

• The Sun lies at one of the foci of the ellipse

• The eccentricity of an ellipse is a measure of how 'squished' from a circle the shape is

• Most planets in the Solar System are very close to a perfect circle

Focus Focus

Kepler's 1st Law: The orbital paths of the planets are elliptical

with the Sun at one focus.

Kepler's Second Law

• Kepler also noticed that the planets sweep out equal areas in their orbit over equal times

• Notice that this means the planet must speed up and slow down at different points

• If it takes the same amount of time to go through A as it does C, at what point is it moving faster?– C, when it is closest to the Sun

Kepler's 2nd Law: An imaginary line connecting the Sun to any planet

sweeps out equal areas of the ellipse over equal intervals of time.

Kepler's Third Law• Finally, Kepler noticed that

the period of planet's orbit squared is proportional to the cube of its semi major axis

• This law allowed the orbits of all the planets to be calculated

• It also allowed for the prediction of the location of other possible planets

32 aP Kepler's 3rd Law Simplified

NOTE: In order to use the equation as shown, you must be talking about a planet in the Solar System, P must be in years, and

a must be in A.U. !!!

Isaac Newton• Kepler's Laws were a revolution in

regards to understanding planetary motion, but there was no explanation why they worked

• That explanation would have to wait until Isaac Newton formulated his laws of motion and the concept of gravity

• Newton's discoveries were important because they applied to actions on Earth and in space

• Besides motion and gravity, Newton also developed calculus Newton (1642-1727)

Newton's First Law• Newton's first law states: An object at rest will remain at rest, an

object in motion will stay in motion - UNLESS acted upon by an outside force

• This is why you should always wear a seat belt!

Outside Force

Newton's Second Law

• Acceleration is created whenever there is a change in velocity– Remember, this can mean a change in magnitude AND/OR

direction

• Newton's Second Law:

• Notice how this equation works:– The bigger the mass, the larger the force

– The bigger the acceleration, the larger the force

maF

Newton's Third Law• Newton's Third Law states: For

every action, there is an equal and opposite reaction

• Simply put, if body A exerts a force on body B, body B will react with a force that is equal in magnitude but opposite direction

• This will be important in astronomy in terms of gravity– The Sun pulls on the Earth and

the Earth pulls on the Sun

Newton and the Apple - Gravity

• After formulating his three laws of motion, Newton realized that there must be some force governing the motion of the planets around the Sun

• Amazingly, Newton was able to connect the motion of the planets to motions here on Earth through gravity

• Gravity is the attractive force two objects place upon one another

Revisions to Kepler's Laws

• Newton's law of gravity required some slight modifications to Kepler's laws