History of Astronomy - Part II. Tycho Brahe - An Observer. Johannes Kepler - A Theorist

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Ralph Sherman
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Histoy of Astonomy - Pat II Afte the Copenican Revolution, astonomes stived fo moe obsevations to help bette explain the univese aound them Duing this time (600-750) many majo advances in science and

Tycho Bahe - An Obseve Tycho Bahe was a pominent schola and aistocat in Denmak in the mid-late 500's He made a huge numbe of obsevations of the stas and planets, all with the naked eye Even without a

1 Histoy of Astonomy - Pat II Afte the Copenican Revolution, astonomes stived fo moe obsevations to help bette explain the univese aound them Duing this time ( ) many majo advances in science and astonomy occued Keple's Laws of Planetay Motion Newton's Laws of Motion and Gavity Waning! - Math and Equations Ahead! Tycho Bahe - An Obseve Tycho Bahe was a pominent schola and aistocat in Denmak in the mid-late 500's He made a huge numbe of obsevations of the stas and planets, all with the naked eye Even without a telescope, he was vey accuate in his measuements Also ecoded the appeaance of comets and supenovae The Tycho supenova emnant is still visible today Tycho (546-60) Johannes Keple - A Theoist Shotly befoe his death, Tycho began woking with anothe scientist named Keple Keple was put to the task of ceating a model to fit all of Tycho's planetay data Keple spent the emainde of his life fomulating a set of laws that explained the motion of the planets Keple (57-60)

Keple's Fist Law Keple fist noted that the obital path of a planet aound the Sun is an ellipse, not a pefect cicle The Sun lies at one of the foci of the ellipse The eccenticity of an ellipse is a

planets ae elliptical with the Sun at one focus.

2 Keple's Fist Law Keple fist noted that the obital path of a planet aound the Sun is an ellipse, not a pefect cicle The Sun lies at one of the foci of the ellipse The eccenticity of an ellipse is a measue of how 'squished' fom a cicle the shape is Focus Focus Most planets in the Sola System ae vey close to a pefect cicle Eccenticity, e ~ 0 fo a cicle Keple's st Law: The obital paths of the planets ae elliptical with the Sun at one focus. Keple's Fist Law =closest to the Sun =fathest fom the Sun Keple's Second Law Keple also noticed that the planets sweep out equal aeas in thei obit ove equal times Notice that this means the planet must speed up and slow down at diffeent points If it takes the same amount of time to go though A as it does C, at what point is it moving faste? C, when it is closest to the Sun Keple's nd Law: An imaginay line connecting the Sun to any planet sweeps out equal aeas of the ellipse ove equal intevals of time.

3 Keple's Thid Law Finally, Keple noticed that the peiod of planet's obit squaed is popotional to the cube of its semi majo axis This law allowed the obits of all the planets to be calculated It also allowed fo the pediction of the location of othe possible planets Keple's d Law Simplified P a NOTE: In ode to use the equation as shown, you must be talking about a planet in the Sola System, P must be in yeas, and a must be in A.U.!!! Keple's Thid Law - Examples Suppose you found a new planet in the Sola System with a semi majo axis of.8 A.U. P P a P yeas A planet with a semi majo axis of.8 A.U. would have an obital peiod of 7.4 yeas Keple's Thid Law - Examples Suppose you want to know the semi majo axis of a comet with a peiod of 5 yeas a 65 a P a A.U. A planet with an obital peiod of 5 yeas would have a semi majo axis of 8.55 A.U.

Keple's Laws wee a evolution in egads to undestanding planetay motion, but thee was no explanation why they woked Isaac Newton That explanation would have to wait until Isaac Newton fomulated his

Some tems Foce: the push o pull on an object that in some way affects its motion Weight: the foce which pulls you towad the cente of the Eath (o any othe body) Inetia: the tendency of an object to

4 Keple's Laws wee a evolution in egads to undestanding planetay motion, but thee was no explanation why they woked Isaac Newton That explanation would have to wait until Isaac Newton fomulated his laws of motion and the concept of gavity Newton's discoveies wee impotant because they applied to actions on Eath and in space Besides motion and gavity, Newton also developed calculus Newton (64-77) Some tems Foce: the push o pull on an object that in some way affects its motion Weight: the foce which pulls you towad the cente of the Eath (o any othe body) Inetia: the tendency of an object to keep moving at the same speed and in the same diection Mass: basically, the amount of matte an object has The diffeence between speed and velocity These two wods have become identical in common language, but in physics, they mean two diffeent things Speed is just magnitude of something moving (5 km/h) Velocity is both the magnitude and diection of motion (5 km/h to the NE) Newton's Fist Law Newton's fist law states: An object at est will emain at est, an object in unifom motion will stay in motion - UNLESS acted upon by an outside foce Outside Foce This is why you should always wea a seat belt! 4

Newton's Second Law Acceleation is ceated wheneve thee is a change in velocity Remembe, this can mean a change in magnitude AND/OR diection Newton's Second Law states: When a foce acts on a body, the

5 Newton's Second Law Acceleation is ceated wheneve thee is a change in velocity Remembe, this can mean a change in magnitude AND/OR diection Newton's Second Law states: When a foce acts on a body, the esulting acceleation is equal to the foce divided by the object's mass F a m F ma Notice how this equation woks: The bigge the foce, the lage the acceleation The smalle the mass, the lage the acceleation o Newton's Thid Law Newton's Thid Law states: Fo evey action, thee is an equal and opposite eaction Simply put, if body A exets a foce on body B, body B will eact with a foce that is equal in magnitude but opposite diection This will be impotant in astonomy in tems of gavity The Sun pulls on the Eath and the Eath pulls on the Sun Newton and the Apple - Gavity Afte fomulating his thee laws of motion, Newton ealized that thee must be some foce govening the motion of the planets aound the Sun Amazingly, Newton was able to connect the motion of the planets to motions hee on Eath though gavity Gavity is the attactive foce two objects place upon one anothe 5

6 The Gavitational Foce G is the gavitational constant G = 6.67 x 0 - N m /kg m and m ae the masses of the two bodies in question is the distance between the two bodies Gavity - Examples Weight is the foce you feel due to the gavitational foce between you body and the Eath We can calculate this foce since we know all the vaiables (6.670 N m )(7kg)(5.970 kg 6 (6.780 m) 4 kg) 705N Newton is appoximately 0. pounds 0.lbs 705N 55lbs N Gavity - Examples What if we do the same calculation fo a peson standing on the Moon? All we have to do is eplace the Eath's mass and adius with the Moon's (6.670 N m )(7kg)(7.50 kg 6 (.780 m) 7N Newton is appoximately 0. pounds 0.lbs 7N 6lbs N kg) 6

7 Gavity - Examples If gavity woks on any two bodies in the univese, why don't we all cling to each othe? Replace the fom pevious examples with two people and the distance with 5 metes (6.670 N m )(7kg)(65kg) kg (5m) N.50 N Newton is appoximately 0. pounds 0.lbs N.750 N lbs Revisions to Keple's st Law Newton's law of gavity equied some slight modifications to Keple's laws Instead of a planet otating aound the cente of the Sun, it actually otates aound the cente of mass of the two bodies Each body makes a small elliptical obit, but the Sun's obit is much much smalle than the Eath's because it is so much moe massive Revisions to Keple's d Law Gavity also equies a slight modification to Keple's d Law The sum of the masses of the two bodies is now included in the equation Fo this equation to wok, the masses must be in units of sola mass (usually witten as M ) P a M M Remembe - fo this equation to wok: P must be in yeas! a must be in A.U. M and M must be in sola masses Why did this equation wok befoe? 7

Chapter 13 Gravitation

Chapter 13 Gravitation Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects