Presentation on theme: "History of Astronomy - Part II"— Presentation transcript:
1 History of Astronomy - Part II After the Copernican Revolution, astronomers strived for more observations to help better explain the universe around themDuring this time ( ) many major advances in science and astronomy occurredKepler's Laws of Planetary MotionNewton's Laws of Motion and GravityWarning! - Math and Equations Ahead!
2 Tycho Brahe - An Observer Tycho Brahe was a prominent scholar and aristocrat in Denmark in the mid-late 1500'sHe made a huge number of observations of the stars and planets, all with the naked eyeEven without a telescope, he was very accurate in his measurementsAlso recorded the appearance of comets and supernovaeThe Tycho supernova remnant is still visible todayTycho ( )
3 Johannes Kepler - A Theorist Shortly before his death, Tycho began working with another scientist named KeplerKepler was put to the task of creating a model to fit all of Tycho's planetary dataKepler spent the remainder of his life formulating a set of laws that explained the motion of the planetsKepler ( )
4 Kepler's First LawKepler first noted that the orbital path of a planet around the Sun is an ellipse, not a perfect circleThe Sun lies at one of the foci of the ellipseThe eccentricity of an ellipse is a measure of how 'squished' from a circle the shape isMost planets in the Solar System are very close to a perfect circleEccentricity, e ~ 0 for a circleFocusFocusKepler's 1st Law: The orbital paths of the planets are elliptical with the Sun at one focus.
5 Kepler's First Law=closest to the Sun=farthest from the Sun
6 Kepler's Second LawKepler also noticed that the planets sweep out equal areas in their orbit over equal timesNotice that this means the planet must speed up and slow down at different pointsIf 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 SunKepler's 2nd Law: An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse over equal intervals of time.
7 Kepler's Third LawFinally, Kepler noticed that the period of planet's orbit squared is proportional to the cube of its semi major axisThis law allowed the orbits of all the planets to be calculatedIt also allowed for the prediction of the location of other possible planetsKepler's 3rd Law SimplifiedNOTE: 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. !!!
8 Kepler's Third Law - Examples Suppose you found a new planet in the Solar System with a semi major axis of 3.8 A.U.A planet with a semi major axis of 3.8 A.U. would have an orbital period of 7.41 yearsyears
9 Kepler's Third Law - Examples Suppose you want to know the semi major axis of a comet with a period of 25 yearsA planet with an orbital period of 25 years would have a semi major axis of 8.55 A.U.A.U.
10 Isaac NewtonKepler's Laws were a revolution in regards to understanding planetary motion, but there was no explanation why they workedThat explanation would have to wait until Isaac Newton formulated his laws of motion and the concept of gravityNewton's discoveries were important because they applied to actions on Earth and in spaceBesides motion and gravity, Newton also developed calculusNewton ( )
11 Some termsForce: the push or pull on an object that in some way affects its motionWeight: the force which pulls you toward the center of the Earth (or any other body)Inertia: the tendency of an object to keep moving at the same speed and in the same directionMass: basically, the amount of matter an object hasThe difference between speed and velocityThese two words have become identical in common language, but in physics, they mean two different thingsSpeed is just magnitude of something moving (25 km/hr)Velocity is both the magnitude and direction of motion (35 km/hr to the NE)
12 Newton's First LawNewton's first law states: An object at rest will remain at rest, an object in uniform motion will stay in motion - UNLESS acted upon by an outside forceThis is why you should always wear a seat belt!Outside Force
13 Newton's Second LawAcceleration is created whenever there is a change in velocityRemember, this can mean a change in magnitude AND/OR directionNewton's Second Law states: When a force acts on a body, the resulting acceleration is equal to the force divided by the object's massNotice how this equation works:The bigger the force, the larger the accelerationThe smaller the mass, the larger the accelerationor
14 Newton's Third LawNewton's Third Law states: For every action, there is an equal and opposite reactionSimply put, if body A exerts a force on body B, body B will react with a force that is equal in magnitude but opposite directionThis will be important in astronomy in terms of gravityThe Sun pulls on the Earth and the Earth pulls on the Sun
15 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 SunAmazingly, Newton was able to connect the motion of the planets to motions here on Earth through gravityGravity is the attractive force two objects place upon one another
16 The Gravitational Force G is the gravitational constantG = 6.67 x N m2/kg2m1 and m2 are the masses of the two bodies in questionr is the distance between the two bodies
17 Gravity - ExamplesWeight is the force you feel due to the gravitational force between your body and the EarthWe can calculate this force since we know all the variables1 Newton is approximately 0.22 pounds
18 Gravity - ExamplesWhat if we do the same calculation for a person standing on the Moon?All we have to do is replace the Earth's mass and radius with the Moon's1 Newton is approximately 0.22 pounds
19 Gravity - ExamplesIf gravity works on any two bodies in the universe, why don't we all cling to each other?Replace the from previous examples with two people and the distance with 5 meters1 Newton is approximately 0.22 pounds
20 Revisions to Kepler's 1st Law Newton's law of gravity required some slight modifications to Kepler's lawsInstead of a planet rotating around the center of the Sun, it actually rotates around the center of mass of the two bodiesEach body makes a small elliptical orbit, but the Sun's orbit is much much smaller than the Earth's because it is so much more massive
21 Revisions to Kepler's 3rd Law Gravity also requires a slight modification to Kepler's 3rd LawThe sum of the masses of the two bodies is now included in the equationFor this equation to work, the masses must be in units of solar mass (usually written as M)Why did this equation work before?Remember - for this equation to work:P must be in years!a must be in A.U.M1 and M2 must be in solar masses