History of Astronomy

History of Astronomy - Part II • After the Copernican Revolution, astronomers strived for more observations to help better explain the universe around them • During this time (1600-1750) many major advances in science and astronomy occurred • Kepler's Laws of Planetary Motion • Newton's Laws of Motion and Gravity • Warning! - Math and Equations Ahead!

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 • Eccentricity, e ~ 0 for a circle Focus Focus Kepler's 1st Law: The orbital paths of the planets are elliptical with the Sun at one focus.

Kepler's First Law =closest to the Sun =farthest from the Sun

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 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. !!!

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 years years

Kepler's Third Law - Examples • Suppose you want to know the semi major axis of a comet with a period of 25 years • A planet with an orbital period of 25 years would have a semi major axis of 8.55 A.U. 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)

Some terms • Force: the push or pull on an object that in some way affects its motion • Weight: 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 direction • Mass: basically, the amount of matter an object has • The difference between speed and velocity • These two words have become identical in common language, but in physics, they mean two different things • Speed is just magnitude of something moving (25 km/hr) • Velocity is both the magnitude and direction of motion (35 km/hr to the NE)

Newton's First Law • Newton'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 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 states: When a force acts on a body, the resulting acceleration is equal to the force divided by the object's mass • Notice how this equation works: • The bigger the force, the larger the acceleration • The smaller the mass, the larger the acceleration or

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

The Gravitational Force • G is the gravitational constant • G = 6.67 x 10-11 N m2/kg2 • m1 and m2 are the masses of the two bodies in question • r is the distance between the two bodies

Gravity - Examples • Weight is the force you feel due to the gravitational force between your body and the Earth • We can calculate this force since we know all the variables 1 Newton is approximately 0.22 pounds

Gravity - Examples • What 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's 1 Newton is approximately 0.22 pounds

Gravity - Examples • If 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 meters 1 Newton is approximately 0.22 pounds

Revisions to Kepler's 1st Law • Newton's law of gravity required some slight modifications to Kepler's laws • Instead of a planet rotating around the center of the Sun, it actually rotates around the center of mass of the two bodies • Each 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

Revisions to Kepler's 3rd Law • Gravity also requires a slight modification to Kepler's 3rd Law • The sum of the masses of the two bodies is now included in the equation • For 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

History of Astronomy - Part II