GravityQuiz: based on your observations of yesterdays lab:1. As a planet falls towards the sun what happens to its apparent velocity?2. Where do you think the earth travels faster in its elliptical orbit, as it approaches the sun or as it leaves the sun?3. What do you think would happen if a large meteorite hit the moon and slowed it down significantly?

Astronomy: Part IPtolemy was an astronomer, mathematician andgeographer. He codified the Greek geocentric view of the universe, and rationalized the apparent motions of the planets as they were known in his time. Ptolemy synthesized and extended Hipparchus's system of epicycles and eccentric circles to explain his geocentric theory of the solar system. Ptolemy's system involved at least 80 epicycles to explain the motions of the Sun, the Moon, and the five planets known in his time. The circle was considered as the ideal orbit even if Hipparchus proposed an eccentric motion. It was only Kepler who finally showed that the planet orbits are elliptic and not spherical.Egypt, from approx. 87 to probably 170 AD.

Copernicuswas a Polish astronomer and mathematician who was a proponent of the view of an Earth in daily motion about its axis and in yearly motion around a stationary sun. This theory profoundly altered later workers' view of the universe, but was rejected by the Catholic church

History of Astronomy - Part IIAfter 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 occurredKepler's Laws of Planetary MotionNewton's Laws of Motion and Gravity

Warning! - Math and Equations Ahead!

Tycho Brahe - An ObserverTycho 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 eyeEven without a telescope, he was very accurate in his measurements

Also recorded the appearance of comets and supernovaeThe Tycho supernova remnant is still visible todayTycho (1546-1601)

Johannes Kepler - A TheoristShortly 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 planetsKepler (1571 - 1630)

Kepler's First LawKepler 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 circleEccentricity, e ~ 0 for a circleFocusFocusKepler'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 LawKepler 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 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.

Kepler's Third LawFinally, 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 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. !!!A.U. = astronaumical unit: How many A.U.s is the earth from the sun?

Kepler's Third Law - ExamplesSuppose 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

Kepler's Third Law - ExamplesSuppose 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.

Your turn: 2B turned in1. Describe Keplers first Law2. Describe Keplers second law3. Describe Keplers third law4. Jupiter is 5.1 A.U. from the sun. How many earth years does it take for Jupiter to orbit the sun?5. Name the scientist who first believed that all planets rotate around our sun

Quiz: Keplers Law1.Pluto is 39.1 amu from the sun. How many earth years does it take for Pluto to make one revolution around the sun?P2 = a32. A meteorite has just been spotted orbiting between the Earth and Jupiter.If it takes 7 years for it to orbit the Sun how far away is it in astonaumical units from Earth?

Isaac NewtonKepler'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 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 has

The 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)

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 force

This is why you should always wear a seat belt!Outside Force

Newton's Second LawAcceleration is created whenever there is a change in velocityRemember, 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 accelerationThe smaller the mass, the larger the accelerationor

Newton's Third LawNewton'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 gravityThe Sun pulls on the Earth and the Earth pulls on the Sun

Newton and the Apple - GravityAfter 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 ForceG 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 - 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 variables Lets say you have a mass (m1) of 72kg, and the earths mass is as indicated with radius to the surface r.

1 Newton is approximately 0.22 pounds

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's

1 Newton is approximately 0.22 pounds

Your turn: 2B turned in6. How much would you weigh on the moon in pounds? 2.2 lbs = 1kg

Gravity - ExamplesIf gravity works on any two bodies in the universe, why don't we all cling to each other?Replace the info from previous examples with two people and the distance with 5 meters

1 Newton is approximately 0.22 pounds

Last one: 2B turned inPick the person sitting next to you and calculate Fg between you and that person. Estimate the distance to that person to the nearest meter.2.2 lbs. = 1kg.

Revisions to Kepler's 1st LawNewton'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 LawGravity 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

HomeworkComplete the homework questions providedNote that on the back of the sheet is information concerning the velocity of satellites in orbit around a body. Read it and be prepared to answer questions next class.