The Motion of Planets Birth of Modern Astronomy OR How Nerds Changed the World!!!

 explain qualitatively Kepler’s first and second laws and apply quantitatively Kepler’s third law explain and apply the law of universal gravitation to orbital notations by using appropriate numeric and graphic analysis  distinguish between scientific questions and technological problems as applied to orbital situations Learning Outcomes (Students will be able to…):

Assumptions of Early Models of the Solar System (from the time of Aristotle…) Geocentric - Earth in the middle Everything orbits the Earth Stars are located on the Celestial Sphere Everything moves in uniform circular motions

Earth Deferent Epicycle Mars Equant Claudius Ptolemy (87-165)

Nicolaus Copernicus ( ) Errors building up Must be a better way! Let’s try a Heliocentric (or Sun- centered) system! Not any better though

Tycho Brahe ( ) Comet – beyond the Moon Supernova – far away Naked eye observations of planets Accuracy through repetition Best observations of planetary positions Hired “nerd” to help calculate model Died….

Johannes Kepler ( ) Worked for Brahe Took data after his death Spent years figuring out the motions of the planets Came up with… Three Laws of Planetary Motion

1 st Law: Planets move in elliptical orbits with the Sun at one foci Sun Foci (sing. Focus) PerihelionAphelion Average distance from the Sun = 1 Astronomical Unit (1 A.U.) = approx km

2 nd Law: Planets move faster at perihelion than at aphelion OR a planet sweeps out equal areas in equal time periods. 1 Month

3 rd Law: Period is related to average distance T = period of the orbit r = average distance T 2 = k r 3 Longer orbits - greater average distance Need the value of k to use the formula k depends upon the situation Can be used for anything orbiting anything else

Special version of Kepler’s third Law – If the object is orbiting the Sun T – measured in years, r – measured in A. U., then…. T 2 = r 3

For planets A and B, Kepler’s 3 rd Law can look like this…

Galileo Galilei ( ) Knew of Copernicus’s & Kepler’s work Used a telescope to look at the sky What did he see?

The Moon was an imperfect object Venus has phases

Jupiter has objects around it Saturn is imperfect The Sun is imperfect

Isaac Newton ( ) The ultimate “nerd” Able to explain Kepler’s laws Had to start with the basics - The Three Laws of Motion

1. Law of Inertia - Objects do whatever they are currently doing unless something messes around with them.

2. Force defined F = ma F=force m=mass a=acceleration (change in motion)

3. For every action there is an equal and opposite reaction. The three laws of motion form the basis for the most important law of all (astronomically speaking) Newton’s Universal Law of Gravitation

F=force of gravity G=constant (6.67 x Nm 2 /kg 2 ) M 1, M 2 = masses R=distance from “centers” Gravity is the most important force in the Universe

Newton’s Revisions to Kepler’s Laws of Planetary Motion: Kepler’s 1 st and 2 nd Laws apply to all objects (not just planets) 3 rd Law rewritten: 4π2 and G are just constant #s (they don’t change) M 1 and M 2 are any two celestial bodies (could be a planet and Sun) Importance: if you know period and average distance of a planet, you can find mass of Sun (2 x kg) or any planet! Mass of Sun is kg Mass of Earth is kg Mass of Mr. J is 100 kg! WOW!

An Inverse Square Law…

Another way to look at “g”…

Another way to look at gravitational potential energy of an object… (h is height but since it is arbitrary, it can be chosen as the distance from the center of the Earth to the position of the object…or r)

Some important orbital applications… Geosynchronous means having an orbit around the Earth with a period of 24 hours

Einstein viewed gravity and the motion of celestial objects, like planets, VERY differently… (1875 – 1955) Curved space-time effects both mass and light!