* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

# Download 2 Kepler`s Laws

Astrobiology wikipedia , lookup

Corvus (constellation) wikipedia , lookup

Kepler (spacecraft) wikipedia , lookup

History of astronomy wikipedia , lookup

Rare Earth hypothesis wikipedia , lookup

Comparative planetary science wikipedia , lookup

History of Solar System formation and evolution hypotheses wikipedia , lookup

Extraterrestrial life wikipedia , lookup

Tropical year wikipedia , lookup

Satellite system (astronomy) wikipedia , lookup

Definition of planet wikipedia , lookup

Aquarius (constellation) wikipedia , lookup

IAU definition of planet wikipedia , lookup

Solar System wikipedia , lookup

Planets beyond Neptune wikipedia , lookup

Copernican heliocentrism wikipedia , lookup

Planetary habitability wikipedia , lookup

Late Heavy Bombardment wikipedia , lookup

Formation and evolution of the Solar System wikipedia , lookup

Dialogue Concerning the Two Chief World Systems wikipedia , lookup

Ancient Greek astronomy wikipedia , lookup

Astronomical unit wikipedia , lookup

Kepler’s Laws AP Physics C Mrs. Coyle Geocentric View Points Aristotle (Greek) 384-322 BC Ptolemy (Alexandrian Greek) 85-65AD Heliocentric Viewpoints Aristarchus (Greek)310-230 BC Copernicus (Poland and Italy) 1473-1543 Galileo Galilei (Italian) 1564-1642 Compromise Theory: The Sun orbits the Earth, but the remaining planets orbit the Sun. Brahe passed along his observations to Johannes Kepler, his assistant. Johannes Kepler (1571-1630) German Astronomer Kepler’s First Law (Law of Orbits): Planets move in elliptical orbits with the Sun at one of the focal points. E LLI PS E http://www.physics.utah.edu/~cassiday/p1080/lec03_files/image004.gif e=c/a For a circle e=0 Pluto has the highest e=0.25 in our system. Earth’s e=0.017 Elliptical orbits are allowed for bound object An unbound object would pass by and not return Paths that are parabolas(e = 1) and hyperbolas (e > 1) A line from the sun to a planet sweeps out equal areas in equal lengths of time. http://astro.unl.edu/naap/pos/animations/k epler.swf The torque caused by the gravitational force on a planet is zero because it is a central force and the F is in the same direction as the r vector. τ=dL/dt =0 , so L =constant The square of the orbital period of a planet is directly proportional to the cube of the average distance of the planet from the Sun. T Kr 2 K for our Solar System 3 K 2.97 x10 19 2 3 s /m T2 = (4π2 / GMs) r3 , K= 4π2 / GMs 1 Astronomical Unit (AU)= average radius of the orbit of the earth about the sun. When T is measured in earth years and r in AU then K for our solar system =1 y2 / AU3 . Hint: The gravitational force plays the role of the centripetal force. 2 ( _ T ___ ) a Tb 3 = ( _ r ___ ) a rb An asteroid revolves around the sun with a mean orbital radius of three times that of the earth. What is the period of the asteroid in earth years? Answer: 5.2y Two same stars are orbitting about the center of mass half way between them. The orbital speed of each star is 220km/s and the orbital period of each is 14.4 days. Find the mass M of each star. Ans: 1.26x1032kg