Keplers Three Laws Keplers First Law The orbit

Kepler’s Three Laws

Kepler’s First Law • The orbit of a planet about the Sun is an ellipse _____ Sun at with the ____ focus one _____.

Kepler’s First Law Planets revolve around the sun in elliptical orbits with the sun located at one focus of the ellipse planet sun focus + center focus

Earth’s orbit A Sun P • Terminology Perihelion (P) _______: January 2 nd • Earth’s closest point to Sun (_____) • d = 147. 1 x 106 km Aphelion (A) _______: • Earth’s most distant point (_______) July 4 th • d = 152. 1 x 106 km 3% variation in Earth’s distance from the Sun

Kepler’s Second Law • A ____ line joining a planet _____ and the Sun ___ sweeps out equal areas ____ in equal intervals _______. of time

Kepler’s Second Law The line from the sun to a planet sweeps out equal areas in equal time intervals. t 1 t 2 area. A t 4 aphelion (slowest) area. B area. A = area. B if t 2 -t 1 = t 4 -t 3 perihelion (fastest)

Elliptical path/orbit followed by planet Sun + ◦

Kepler’s Third Law • The square of a planet's orbital period is proportional to the cube of the length of its semimajor axis. 2 = R 3 T • Or simply… _______ if T is measured in years and R is measured in astronomical units.

Kepler’s Third Law For any two planets, the ratio of their mean distance from the sun cubed equals the ratio of their orbital periods squared. Planets ___ far from the sun take _______ longer to orbit the sun than do planets _____ nearer the sun.

Kepler's Third Law The greater the distance from the sun, the longer the period of revolution. Two reasons: Longer orbits • ______ Slower orbital velocities. Mars – 228 mill. Km, 687 days Earth – 150 mill. Km, 365 days Not drawn to scale.

Kepler’s Laws 1. Planets move on _______ elliptical orbits 2. The planet’s radius-vector sweeps out the _____ same areas in ______ equal times 3. The squares of the periods of the planets are proportional to the cubes of their semi-major axes

Kepler’s Laws. . . Simply • Law 1: Elliptical orbits… • Law 2: Equal areas in equal times… • Law 3: T 2 = R 3 (Farther, longer …)

http: //www. geocities. com/rockhead 2333/257, 13, Slide 13 http: //www. hannibal. cnyric. org/Teacher. Webs/Toneil/power%20 point/296, 41, Structure of the Universe