Kepler’s Three Laws

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

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

Earth’s orbit Terminology Perihelion (P): Sun Terminology Perihelion (P): Earth’s closest point to Sun (January 2nd) d = 147.1 x 106 km Aphelion (A): Earth’s most distant point (July 4th) d = 152.1 x 106 km P 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. t1 areaA t2 t4 aphelion (slowest) perihelion (fastest) areaB areaA = areaB if t2-t1 = t4-t3 t3

Speed During Orbit ***Slower at Aphelion(Further away) ***Faster at Perihelion(Closer to)

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. Or simply… T2 = R3 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. Mars – 228 mill. Km, 687 days Two reasons: Longer orbits Slower orbital velocities. Earth – 150 mill. Km, 365 days Not drawn to scale.

Kepler’s Laws 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: T2 = R3 (Further, longer …)