Nicolaus Copernicus1473-1573

Tycho Brahe1546 - 1601

Johannes Kepler1571 - 1630

Kepler’s Laws of Kepler’s Laws of Planetary MotionPlanetary Motion

First Law – Elliptical OrbitsFirst Law – Elliptical Orbits

• All planets travel around the sun in an All planets travel around the sun in an elliptical orbit (LAB) with the (LAB) with the sun as one of the foci

• Because the orbits are not circular, the Because the orbits are not circular, the distance between the sun and the planet distance between the sun and the planet changeschanges

• Eccentricity is how stretched out the the planet’s orbit is (Ref. Tables, LAB) planet’s orbit is (Ref. Tables, LAB)

eccentricity = eccentricity = dist. between focidist. between foci length of major length of major

axisaxis

• When a planet is closest to the sun it is When a planet is closest to the sun it is called called perihelion, when it is farthest from the , when it is farthest from the sun it is called sun it is called aphelion

Peri = CloseAp = AwayHelion = SUN

• Earth’s perihelion is Dec. 21Earth’s perihelion is Dec. 21stst – first day of – first day of winter, and Earth’s aphelion is June 21winter, and Earth’s aphelion is June 21stst – – first day of summerfirst day of summer

Second LawSecond Law – – Equal AreaEqual Area

• when the planets are when the planets are closest to the sun they move faster, and when they are , and when they are farthest from the sun they move slower

• Because of this, an imaginary line Because of this, an imaginary line connecting the planet and sun would connecting the planet and sun would cover an equal amount of area during cover an equal amount of area during any part of its orbit any part of its orbit

Third LawThird Law – – Harmonic LawHarmonic Law

• the the farther a planet is from the sun, the longer its period of revolution (the (the longer it takes to go around the sun – longer it takes to go around the sun – common sense)common sense)

• Kepler stated this using the formula Kepler stated this using the formula P² = D³, where P is the period of revolution , where P is the period of revolution (in Earth years) and D is the distance (in Earth years) and D is the distance from the sun (in AU’s)from the sun (in AU’s)

Astronomical Unit - the average distance Astronomical Unit - the average distance between the Earth and the Sun between the Earth and the Sun

1 AU = 93 million miles or 147 million km1 AU = 93 million miles or 147 million km

Newton’s Universal Law of Newton’s Universal Law of GravitationGravitation

• the force of gravity between any two objects the force of gravity between any two objects is directly related to the masses of the two is directly related to the masses of the two objects, but inversely related to the square objects, but inversely related to the square of the distance between the centers of the of the distance between the centers of the two objectstwo objects

Change in force = 1/distance²Change in force = 1/distance²

Simplified:Simplified:

• The The larger the objects, the greater the force of gravity between thembetween them

• Also, the Also, the greater the distance between the two objects, the less the force of gravity pulls on them pulls on them