Nicolaus Copernicus 1473-1573 Johannes Kepler 1571 - 1630 Tycho Brahe 1546 - 1601

Kepler’s Laws of Planetary Motion

First Law – Elliptical Orbits All planets travel around the sun in an elliptical orbit (LAB) with the sun as one of the foci Because the orbits are not circular, the distance between the sun and the planet changes Eccentricity is how stretched out the planet’s orbit is (Ref. Tables, LAB)

eccentricity = dist. between foci length of major axis

When a planet is closest to the sun it is called perihelion, when it is farthest from the sun it is called aphelion Peri = Close Ap = Away Helion = SUN Earth’s perihelion is Dec. 21st – first day of winter, and Earth’s aphelion is June 21st – first day of summer

Second Law – Equal Area when the planets are closest to the sun they move faster, and when they are farthest from the sun they move slower Because of this, an imaginary line connecting the planet and sun would cover an equal amount of area during any part of its orbit

Third Law – Harmonic Law the farther a planet is from the sun, the longer its period of revolution (the longer it takes to go around the sun – common sense) Kepler stated this using the formula P² = D³, where P is the period of revolution (in Earth years) and D is the distance from the sun (in AU’s)

Astronomical Unit - the average distance between the Earth and the Sun 1 AU = 93 million miles or 147 million km

Newton’s Universal Law of Gravitation the force of gravity between any two objects is directly related to the masses of the two objects, but inversely related to the square of the distance between the centers of the two objects Change in force = 1/distance²

Simplified: The larger the objects, the greater the force of gravity between them Also, the greater the distance between the two objects, the less the force of gravity pulls on them