Geometry of Earth’s Orbit Kepler’s Laws of Planetary Motion

Johannes Kepler German mathematician and astronomer Postulated the three laws of planetary motion based upon heliocentric model of solar system His model explains motions of the earth and celestial objects

Kepler’s First Law The orbit of a planet about a star is an ellipse with the star at one focus The star is considered a “primary” and the planet a “satellite”

Part of an ellipse: To calculate eccentricity- see esrt pg 1

Eccentricity of an ellipse e=d/L E=eccentricity D=distance between foci L=length of major axis Value calculated are between 0 and 1 (and should include a zero in front ex: 0.007) 0=most circular 1=most elliptical

Kepler’s Second Law: The radius between a satellite (such as a planet) and it’s primary (such as the sun) sweeps out equal areas in equal times. Perihelion- planet Is closest to its primary Aphelion- Planet is Furthest From its primary

Kepler’s Third Law The closer a satellite is to its primary, the faster it moves in its orbit. The closest planets move the fastest. Where is the Planet moving The fastest? C

Sir Isaac Newton (1687) Used Kepler’s Laws in developing his ideas on gravity Newton’s ideas: (universal law of gravitation) 1. Gravity is a force of attraction between objects 2. It is dependant upon the mass of the object and the distance between the objects Weight is dependant on the amount of matter in an object and the gravitational pull upon that object Elliptical shape of orbits is due to two forces- gravity and inertia

What does this mean? The faster the planet orbits its primary is due to its closeness to the primary and its mass and the mass of the primary Circular orbits have equal gravitational and inertial forces Elliptical orbits have unequal gravitational and inertial forces- Why? The force of gravity pulls the planet around its focus faster when it is closer, and slower when it is further away…

Sum it up: 1.Which planet has the most eccentric orbit? Why? 2.Which planet moves the fastest around the sun? Why? 3.Which planet moves the slowest around the sun? Why? Mercury …closest to 1 Mercury-because it is closest to the sun and smallest Neptune-because it is the furthest away