Orbits and Kepler’s Laws

To stay in orbit… By stay in orbit, you are being pulled down by gravity and you have to miss the planet you are orbiting around Must maintain the speed, v where 𝑣= 𝐺𝑀 𝑟

Kepler’s First Law Each planet/object moves around the sun in an orbit which is an ellipse. The sun is at one of the two foci of the ellipse Also known as the law of ellipses A circle is a special type of ellipse where the two foci are in the same spot A parabola is just a part of an ellipse

Kepler’s Second Law 2) The straight line joining a planet and the sun sweeps out equal areas in space in equal intervals of time

Kepler’s Second Law As the object get’s closer to a foci, it’ll move faster

Kepler’s Third Law The cube (x3) of the average radius (r) of a planet’s orbit is directly proportional to the square of the period (T) of the planet’s orbit 𝑟 3 ∝ 𝑇 2 𝑟 3 = 𝐶 𝑠 𝑇 2 Cs- Constant of Proportionality (m3/s2)

Derive Cs from speed and orbital speed 𝐶 𝑠 = 𝐺𝑀 4 𝜋 2

The Search For Exoplanets We look for a dim spot passing across a star (equivalent to a fly moving across a spot light) If we know the time it takes to complete one orbit and the approximate mass of the star then… We can find out the average distance of the orbit