Keplers Laws Keplers Laws Initially it was thought

Kepler’s Laws

Kepler’s Laws • Initially it was thought of that the planets and sun revolve around the earth. • Kepler determined that – the planet must revolve around the sun – Planets move in elliptical orbits

Kepler’s 1 st Law • Law of Elliptical Orbits: ØEach planet moves in an elliptical orbit, with the sun at one focal point. ØThe planet’s orbital radius is always changing, so we use an average value.

Kepler’s 2 nd Law • Law of Equal Areas ØDuring equal time intervals, a straight line drawn from the sun to the planet will sweep out equal areas. ØSpeed must change throughout its orbit. Faster Slower

Kepler’s 3 rd Law • Law of Periods Ø The period of revolution is related to its radius of revolution

ØThe value of K is the same for all planets orbiting the sun. ØWe can compute the constant using Earth’s orbital distance and period. Ø re = 1. 49 x 1011, Te = 365 days

• To represent astronomical distances, we use the measurement called the astronomical unit (AU). • One AU is the mean distance (orbital radius) between the earth and the sun. • 1 AU ≈ 1. 49 x 1011 m

• Kepler’s constant using AU:

Example: Venus has an orbital radius of 0. 723 AU. What is its orbital period?

• The K constant is different when the object is orbiting something other than the sun. – Ex: K is different for each planet with orbiting moons. • We can set up ratios to solve problems for a planet with more than one moon.

Example: • Triton is one of Neptune’s moons with an orbital period of 5. 8766. Using the data for Proteus, another moon of Neptune, determine Triton’s orbital radius.

Homework: • Page 272 #1 -3 • Page 275 #1 -3