Kepler’s Laws 1.Definitions: Law, Theory, etc. 2.Johannes Kepler 3.Patterns of Orbits 4.Bonus: Tycho Brahe

Definitions Fact Law Theory

Hypothesis A reason why that has NOT been tested Must be an explanation “Rain is caused by angels crying.”

Prediction Something measurable that can be used to test a hypothesis “If I kill a kitten, then that will make the angels cry and it will start raining.”

Fact Data, measurements. –“This winter Boston got inches of snow.” Sometimes, obvious conclusions from data. –“Boston’s winter of was the snowiest winter on record.”

Law A simple relationship or formula that is found through observations or experiment, and describes what happens, and may or may not address why it happens. Laws can later be explained (and turn into a theory), or can remain unexplained and thus just be coincidences (sometimes called an empirical law).

Bode’s Law Well, it’s also possible we just don’t understand planet formation well enough yet…

Theory A hypothesis (reason why) that has been tested many times and is accepted by the scientific community.

Example Theories Gravity Big Bang Nuclear fusion and fission Germs cause disease Dinosaurs were killed by an asteroid Evolution Global warming / climate change

Kepler’s Laws don’t say WHY things happen, they only describe WHAT happens.

Johannes Kepler Germany

Kepler = Heliocentric Tycho Brahe’s student, used his data to support heliocentric

Kepler’s Laws 1.Ellipses 2.Equal Areas 3.P 2 =a 3

1. Planets orbit the Sun in ellipses, with the Sun at one focus

Kepler’s Laws 1.Ellipses 2.Equal Areas 3.P 2 =a 3

2. Planets’ orbits sweep out equal areas in equal times.

2. Planets’ orbits sweep out equal areas in equal times. When one planet is closer to the Sun, it moves faster than when the same planet is farther from the Sun.

Kepler’s Laws 1.Ellipses 2.Equal Areas 3.P 2 =a 3

Period - in Earth years Semi-major axis (average distance from the Sun) - in AU One planet close to the Sun orbits in a shorter time than a different planet farther from the Sun.

Kepler’s Law of Periods Multiple Versions 1.P 2 =a 3 – around the Sun, years and AUs 2.P 2 =ka 3 – any units, but k is different for each unit set and for each central object 3.(Below) – true for all units, all central objects

P^2=a^3 PlanetP (years)a (AU) Mercury Venus0.615 Earth11 Mars1.524 Jupiter11.86 Saturn9.537 Uranus83.75 Neptune30.07

Planets PlanetP (years)a (AU) Mercury Venus Earth11 Mars Jupiter Saturn Uranus Neptune

Ex 4 The Moon orbits the Earth in 27.3 days. The Space Shuttle orbits the Earth in 90. minutes. How many times larger than the Space Shuttle’s orbit around the Earth is the Moon’s orbit? –NOTE: All calculations are from the center of the objects. For problems like this, often the size of the objects are very small compared to the distances.

Newton’s Laws (including gravity) explain all of Kepler’s Laws.

Newton’s Theories explain Kepler’s Laws 1.Ellipses Gravity (F=GMm/r 2 ) makes objects move in this sort of shape. 2.Equal Areas Conservation of Angular Momentum, which follows from Newton’s Laws. 3.P 2 =a 3 Gravity (F=GMm/r 2 ) causes this too.

Kepler’s Laws 1.Ellipses 2.Equal Areas 3.P 2 =a 3

Tycho Brahe Germany

Tycho Brahe = Geocentric Best measurements of planets

Post-Test