“Kepler’s” Laws of Orbital motion Ms. Susinno’s Earth Science Class

TYCHO BRAHE The scandalous life of Tycho Brahe https://youtu.be/7QDvKzY4aqA

Kepler’s 1st Law The planets travel in elliptical orbits around the sun and the sun is at one focus. Earth is at aphelion around July 3 Earth is at perihelion around January 3 Hmmm... But why is it warmer when we’re further from the sun?

Perihelion and Aphelion Apparent diameter is larger Apparent diameter is smaller Not to scale 

Kepler’s 2nd Law The radius between a satellite (the body doing the orbiting) and its primary (the body it orbits) sweeps out equal areas in equal times. If this takes 1 day =area =area ...this takes 1 day

Kepler’s Third Law The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit. So... If This is where the planet travels the fastest Click here for a simulation of all 3 laws! Then http://astro.unl.edu/classaction/animations/renaissance/kepler.html

And... So... If the mass of this guy is doubled.... what will happen to the gravitational force between them?

BY Alec Marshak & Kyle Harding LABORATORY SKILL Making an ellipse BY Alec Marshak & Kyle Harding

Vocabulary Review Ellipse- the actual SHAPE that the planet’s orbital path follows. a closed loop around two central foci (one focus, two foci). Eccentricity- the NUMBER describing the shape e= distance between foci length of the major axis Distance between foci major axis

Supplies Two pushpins A piece of computer paper A big piece of cardboard A 20cm long piece of string that is tied together to form a loop Lastly you need a pencil

Steps # 1-3 The lab test is 90% following directions! First fold the paper in half like a hot dog then open it and place it on the cardboard Now draw two dots that are____centimeters apart in the middle of the paper (d will be given to you) Now, follow the directions to mark one focus as the sun. The lab test is 90% following directions!

Steps #4-7 Place the pushpins into the two dots. Make sure to have pushed the pushpins all the way into the cardboard Now you will put the string around the pushpins and insert your pencil inside the string loop Use it by drawing an elliptical shape while pulling outward on the string with your pencil (make sure the string stays on the pins)

Steps 7-10 Take out the pushpins Now draw a straight line through the middle of the ellipse connecting the foci to the outside of the ellipse and label it the major axis 9.Read directions and mark the point on the ellipse where your planet would travel the fastest 10. Read your directions and compare Your ellipse to a planet’s ellipse.

Finding the Eccentricity When finding the eccentricity of an ellipse, you use the equation e=d/l . e=eccentricity, d=distance between foci, and l=length of major axis. So the steps are… Measure the distance between the foci.(cm) Measure the length of the major axis.(cm) Divide the distance between the foci by the length of the major axis and the answer is the eccentricity.(cm to the nearest thousandth)

Our Ellipse So using the steps from the last slide, we will figure out our ellipse’s eccentricity. The d=2.0 cm and the l= 10.8 cm.Next we divide 2cm by 10.8cm which equals .185.So our ellipse has an eccentricity of .185 (rounded to the nearest thousandths place FOLLOW DIRECTIONS) Now that we know our ellipse’s eccentricity we can compare it to another planet’s eccentricity (planet will be given) Our planet has a less elliptical (more circular) orbit because the eccentricity of its orbit is less than the eccentricity of Mercury’s orbit! Thank you Alec and Kyle

The sentence Be sure to discuss the SHAPE (more or less elliptical) And the NUMBER (eccentricity is lower or higher) Example: My planet’s orbit is ________________elliptical because the orbit’s eccentricity is _______________. More or less Closer to 1 (higher) OR closer to 0 (lower)

Things to remember about eccentricity Eccentricity is always a decimal. *if you get a number larger than 1, it is wrong! (you probably reversed the formula) Follow rounding directions! e has no unit! a larger decimal means the orbit’s path is more elliptical A lower decimal means that the orbit’s path is less elliptical

Who has a very elliptical orbit? All of the planets have slightly elliptical orbits with the sun at one focus. Use your ESRT and evidence from it to see which has the most elliptical orbit! Pluto (the dwarf planet) has an orbit that is much more elliptical.

Predicted next perihelion: Comets Halley’s Comet Predicted next perihelion:  July 28, 2061 A comet is an icy small Solar System body that, when passing close to the Sun, heats up and begins to outgas, displaying a visible atmosphere or coma, and sometimes also a tail. These phenomena are due to the effects of solar radiation and the solar wind upon the nucleus of the comet. 

In a world full of Tychos....

Be a Kepler.