Background Material

20 Aug Background Material

Background Material

Answer the following questions after reviewing the “Kepler’s Laws and Planetary Motion” and “Newton and Planetary Motion” background pages.

Question 1: Draw a line connecting each law on the left with a description of it on the right.

 

planets move faster when close to the sun

 

planets orbit the sun in elliptical paths

 

planets with large orbits take a long time to complete an orbit

Question 2: When written as P2 = a3 Kepler’s 3rd Law (with P in years and a in AU) is applicable to …

a) any object orbiting our sun.

b) any object orbiting any star.

c) any object orbiting any other object.

Question 3: The ellipse to the right has an eccentricity of about … a) 0.25

b) 0.5

c) 0.75

d) 0.9

Question 4: For a planet in an elliptical orbit to “sweep out equal areas in equal amounts of time” it must …

a) move slowest when near the sun.

b) move fastest when near the sun.

c) move at the same speed at all times.

d) have a perfectly circular orbit.

 

Question 5: If a planet is twice as far from the sun at aphelion than at perihelion, then the strength of the gravitational force at aphelion will be as it is at perihelion.

a) four times as much

b) twice as much

c) the same

d) one half as much

e) one quarter as much

Kepler’s 1st Law

If you have not already done so, launch the NAAP Planetary Orbit Simulator.

·

 

Tip: You can     change the value of a slider by     clicking on the slider bar or by entering a number in the value box.

Open the Kepler’s 1st Law tab if it is not already (it’s open by default).

· Enable all 5 check boxes.

· The white dot is the “simulated planet”. One can click on it and drag it around.

· Change the size of the orbit with the semimajor axis slider. Note how the background grid indicates change in scale while the displayed orbit size remains the same.

· Change the eccentricity and note how it affects the shape of the orbit.

Be aware that the ranges of several parameters are limited by practical issues that occur when creating a simulator rather than any true physical limitations. We have limited the semi-major axis to 50 AU since that covers most of the objects in which we are interested in our solar system and have limited eccentricity to 0.7 since the ellipses would be hard to fit on the screen for larger values. Note that the semi-major axis is aligned horizontally for all elliptical orbits created in this simulator, where they are randomly aligned in our solar system.

· Animate the simulated planet. You may need to increase the animation rate for very large orbits or decrease it for small ones.

· The planetary presets set the simulated planet’s parameters to those like our solar system’s planets. Explore these options.

Question 6: For what eccentricity is the secondary focus (which is usually empty) located at the sun? What is the shape of this orbit?

Question 7: Create an orbit with a = 20 AU and e = 0. Drag the planet first to the far left of the ellipse and then to the far right. What are the values of r1 and r2 at these locations?

 

r1 (AU)

r2 (AU)

 

Far Left

 

Far Right

Question 8: Create an orbit with a = 20 AU and e = 0.5. Drag the planet first to the far left of the ellipse and then to the far right. What are the values of r1 and r2 at these locations?

 

r1   (AU)

r2   (AU)

 

Far Left