Question

Kepler’s 1st Law

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

• 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 semi-major 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.  

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

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 orbital options let you set the simulated planet’s parameters to those like our solar system’s planets. Explore these options.

Question It is easy to create an ellipse using a loop of string and two thumbtacks. The string is first stretched over the thumbtacks which act as foci. The string is then pulled tight using the pencil which can then trace out the ellipse. Assume that you wish to draw an ellipse with a semi-major axis of a = 20 cm and e = 0.5. Using what you have learned earlier in this lab, what would be the appropriate distances for a) the separation of the thumbtacks and b) the length of the string? Please fully explain how you determine these values.

Answer 1