Determine the rectangular equation of the elliptical orbit in standard form. Using a reasonable scale, sketch on paper the orbit for Halley's comet, marking the focus that is the sun. Include on the sketch the lengths of the major and minor axes and the focal distance. Find the least distance and the greatest distance between Halley's comet and the sun. In Function mode, In Parametric mode, Compare the results from the Function and Parametric modes.
Students can research orbits of other comets and orbits of planets.
In space science, orbital velocity of a celestial body is sometimes measured as a function of position. A similar problem is to find the relation between the velocity of a pendulum and its displacement. L 3 respectively. Students should see that the plot appears to be an ellipse, centered at the origin, with a nearly vertical major axis. To write an equation of the ellipse that might fit the data they could estimate a and b from the plot.