Nodes and Inclination
Chapters 12 and 13
Earth and Mars going about the sun. Lines are drawn from the sun through the Earth and Mars to the sphere of the stars, and from the Earth through Mars as well (green). The ecliptic is the blue line on the sphere, the inclination is red, and the observed latitude is green. There are only two times that the red inclination and the green latitude line up:
In chapter 13, Kepler uses (2) to find the inclination of Mars. By using observations when the Earth and Sun are equidistant from Mars, the inclination of Mars can be determined. If two people on a relatively level field are the same distance from an object, it will appear equally tall to them -- this is what your mind does all the time to estimate sizes and distances. If you see a person who looks tiny in your field of vision (latitude from head to toe), it is because the person is far away! Likewise, when a familiar object is large in your field of view, it is because it is close. Watch the blue and red bars at the bottom of the animation -- when they are equal, the inclination and latitude do indeed coincide. An interactive 3D animation is available here. Kepler also offers two other ways to determine inclination in chapter 13, available by clicking here.