Page 17 - GALIET PHYSICS BLOSSOMS II+

[The above has been compiled from slides from my EOSC 310 Earth Science Course by Dr. Mindel, and from Astronomy Today. Volume I, the Solar System. 708-721].
(iii) Explain Kepler’s 1st and 2nd laws, using accurately drawn diagrams where necessary. There is no need to go into great detail - the key is to make things clear.
Kepler’s 1st Law
Kepler’s first law of planetary motion refers to the shapes of planetary orbits:
Each planet moves around the sun in an elliptical (not circular) orbit, with the Sun at one focus.
An ellipse is a flattened circle. We can draw an ellipse with a piece of string and two thumbtacks. Where we pin the string is the ellipse’s focus (plural: foci). The ellipse’s long axis containing the two foci is the major axis. Half of it is the semimajor axis, a measure of the ellipse’s size. In a circle, the two foci coincide, and its radius is its semimajor axis.8
The ellipse’s eccentricity is the measure of its flatness. Eccentricity is the ratio of the distance between the foci to the length of the major axis. In zero eccentricity, there is no flattening, only a perfect circle, whereas in a one eccentricity, the circle is squashed down to a straight line.
While the sun resides at one focus of the elliptical orbit, the other focus is empty and physically insignificant. Yet, we can still know its location since the two foci are placed symmetrically about the center, along the major axis.
Both, the length of the semi-major axis and the eccentricity are necessary to describe the size and shape of a planet’s
8 Drawings and study summary of Kepler’s First Law from class notes and slides and from Chaisson, McMillan. Astronomy Today. 43-44. •17•