Editing Mass (section)

=== Planetary motion ===
{{see also|Kepler's laws of planetary motion}}
In 1600 AD, [[Johannes Kepler]] sought employment with [[Tycho Brahe]], who had some of the most precise astronomical data available.  Using Brahe's precise observations of the planet Mars, Kepler spent the next five years developing his own method for characterizing planetary motion. In 1609, Johannes Kepler published his three laws of planetary motion, explaining how the planets orbit the Sun. In Kepler's final planetary model, he described planetary orbits as following elliptical paths with the Sun at a focal point of the [[ellipse]]. Kepler discovered that the [[square (algebra)|square]] of the [[orbital period]] of each planet is directly [[Proportionality (mathematics)|proportional]] to the [[cube (arithmetic)|cube]] of the [[semi-major axis]] of its orbit, or equivalently, that the [[ratio]] of these two values is constant for all planets in the [[Solar System]].<ref group=note>This constant ratio was later shown to be a direct measure of the Sun's active gravitational mass; it has units of distance cubed per time squared, and is known as the [[standard gravitational parameter]]:
: <math qid=Q140028>\mu=4\pi^2\frac{\text{distance}^3}{\text{time}^2}\propto\text{gravitational mass}</math></ref>

On 25 August 1609, [[Galileo Galilei]] demonstrated his first telescope to a group of Venetian merchants, and in early January 1610, Galileo observed four dim objects near Jupiter, which he mistook for stars.  However, after a few days of observation, Galileo realized that these "stars" were in fact orbiting Jupiter.  These four objects (later named the [[Galilean moons]] in honor of their discoverer) were the first celestial bodies observed to orbit something other than the Earth or Sun.  Galileo continued to observe these moons over the next eighteen months, and by the middle of 1611, he had obtained remarkably accurate estimates for their periods.