I am sure that you, like me, followed the 'Wake Up Rosetta' campaign with great interest, as the tiny European explorer was awoken from its 31 month slumber. It is great to see that after all that time the systems have come back online and the craft is fully functional, ready for its rendezvous with Comet 67P/Churyumov-Gerasimenko this November. I only wish my car was so reliable.
As I followed the updates, my mind drifted off to how wonderful it is that we can actually send man made objects many millions of kilometers to tiny pieces of rock and actually arrive in the right place at the right time -- particularly as the targets are often moving at many thousands of kilometers per hour themselves. Navigating around the solar system is a tricky business but it was made a whole lot easier with the 'discovery' of three laws that govern planetary motion.
It was back in the 1600's that Johannes Kepler published his three laws of planetary motion and they are still as relevant today as they were over 400 years ago. Not only do they govern the motion of the planets around the sun but they also govern the motion of moons around planets and even exoplanets around distant stars. The laws have been invaluable in understanding not only the movements of the planets in our own solar system but also help us learn about families of new planets in the depths of our galaxy.
The first of the laws states that all planets in our solar system move in elliptical orbits with the sun at one of the points of focus of the ellipse. That is not surprising, perhaps as many of us have grown up knowing that the Earth's orbit and indeed the orbits of all the planets are elliptical.
An ellipse is essentially a squashed circle and you can imagine how it might have two points of focus if you first visualize a circle with a point at its center. If you were to squash the circle from top and bottom, the central dot would split in two and both would move outward. In the case of the planets in the solar system; the sun is found at one of these points and it is that point that they all appear to orbit.
Kepler's second law states that a line joining the sun to a planet, known as the radius vector, sweeps out equal areas of space over equal time intervals. Put another way, planets move faster when they are closer to the sun and slower when further away. But it is Kepler's third and final law that was only published ten years after the first two which describes the mathematical relationship between the time it takes for a planet to complete an orbit and its distance from the sun. In the words of Kepler, "...the square of the orbital period of a planet is directly proportional to the cube of its mean distance from the sun." This means that we can measure how long an object takes to orbit the sun from simple observation and by knowing that, we can calculate its average distance with some accuracy.
Understanding these three laws gives us a great understanding as to the movement of the planets around the solar system and using them in conjunction with other laws -- such as Newton's laws of motion and small corrections for Einstein's general relativity -- means that we can navigate our way around the solar system and do it with such accuracy that we know exactly where Comet Churyumov-Gerasimenko will be 10 years after Rosetta was launched!