Kepler’s 3rd Law

The STEREO spacecraft will drift in space in front of, and behind, the Earth according to a physical principle known as Kepler’s Law.

Johannes Kepler was German and lived between 1571 and 1630. He was an assistant to another astronomer, the Dane Tycho Brahe.  Tycho had spent years carefully measuring the positions of stars and planets. But Tycho and Kepler did not get along well. Tycho didn't trust Kepler.   He thought that his brilliant, young assistant might use his hard won data and and become more famous than he was. So to keep Kepler busy he set him the task of understanding the orbit of the planet Mars, which Tycho could not make any sense of.  Meanwhile Tycho  worked on his theory of the structure of the Solar System, which he thought had the Earth at its centre.  Big mistake!  The Martian  data allowed Kepler to formulate the correct laws of planetary motion, achieving more  than Tycho ever did.

Kepler found three laws of planetary motion .   It's the third that will help you design STEREO's orbits.

 

Kepler’s Third Law

 

“The period of a body to complete an orbit is related to the distance that it is from the body that it is orbiting.”

 

In other words the further away something orbits, the longer it takes to go around.

 

Kepler came up with a mathematical relationship between the two; the ‘period squared’ is proportional to the ‘distance cubed’

For our solar system, if you use Astronomical Units (AUs) and earth years, you can actually say the period squared equals distance cubed. 

 

Mathematically, this is:

 

 

This was really handy as it allowed early astronomers to work out things like the size of the solar system by observing how long it took for the planets to complete an orbit of the sun.

Initially they could only find the relative sizes of orbit because they didn't know how big an astronomical unit was.   But with the Transit of Venus of 1769 a distance for the Earth to the Sun could be calculated and the distances of all of the other planets could be worked out from this.

 

You can use this formula to work out the orbits needed for STEREO.   For STEREO A to drift ahead of Earth it needs to be closer to the Sun than the Earth and for STEREO B to drift behind the Earth it needs to be further away from the Sun than the Earth.   Exactly how much closer, and further, the spacecraft need to be is what you will calculate in Part 1 of the investigation.