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Andrew Zimmerman Jones

Kepler's Laws Rule the Worlds (that's right ... all of them)

By June 21, 2012

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The Day the World Discovered the Sun by Mark Anderson (book cover)Earlier this month, fans of science may have heard a lot of commotion about the transit of Venus. The transit of Venus describes an event that happens at most twice a century in which Venus passes directly in a path directly between the Earth and the Sun. When the moon does this, it's an eclipse. When Venus does it, it's the transit of Venus.

The commotion was mostly related to the rarity of the event and the fact that it was truly beautiful, for those who were able to witness it. (Remember, don't stare directly at the sun to observe any astronomical event.) If you missed it, then you can check out the transit of Venus images over at About.com Space. Comedian/faux political pundit Stephen Colbert nailed it when he identified the transit of Venus as:

"Truly one of the most majestic examples of something passing in front of something else."

But once upon a time, the transit of Venus carried some pretty heavy stakes. In 1769, nations around the world (well, okay, mostly Europe) sent expeditions to measure the time of the transit of Venus. Using these calculations, they were able to apply Kepler's laws of planetary motion to figure out the distance between the Earth and the Sun. By having a more precise measurement of this distance, it improved a navigator's ability to calculate longitude while at sea, which ultimately had benefits for warfare and trade. (Back then, it seems, funding pure scientific endeavors wasn't any more popular than it is now.)

The reason this works is that Kepler's laws govern the motion of planets orbiting the sun, defining the paths that these planets take and the rates at which they move. Kepler derived these values from careful observations maintained by his mentor, astronomer Tycho Brahe, over the course of his lifetime. So, in other words, Kepler knew that his laws applied to the motion of the planets, but he didn't have a firm theoretical explanation for why this was. It was later shown that Kepler's laws could be derived from Newton's law of gravity, developed nearly a century later in 1687, thus providing Kepler's laws with a theoretical framework as well as the empirical support of evidence. It is always nice to have both, after all.

Kepler's second law of motion
Kepler's Second Law:
A line from the sun to each planet sweeps out equal areas in equal time.
Source: Wikipedia via GNU Free Documentation License

With these laws firmly in place, the only thing that remained was to make measurements of the transit of Venus and then apply some angular calculations to figure out the resulting details about the solar system ... which is where the 1769 transit of Venus expeditions come in.

The adventure of three of the major expeditions is described in thrilling detail in Mark Anderson's recent book The Day the World Discovered the Sun.  I've got to admit that I'm not necessarily the sort of guy who jumps at the chance to read travelogues of eighteenth century scientific expeditions ... but if you are, then it should definitely rank high on your reading list!

Comments

June 25, 2012 at 11:11 am
(1) Ken Koskinen says:

It’s a nice short piece. One has to keep in mind what it means that Kepler derived his laws from Tycho Brahe’s observations. It literally means the resulting planetary elliptical orbits fell in line after Copernicus’ heliocentric assumption was applied. This resulted in casting out the epicycles assumed in the then predominant geocentric model. Newton’s later laws became explanatory since the larger mass of the Sun caused the lower masses of the planets to orbit around the Sun. The upshot is you can derive Kepler’s Laws from Newton’s but not vice versa. The problem is once one begins to account for more than just a few solar system objects the calculations become so complex that accuracy suffers.

In any case, one has to keep in mind that it is not impossible for a planet to have a circular orbit about some other star. One point is there are so many degrees of departure from a perfect circular orbit that it makes it highly unlikely. This directly relates to the disturbances of all of the masses within any solar system. This means Newton’s Laws reign but Kepler’s were based on the special case of our solar system. They also most probably apply to most others.

July 11, 2012 at 7:20 am
(2) Subhrangsu Pal says:

It is a very nice and good blog by you…thank you very much to you…It is clear that Sir Kepler’s Resurch is as important as Newton….
He was confident about his work…..Great…

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