## Wednesday, June 27, 2012

### Uncovering the Secrets of the Solar System

The cosmos: ethereal, mysterious, and unfathomable. At least, for a little while. However obscure and mystical the first speculations about the universe were, over time they were no match for astronomers looking through the lenses of empiricism.

Aristotelian "physics" was not physics in the sense we think of now. It was actually a philosophy, one of the most influential theories on the workings of the universe, accepted as the standard work to reference for over 1,000 years. Widely considered one of the greatest thinkers of all time, Aristotle proposed that the universe and the "heavenly lights" were contained in perfect concentric spheres composed of an eternal substance called "aether." However romantically arcane these ideas seem to be, they were obviously not formed from a foundation of deep scientific study. For example, another one of Aristotle’s “truths” was that flies have four legs, which was accepted by scientists for years until someone actually made some basic observations. Similarly, it would require someone to take a good look at the night sky in order to dispel Aristotle’s hypotheses about the universe.

Cue Tycho Brahe, a man as quirky as his nearly unpronounceable name, and yet a brilliant astronomer. Brahe was the first scientist to accurately observe and measure the night sky and its heavenly lights, and thus he refuted much of Aristotle's axioms. In 1572, a supernova that we now know to be 5700 light years away appeared to Brahe as a bright new star in the sky. At the time, it was believed this new star was "in the terrestrial sphere below the moon," meaning it was between the Earth and the moon. Brahe observed that the star had no parallax motion, and thus concluded it must have been past the moon and past all of the planets. Although he was the last and possibly greatest of the naked-eye astronomers, his data was later found to have some observational inaccuracies.  He claimed his measurements were within one arcminute of accuracy, but after his death it was noted that the average error was around two arcminutes, in some cases even three. However, these errors certainly do not overshadow the rest of Brahe’s accomplishments; one of his defining achievements was creating tables that corrected for atmospheric refraction in observation near the horizon. Unfortunately, soon after his remarkable discoveries he suddenly was afflicted by a fatal dose mercury poisoning. It is debated whether this was due to some kind of sinister sabotage from an enemy, or Brahe’s fondness for wearing prosthetic metal noses.

 Brahe definitely would have made People magazine's "Sexiest Men Alive" list, if he were alive

After "[living] like a sage and [dying] like a fool" (Brahe's autobiographical epitaph), his data was picked up by his student, Johannes Kepler. In addition to being a mathematics teacher and strong proponent of the Copernican heliocentric system, Kepler was a devout Christian and often related theology and religion to his research on the universe. He used Brahe’s measurements to develop his three famous laws of planetary motion, the most crucial of which to modern planetary science being the third, which states that the square of the orbital period of a planet is directly proportional to the cube of its semi-major axis. His first law states that every orbit of a planet is an ellipse, and these crucial discoveries chipped away at Aristotle’s original theories of perfect heavenly spheres. Brahe and Kepler’s contributions to observational science led the way in the Scientific Revolution, and began to demystify our solar system.

## Monday, June 25, 2012

### What About Mercury?

The transit of Mercury occurs about thirteen or fourteen times per century. They are much more common than Venus transits, and thus they may get slighted a bit by avid stargazers! So, why do they happen so often?

In general, a planet’s orbital plane can have any orientation relative to our line of sight, but only a fraction of these produce a transit. In order to calculate the probability of a transit, we need to know the range of these specific orientations as a fraction of the total possible configurations.

First, let’s assume that the planet’s orbit is perfectly circular and that its radius is much smaller than the star’s. And for the time being, we assume that the star-planet system is infinitely far away, such that all lines of sight to the system are parallel. Two angles specify all possible orientations of the planet’s orbit, with respect to our line of sight, and we integrate over the ranges of these two angles that produce transits. A two dimensional angle is called a solid angle, which maps out an area in angle-space, and in spherical coordinates this integral looks like:

$\int_{0}^{2\pi}\int_{(\frac{\pi}{2}-\arcsin\frac{R_*}{a})}^{(\frac{\pi}{2}+\arcsin\frac{R_*}{a})} \sin\theta\, d\theta d\phi$

After dividing by the sphere of total angles, which is simply equal to 4π, we are left with the probability that we will observe a transit,

$\frac{R_*}{a}$

which is just a function of stellar and orbital radii!

So we see that Mercury, which has a much smaller value of a, will have a higher probability of transit than Venus. In fact, this applies for all stars and their companions. The closer the planet, the more likely a transit is!

## Monday, June 11, 2012

### The Transit of Venus

Last Tuesday afternoon marked the last transit of Venus across the sun this century!

Our solar system was born in such a way that Earth is more-or-less aligned with the orbital planes of the other inner planets between us and the sun: Mercury and Venus. This makes it possible to view from Earth these planets trekking across the face of the sun in what scientists dub a transit. Though you might think this happens pretty often, actually witnessing a transit is a rare event, as Venus's orbital plane is tilted slightly relative to ours. Thus, Venus transits occur in pairs, and though there are only eight years in between the two, the next pair rolls around every 105-120 years!

This is an actual image of the transit taken by NASA!

The transit detection technique is used when a planet passes in front of its star, and there is a consequent drop in the measured luminosity emitting from the star. These drops are graphed and from them, we can discern the planet's mass and orbital period. In addition, a somewhat counterintuitive part of transits is when the planet passes behind the star, and the luminosity of the planet itself (however small) is lost. Transit detections can be so precise, they can detect a drop in the light curve of 1.5%! But what's really cool about the transit method is this: When the planet passes in front of the star, light shines through its upper atmosphere. By observing the resulting spectrum at various wavelengths, we can actually determine the composition of the planet's atmosphere!

Transit detection requires two conditions to work optimally. First, the plane of the orbit must be aligned with the plane of the observer. Second, this method is ideal for very large planets with small orbital radii, as their light curve will be much more pronounced.

The Kepler mission is a NASA project that's looking for Earth-size planets within the mysterious "habitable zone" of a star where liquid water can potentially exist. The telescope stares at about 100,000 stars for about 3.5 years, and can detect changes in the light curve up to 1/10,000, or 100 parts per million.

Check back later for more on the eponym of the Kepler mission, Johannes Kepler, and his contributions to astronomy.

"... the ways by which men arrive at knowledge of the celestial things are hardly less wonderful than the nature of these things themselves." -Johannes Kepler