Lucky Raj. This week he gets time on the biggest optical telescope in the world, the Keck Observatory. (Well now second biggest, see comments.) “The Keck” has two telescopes each 10 meters (33 feet) in diameter.

The Keck Telescopes are the largest optical telescopes in the world. Operated by University of California (my own university) and Caltech, they sit atop Mauna Kea in Hawaii at 13,800 feet above sea level
A large telescope helps you twice. First of all, a larger area means a bigger bucket with which to catch light from distant objects. The more light you can collect, the fainter objects you can see. Second, it is an inescapable law of optics that the finer detail (resolution) you want see, the bigger the lens (or in this case, curved mirror) diameter must be. That’s the main reason you might use binoculars at a baseball game or opera. There’s plenty of light. But instead of your own quarter-inch pupils you can see more detail using the 1-2 inch lenses of binoculars to create an image you can see in finer detail.
What about the Hubble Space Telescope, surely the best telescope in the world? Actually the Keck telescope is better than Hubble in all but one aspect. It is on the ground. Ground-based telescopes have to look through the air between them and space. Most of us are familiar with when looking a great distance, either down from a mountain or across a large body of water, objects on the other side are seen moving around as if they are under water. That distortion is due to rapid changes in the air, called turbulence, which mess up the image you are trying to see. Hubble’s strength is that it is above all the atmospheric turbulence.
Still Keck’s astronomers are up to a challenge. They monitor what should be point-like stars and they deform their telescopes’ mirrors within thousandths of a second to undo the atmospheric distortion. They call it “adaptive optics”. Under the right conditions, Keck can use adaptive optics to observe objects better than even the Hubble Space Telescope.
The best ground-based telescopes are located on tops of mountains to be above as much of the atmosphere as possible, or at least in locations with very stable atmosphere. Astronomers say such locations have “good seeing”. The Keck telescopes are located atop Mauna Kea, the highest point in Hawaii, at almost 14,000 feet elevation. So lucky Raj, not only does he get time on the biggest optical telescope in the world, he gets to go to Hawaii, right?
Not so fast. He only went down the hall. Professional operators point the telescopes. Modern astronomers don’t look through an eye-piece anyway, they record images with digital cameras. They receive images over the internet. So Raj just went down the hall, to a dingy little conference room with a bunch of computers. (Did anybody notice what email client Raj still uses?) If you are interested in becoming an astronomer don’t despair. Students and faculty still sometimes do go to Hawaii, or even Chile, to observe.
Raj had something exciting to do tonight, looking for planets in a stellar system outside our own. Also called extrasolar planets or exoplanets, astronomers’ instruments are actually sensitive enough to find planets orbiting other stars. But generally not by direct imaging. The nearby star is too bright and the planet is almost always too dim. In Raj’s case he was looking for a star passing in front of the star Epsilon Eridani, a star from Sheldon’s song.
Imagine you were an extra-terrestrial watching our own Earth go around the Sun from another stellar system. Our Earth has a diameter about 1/100-th the size of the Sun. So a distant observer around another star could hardly see the little bit of light reflected by the Earth from the Sun compared to the enormously bright Sun itself. But if you, the alien observer, are in just the right place, sometimes the Earth will pass between us and the S It makes a kind of tiny eclipse called a “transit”. Because area goes as the square un. of the diameter, our Earth would block out 1/10,000-th of the Sun’s brightness. A sensitive enough measurement would see its transit in principle. Observers in our stellar neighborhood would see this dimming for at most a few hours, but regularly every year. Jupiter would be much easier, it would block a full 1% of the Sun’s intensity, although only once every twelve years, the time it takes Jupiter to orbit the Sun.

During a "transit", an extra-solar planet passes in front of a star, dimming it ever-so-slightly ever-so-briefly.
Astronomers have other techniques, too. Just as stars’ gravity pulls on planets to make them go around their orbits, the planets pull on stars. Newton’s third law requires it. For every force (in this case gravitational pull of a star on a planet) there must be an equal and opposite force (in these case the pull of the planet on the star). The only difference is the stars are much more massive and don’t change their velocity anywhere near as much as the planets do in response to the same force. Thus the stars move in tiny circles with the period of the planets orbiting them. For the same reason when you jump off a table, not only does the Earth pull you down, but you pull the Earth up towards you with exactly the same force. Astronomers can measure this tiny dance of the stars by measuring their motion towards and away from us. A star that is heading towards us will emit radiation just a little bluer than one heading away from us which is just a little redder, due to a shift called the Doppler effect (remember the Halloween episode?):

The "Doppler Effect" precisely measures the motion of stars, which changes as their own planets pull on them.
Want to find more exoplanets? There’s an app for that. The iPhone has a (free) exoplanet app. It beeps every time a new extra-solar planet has been discovered. (And besides, the app has really cool animations.) So far, it is easiest to find the largest, Jupiter-sized, planets, which are closest to their host star. But as the technique improves astronomers will find smaller and smaller planets. We have not yet found a planet at the right size and distance to host water on an Earth-like surface. But it may come soon. The Kepler satellite uses the same technique as Raj, but using a space telescope so it is even more sensitive. I would not be surprised if they announce an Earth-like neighbor within the next year or so.
Astronomers know of over 500 exo-solar planets to date. Since the technique only finds really large ones so far, they are safe from Drs. Tyson and Brown.