This is a classical type of problem in physics. Imagine you are on the beach, and you throw a ball somewhere in the ocean. You the decide to have a race with someone who can get to the ball faster. Both of you run at the same speed, and when you enter the ocean, you slow down due to the water’s resistance. Therefore, the only thing that will affect who will win the race is what path each one of you takes. So the question is, which is the fastest path?
On Earth, one can indirectly find what the structure of inside the planet is by measuring the waves created by an earthquake. The Earth’s interior, having layers with different compositions, will refract and reflect those waves, and by measuring the wave all over the Earth, what can make a reasonable assumption as to what the Earth is like inside it. Unfortunately, we can’t exactly place seismographs in other planets. In the case of Saturn, though, there is a structure you can measure which will indirectly tell us what is going on inside the planet. It is the rings, which it turns out that while its shape is predominantly affected by Saturn’s moons, they alone don’t account for all the waves on it. The planet itself affects the rings, and one of the findings is that the inside of the planet is sloshing around. More details is in the link above.
I didn’t think I would live to see the day, but they did it. Obviously I have underestimated way too much the capabilities of our current technology ^_^ . The planets did have the benefit of being far away from their parents star, and they are huge, but still, it is quiet the accomplishment. I also found a science paper (which I found thanks to this) about the spectroscopy of the planets, if you want to read it (beware, not for your average joe). Yeah, not much to say about this one, the links will tell you everything.
There is exciting news for extrasolar planet enthusiasts. A planet smaller than Mercury has been discovered around a regular star, one similar to the sun. This is another excellent discovery done with the already very productive space telescope Kepler. The discovery was helped by the fact that the planet rotated very close to the star. After all, an astronomer needs to detect at least three signals in order to confirm a planet, and finding a planet that comes in front of the star from Earth’s view is more probable the closer it is. The latter is important because Kepler finds planets by looking at a dip in the star’s brightness caused by the plane moving in front of it.
Now, is it the smallest planet discovered ever? Possibly not, it is probably one of the planets of a pulsar system. But it kind of isn’t fair, since pulsars have a very regular rotation period, which one can measure because it sends out jets of lights that crosses the Earth everytime it rotates. One can use discrepancies in the rotational period to detect planets that are very small in mass. For the transit method, though, this is very good. It means we are well on our way to discovering rocky planets in habitable zones. We just need to observe a lot longer. Three years for an Earth sized object that goes around in one year. And we get even more variety in our discoveries, instead of just gas giants and superearths, which have been dominating discoveries because finding bigger things is easier.
Kepler’s first law states an object orbits another object under a gravitational pull in a conic section orbit. If the orbit is closed, it is an ellipse. It also turns out to be really hard to prove. You either have to use calculus and differential equations, or use geometry with lines and stuff and know well the properties of the ellipse. Either way, you have to set up the problems in creative ways. In this post, I would like to collect all the ways Kepler’s first law can be derived. I have always found it annoying how scattered the proofs were, and I would like to leave this behind for anyone who is itching to find out how Newton’s laws implies elliptical orbit and vice versa.
For a newbie, the best proof out there is in my opinion Feynman’s geometric proof. While it is still complicated, it is not as hard as the other proofs to understand. You don’t have to know anything too complicated except for some of the properties of the ellipse, and get used to the methods of geometry. It is also great for its clarity, unlike Newton’s geometric proof. Newton’s proof is convoluted and use really complicated geometry, but if you would like to know how the master himself did it, there it is.
The most common derivation is the differential equation approach. It is the standard textbook approach, and if you know something about calculus and differential equations, it is easier to swallow. Then there is the more complicated version which takes account of the fact that two move around a center of mass, instead of one around the other.
My favorite version, though, is the one that uses the Laplace-Runge-Lenz vector. Its derivation is elegantly simple, following directly from the approach. In the other differential equation method, you have to find the acceleration in terms of polar coordinates and then do a creative substitution that makes them end up as a simple second order differential equation. This one is somewhat less convoluted than that, and once you get the vector, you are only one step away from Kepler’s first law. In The Mechanical Universe and Beyond, video 22 titled The Kepler Problem uses this derivation.
Finally, I know there is the one that uses the complex function. Unfortunately, I can’t find it online. It is contained in this book, though.
If anyone knows of other alternatives, I can post it here.
Okay, recently, I found a new lecture on cosmology, the origin and property of the universe, and what our future universe would look like in a hundred billion years’ time. The lecture is done by professor Lawrence Krauss. He is an amazing lecturer, and I love his injection of humor into it. Trust me when I say you will learn a lot of amazing things about the universe. Some of it may be speculation, but a lot of it is experimentally verified. Check it out:
Hat tip: Pharyngula commenter Lewelly
Secondly, and this is the best of all news, they have discovered over a thousand candidates of stars harboring planets. Over the next few years, expect the number of planets discovered to increase dramatically.
hat tip: badastronomy and io9
Recently, I don’t know how long ago, though, the Zoo Universe project, which tries to involve citizens in helping out the professional astronomers sort through data, have added a new project to its list. It is called Planet Hunters. What it does is, it gathers the light curve data of stars (basically, the star’s brightness through time) from the space telescope Kepler and allows us to look at them. The basic premise is that stars have planets (well, duh), and some of those stars might have planets that orbit right in front of the star from our point of view. Those planets block some of the light from the star, thereby dimming it. By looking at the change in brightness in the curve, mainly the dipping of brightness at certain moments in time, one can detect planets, as shown in the picture below:
Of course, things aren’t as simple as that. As you will find out from checking out the web page and the tutorial, data is full of noise. The team behind this project, though, believe that because the human brain is so effective at noticing patterns, that we might be better at detecting these dips in between all of the noise than the machines. Maybe.
Anyways, go ahead and try! Who knows, maybe you might discover a planet.
This is so last year, but I want to post this for the interest of general education. The reason I am posting it this late is because I forgot, but now that I remembered, here it is. The reason I am posting this is that in astronomy, the search for extrasolar planet is more relevant than ever. Better and better technologies like the Kepler space telescope are being used to probe the vast expanses of our galaxy in search of habitable planets. The e-mail interview below is one I did for my English research report for college, but I believe you may find it of benefit too. The topic is on the method of searching extrasolar planets and some of the discoveries astronomers have made. The one being interviewed is Christine Pulliam, public affairs specialist from the Harvard-Smithsonian Center for Astrophysics, to whom I am very thankful for spending some of her probably precious time answering my request and allowing me to post this. I hope you enjoy it: Read the rest of this entry »
Wow, already the year is 2011, huh? For the first post of the year, I thought I could show you some of the pictures I took for the winter solstice lunar eclipse. It isn’t great, considering I had no telescope or tripod for my camera, but it will at least show you a general idea of what it looks like. Note, there has been a few photo manipulation just for clarity, although the difference is minimal at best, considering how small the moon looks in the pictures. Also, I used various settings in my camera, so if you wonder why two pictures similar pictures look kind of different, that is why:
The shadow of the Earth just started covering the moon.
Once the shadow is over halfway covering the moon, the moon begins turning red due to Earth’s atmosphere, which scatters the light reflected from the moon. Notice how I paid the price of not having a tripod in the middle of the three pictures above, since I had to lie on the ground perfectly still. Of course, my arms were shaking, so the moon looks like it is above the images of multiple moons.
The above two pics happened right when totality was about to happen. They are also, personally, my best pictures. Look how you can see the dark maria of the moon more clearly. Also notice that the darker part is where the moon is farther in the Earth’s shadow.
This is during totality. This is the one in which I did the most alteration with. You see, while our eyes may be able to see the moon very well, even during totality, my camera can’t. The moon is too dark, so seeing the picture kinda sucked. If I had a tripod, I could have done exposures or something. Oh woe is me without a tripod!