Have We Found Planets Using Math?

Planets Found by Math

Urbain Le Verrier

Ancient peoples have always known about Mercury, Venus, Mars, Jupiter and Saturn because you can easily see them with you eyes. The discovery of Uranus was the first time a planet was found that needed the aid of a telescope to be see. William Herschel discovered this planet in 1781.

In the next century, another planet was discovered, and this one was discovered in a very interesting way. The credit for finding planets is usually thought to go to the first person to point their telescope at it, but this case is a little different. In the 1845, Urbain Le Verrier looked very closely at the orbit of Uranus, and discovered it to be slightly off from what was known from Kepler about planetary motion. Soon after, he had a hypothesis that another planet beyond the orbit of Uranus could account for the perturbations in the orbit he observed. Le Verrier contacted Johann Gottfried Galle at the Berlin Observatory and told him to point his telescope at a particular location at a particular time to look for this eighth planet.

Johann Gottfried Galle

Sure enough, when Galle peered through the telescope lens on September 23^rd in 1846, there sat Neptune, 1° away from Le Varrier's predicted position. Interestingly, the director of the Cambridge observatory, James Challis, later realized he too had seen Neptune on two separate occasions before that, but failed to recognize it as a planet.

This, however, was not the only planet found by math. Later on, small perturbations were noticed in the orbit of the planet Mercury, again by Le Verrier. A small planet was hypothesized, this time inside the orbit of mercury, too close to the sun to see. This theorized planet was given a name – Vulcan.

Yes, the one and same, though the hypothesized planet came before the Star Trek series by more than a century (and was the Roman god of fire, volcanoes, and metalworking well before that). This planet does not actually exist. We have since sent spacecraft close enough to the sun to see any potential Vulcanoids, and to date have found none. So what of the perturbations of the Mercurial orbit? The answer is relativity. Because Mercury is so deep in the sun's gravity well, it experiences relativistic affects, and this accounts perfectly for the precession observed in its orbit.

Image: Terry Virts

LLAP

Cheers,

    - Scott

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How Random is a Deck of Cards?

A Humble Deck of Cards

Here is a short post about a humble deck of cards. Statistically speaking, after 7 riffle shuffles (below) of a deck of cards, a deck of cards is appropriately shuffled, meaning that the deck could now be in any one of 10⁶⁸ possible arrangements.

Image: Johnny Blood

To put that number in perspective. If there were a quadrillion galaxies (10¹⁵), each galaxy with a trillion suns (10¹²), each sun with a trillion planets (10¹²), each planet with a trillion inhabitants (10¹²), and each inhabitant shuffled a deck of cards every second, and had been doing this since the beginning of the universe (10¹⁷), we would only now be expecting to be getting repeats.

Every shuffled deck of cards, to an extraordinary significance can be said to be truly unique, that is no deck of cards has ever been in that order before, nor will any ever be in that order again.

Except the order that new decks come in. That happens all the time.

Cheers,

     - Scott

What Can We Learn From Twinkling Starlight?

When you look up at the night sky, the stars twinkle. This is interesting, but not what I am talking about today. If you are curious why the stars twinkle from here on Earth check out this video:

There ya go. Now, the 'twinkling starlight' I'll be mainly talking about is related to exoplanets, or planets orbiting stars other than our own. If you look carefully at stars from outside our atmosphere, or correct for atmospheric effects, the stars still twinkle, but for what I think is a much more interesting reason.

Do you want to know something interesting about starlight?

Great!

For the longest time, it was thought that our planet and our solar system were pretty unique. Aristotle laid down the thinking about many topics including astronomy for many centuries, and as it turns out he was wrong about a fair bit of it. While understandable for his time, by the 1600's, times were changing. In the early 1600's Galileo looked up at the moon with a telescope he made (didn't invent) and observed the moon's terminator, the area where light met dark. In the shadows he saw craters, bumps, and ridges; the moon wasn't a perfect celestial orb, it was its own world with its own unique features. Couple that with his discovery of moons orbiting Jupiter, and we were on our way to discovering other worlds, inferred from points of light.

*IC6.G1333.610s, Houghton Library, Harvard University

Both the cratering of the moon and the motion of the Jovian
moons were published by Galileo in 1610 in this pamphlet.

We have now sent spacecraft to nearly all of the thirty or so largest bodies in the solar system. With missions visiting the asteroids Vesta and Ceres, and the upcoming mission to Pluto, New Horizons, our curiosities about other worlds just took steps much farther afield.

Just as we could see other worlds in our own solar system, we can now look for worlds orbiting other stars using several methods of analyzing flickering starlight from their home star. With few exceptions, we cannot just take pictures of the planets because their star outshines them by many orders of magnitude, what we can see it the influence they have on their star.

Transit method -

One way to detect exoplanets is too find a planet that passes directly between its home star and us here on earth. A bit like a solar eclipse. When this happens, the planet blocks a little bit of the light, and the star dims. We can track the stars brightness and if it dims consistently and periodically we can tell that there is probably a planet orbiting that star. Here is what one of these dips looks like:

Image: Nikola Smolenski

The transit method is currently by far the most common way to detect exoplanets, but it has its drawbacks. Due to the fact that the planet has to pass between the star it is orbiting and the observer here on earth, it biased toward planets that orbit "edge - on" to us here on earth. Imagine flipping a coin, and taking a picture when the coin is exactly edge-on. Most of the pictures are going to show at least some of either the heads side or the tails side. This is roughly the same probability as a particular star system appearing exactly edge on to ours so the planet passes in front of the sun.

This method tends to be biased in finding large planets orbiting close to their stars. The larger and closer to its star that a planet is, the more likely it is to cross in front of the star and dim the light we see. These planets are known as "hot Jupiter" because they tend to be larger than Jupiter and closer to their star than Mercury is to our sun. This flies in the face of how we think planets developed, suggesting that hot Jupiters are quite rare. If this is the case, there could many, many more planets out there than we can currently find using this method.

It is important to note at this point that we cannot see the outline of the planet in front of the star. The only thing we can detect from here on earth is the slight dimming from a distant point of light.

Other Methods

Two more ways I'll briefly touch on on the radial velocity method and something called astrometry.

To describe the radial velocity method I first have to talk about the Doppler effect.

<sidenote>
I always thought "Christain Doppler and the Effects" would make a great band name
</sidenote>

There are plenty of great video about how this works, so I'll only go into it very briefly here. When a noise-making object approaches you, the sound waves "stack up" and compress on their way to your ears. This registers as a higher pitch. When the noise-making object moves away from you the sound waves "stretch out" and you register this as a lower pitch. This is why cars passing you make the characteristic "weeeee-yahhhhhh" sound.
The same goes for light. When an object is moving toward you, you register the compression of the waves as a "blueshift," the object literally looks a bit bluer. When the object travels away, the light looks redder, a "redshift."

TL;DR: Stars look bluer moving toward you, redder when they're moving away.

Alright, on to radial velocity. A large planet orbiting a star will cause the star to wobble a little bit, as seen below:

This is because the planet gravitationally tugs on the star, just as the star tugs on the planet. Notice how the star moves up and down. If we look at this star from earth, we can see it getting redder and bluer as it travels farther and closer to us, and from that, infer the presence of a planet by looking at the rate of the wobble.

On to Astrometry!

If you imagine looking at the system above from earth just as it is portrayed, you would see the star travelling in a little circle. If you look at both the foreground star as well as background objects, you can see the motion of the star and from that find out characteristics of the planet orbiting it.


This topic is difficult to convey through writing alone, so if you're interested check out YouTube for some great videos about exoplanets and exoplanet detection. Here are a few of my favorites:

Overall, it is truly amazing what we can discover merely by looking at twinkling starlight.


Cheers,

   - Scott



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Bonus!

On Gravity

When thinking about the force of gravity, it is tempting to think that it is a very strong force. After all, it seems to be quite dominant in our lives. Rockets struggle against it, it limits the feats of many athletes to fewer home runs, fewer field goals and fewer slam dunks. It is the force that in massive amounts can break the very fibers of spacetime with black holes.

However, this force is minuscule compared to the forces at work on an atomic scale. In an atom, there are neutrons and protons in the nucleus and electrons that surround the nucleus. The neutrons repel each other and yet are held together by strong nuclear forces.

If we existed at this scale, we would most likely not know about gravity. Gravity at this scale only accounts for about one ten thousand trillion trillion trillionths of the force you feel. That is 40 orders of magnitude.

It begs the question: what forces are out there that we cannot detect at our scale?