Surfing the cosmic distances (AU)…

I’m happy that we’re getting into our area, the field which got Physics started with the heroes like Galileo, Kepler, Newton, Einstein, Hubble, Hawking and many others (whom I forget now) and also, the field where I really know something – Astronomy. As this is gonna be our first post on Astronomy, we should be familiar with scaling up the universe. So this week, that would be our topic. You’re gonna slice out the cosmos. Although there’s so much hard work & overwhelming enthusiasm going on inside, these distances are not very hard to interpret. Just like you say, “Well, it took about an hour for me to drive from Baltimore to Washington, DC”, the astro-guys say, “Well, it takes about 2.5 million light years for a light photon emitted from the Sun to reach the Andromeda”. You say, “Heck, that’s inconceivable”. Yep, and crazy guys like me, love to state such unimaginable catastrophic “stuff”…

Formally, these things are a subset of the Astronomical system of units, as they use all these weird numbers. If it were otherwise (i.e) usage of normal units like kilometers, we’d have to deal with a gazillion zeros. The “Fun To Imagine” series has a video on these big numbers, where our beloved theoretical physicist Dr. Richard Feynman is being interviewed on the topic…

The most familiar “measure”…

We’re not here to speak about “meters & rulers”. We’re here to scale the universe using measurements like the astronomical units, light years & parsecs. For what it’s worth, we’ll have a look at the definition at least. You may have gone through this ridiculous definition of a meter, that it’s approximately equal to 1,650,764 (big number again) wavelengths of the orange-red emission line in the visible spectrum of Krypton-86 atom in vacuum. But, that’s old school. Today we’re gonna go with the standard definition (which is being followed for a decade, to reduce the uncertainty, though there are still other ludicrous ones) that convinces the astro people, as it makes use of the speed of light c in vacuum (I was just kidding, this has nothing to do with them, they just move on with their own system of units).

\mathrm{1\ meter = Distance\ traveled\ by\ light\ in} \mathrm{\frac{1}{299,792,458}} \mathrm{th\ of\ a\ second\ in\ vacuum}

Well, it may seem familiar to you. Because it’s just the “velocity equals distance over time” analogue. If light covers a 300 million meters in a second (or 1 light-second), then the definition that meter is the distance covered by light in one-three millionth part of a second, is also true. Additional prefixes like kilo, mega, giga, tera, etc. may be applied to this unit (and I’ve come across measuring in “gigameters” for planets in our solar system). So, that’s easily imaginable, which explains why it’s boring (because, you’ve got a nice everyday experience of this familiar “unit of fame”).

Dunno why this stupid thing arrived…

Wikipedia’s history on how this unit arrived doesn’t convince me why this unit arrived at all..!!! But, this horrible thing (being a giant quantity) has its unique purpose. On one hand, you’ve got meters and kilometers (which are too small) while on the other hand, you’ve got light years and parsecs (which are a way too large). In the midst of those, you need a unit to calculate the interplanetary distances in our solar system. The unit should be intermediate unlike the other terrible measures. And, looks like the distance between Sun and the Earth, about 150 million kilometers, or about 8 light-minutes (well, it takes eight minutes for light to travel from Sun’s photosphere to Earth) may well fit our bill. That’s the Astronomical unit.

And, I’ve got something for you on that. Say your friend asks you for the distance to any of the planet if you were to cruise from Earth, say Mars. Within a jiffy, I can tell you that it’s about 0.6 AU from Earth. You may argue, “Well, you plagiarized from the internet”. It’s true in some sense that whatever I speak from my mind comes from the internet, this is not quite. Truly, I plagiarized from the Titius-Bolde law. Things like these do happen in Astronomy. The physicists always imagine, deduce, guess & experiment to check their guess. And luckily, that guesswork turns out to be true most of the times. But, we don’t want the places where our law holds good. We look out for where something might not work, so as to develop a new one. Now, this mystical law is more an approximation and it fails over large distances. Now, all you have to do, is remember this series…

n_i= {0,3,6,12,24,48,96,192,384,768}

It’s quite easy. Just like a squeeze of toothpaste. From 3, you’re just doubling the numbers. Now, take a number from the series, add 4 to it and divide the thing by 10. The nth number from the series, is the nth object from the Sun and the result you obtain after you’ve played with the numbers, gives you the distance of the object from the Sun in astronomical units. It maybe summarized as…

a_i= \frac{n_i+4}{10}

Now, subtract Earth’s 1 AU from it, to obtain the distance from Earth. Delicate and wonderful as it may seem, it has its own flaws. The figure shows how the law’s prediction varies from the actual distance (the error). Looks like it fails to predict the observed distances of Neptune and Pluto. (But still, it was a beautiful discovery in those days, although it was temporal)…

Why Ceres & Pluto are in there at all? This law is about three centuries old, when every single dot on the night sky that caught the astronomers’ attention, were speculated to be either planets or stars. Ceres (an asteroid) and Pluto (the dwarf planet) were considered as planets, which is why they’re in the law’s prediction. Now, you can correct this law by removing “384” from the series, so that Pluto’s value comes to Neptune (which is quite true). So, you can predict the distances of all the planets along with Ceres and now, you can show off…

Now, this law (the AU measurement itself..!!!) doesn’t have any special significance in astronomy. As I’ve said previously, the choice of units is totally up to the theorist. So, when you’re theorizing, you can freely use any system of units and set any coordinate system you want. But, keep in mind that once you’ve wrapped up, you should check whether your theory signifies something. And…

As numbers fool you, don’t blindly rely on them..!!!

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