This Week in Science - May 13 - 19, 2013:

• Magnetar at black hole here.
• Cloned human stem cells here.
• Cell calculators here.
• Music matched to color here.
• Scientists agreeing on climate change here.
• Remote-piloted plane here.
• Earth’s core here.
• Bright lunar explosion here.
• American asteroid sampling here.
• Hofstadter butterfly effect here.
• Electric shocks aid math skills here.
• Printable solar panels here.

(Source: thescienceofreality)

scienceisbeauty:

Potential flow around an airfoil, constructed with a Joukovski transform and inviscid, incompressible flow. Levels of blue represent pressure (darkest is highest).

By Thierry Dugnolle (Own work) [CC0], via Wikimedia Commons

atomstargazer:

Astronomical Distances and Magnitudes

Measuring Astronomical distances
In the words of Douglas Adams, the author of The Hitch-Hiker’s Guide to the Galaxy:

Space is big. You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space.
The distances involved in the universe are so vast that metres or kilometers will just not suffice. We must introduce new length scales with which can span the heavens.

THE ASTRONOMICAL UNIT A.U.

One natural and practical unit we can devise is the distance from the Sun to the Earth. This is the A.U. or Astronomical Unit. 1 Astronomical Unit = 149 598 000 km

LIGHT YEAR

Moving to larger distances even the AU becomes unweildly and so the next suitable unit is the light-year. The light-year, as its name would suggest, is the distance travelled by light in one year. All electromagnetic waves travel at a speed of x 299,792,458 ms-1 in a vacuum and with an average year being 365.25 days, one light year is 299,792,458 x 108ms-1 x (365.25 x 24 x 60 x 60) s =

9.46073 x 1015 m. or 9.46073 x 1012 km.

1 lt-yr = 63 239.6717 AU

With our new measuring sticks to hand we can give a few examples of the scale of the universe.

The distance from the Earth to the nearest star (Alpha Centauri A or B) after our Sun is 4.3 ly.

The Milky Way Galaxy is about 150,000 light-years across

The andromeda galaxy is 2.3 million light-years away.

The edge of the observable universe is 46.5 Giga light years away.

THE PARSEC

The other commonly used unit in astronomy and in Star Trek is called the Parsec (parallax of one arc second). The parsec is defined to be the distance at which a star would have a parallax angle p equal to one second of arc (1/3600 deg). The two dimensions that specify this triangle are the parallax angle (defined as 1 arcsecond) and the opposite side (defined as 1 Astronomical Unit (AU), the distance from the Earth to the Sun).

The parsec defined as the distance required to create a parallax angle of one second of arc.
Parallax is the apparent shift in the nearest stars due to the motion of the Earth around the Sun. The method of parallax gives rise to a natural distance unit that astronomers call the parsec (which we shall abbreviate as pc).

The parsec in trigonometric terms.
1 Parsec = 3.08568025 × 1016 m. also used are kpc =1000 pc and Mpc =1 million pc


1 Parsec = 3.26 lt yrs.

If the star is not further than 500 light-years, then the parallax shift of the star can be used to find the distance from the Earth.

Distance (in parsecs) = 1/parallex angle.

Magnitude of Stars
Apparent Magnitude
Early Greek astronomers used a scale of magnitude devised by Hipparchus around the 2nd century BC, which was based on how bright stars appeared with the naked eye. The Hipparchus scale went from magnitude 1, for the brightest stars, up to magnitude 6, for those stars which were barely visible.

Improvements in the light gathering power of telescopes made it possible to compare the intensities of the light from stars more accurately. In 1856, Norman Robert Pogson formalized the system by defining a typical first magnitude star as a star that is 100 times as bright as a typical sixth magnitude star. Thus, a first magnitude star is about 2.512 times as bright as a second magnitude star. The fifth root of 100 (since magnitude 6 stars must be 1: x5 is known as Pogson’s Ratio. In calculations, however, the factor 2.5 is often used.

To make things more confusing, the brightest stars in the sky exceed magnitude 1. These bright starts are accommodated by allowing negative magnitudes. The Sun has an apparent magnitude of -26.74, while Sirius has a magnitude of -1.46. At the other end of the scale, as the light gathering power of telescopes has increased, the magnitude scale has extended to encompass much fainter stars. The dimmest object currently observable with the largest telescopes have a magnitude of 30. As a useful reference point, the star, Vega is taken to be of 0 magnitude. More accurate measurements put its apparent magnitude at 0.03.

It is also important to note that the magnitude system is only meaningful when magnitudes are compared when measured through the same wavelength band.

Name Apparent Magnitude Distance from Earth
Sun -26.74 1 AU
Full Moon - 12 200,000 km
Venus -4.71 38 million km
Sirius -1.46 2.6pc
Vega 0.03 13pc
Canopus 0.7 96pc ±5pc
Faintest Stars 30 as seen with the European
Extremely Large Telescope (E-ELT) or Hubble Space
Telescope -
The apparent magnitude m is given by

m = - 2.5 log10(b) + C(1)

Where, b is the observed intensity or brightness of the star and C is a constant, depending on the band the object is observed in, i.e. ultra-violet U, blue, B or visible V.

If we measure the brightness of two different stars, using a detector in the same band, we can determine their difference in magnitude. The difference in their apparent magnitude is given by

m1 - m2 = - 2.5 log10(b1/b2)

where m1 and m2 two are apparent magnitudes of the two stars, and b1 and b2 are their respective brightness.

From the properties of logarithms, the ratio of the intensities / brightness of the two stars is.

m1 - m2 = - 2.5 [log10(b1) - log10(b2)]

m1 - m2 = - 2.5 log10(b1/b2)(3)

Absolute Magnitude
The apparent brightness of a star is how bright it seems when viewed from the Earth, but a large, bright star can appear dim if it is a long way from the Earth and a dim star can appear to be bright if it is close to the Earth. Therefore, the apparent magnitude has no bearing on the distance from the Earth.

To give an acurate measurement of the brightness of a star we need to make an absolute magnitude scale. The absolute magnitude is how bright a star is when viewed from a set distance. Stars being rather large objects, a distance of 10 parsecs was chosen.

The absolute magnitude is the brightness of a star at a distance of 10 parsecs.
Absolute Magnitude and Inverse Square Law of Intensity
In order to find the absolute magnitude, we need to know the distance of the star from the Sun. How do we do this? The intensity or brightness of light decreases with distance from the star. The rate at which it decreases is inversely proportional to the square of the distance. Thus, if we have a star of luminosity L and we move a distance d the same quantity of light has to cover a larger spherical area. Therefore, the brightness or intensity is given by
b = L/(4πd2) (4)

Or in more simple terms, the apparent brightness of the star is proportional to the 1/distance2

To calculate the absolute magnitude we are essentially using the relative magnitude formula and the inverse square law to allow us to substitute distance for brightness. Now we can compare its magnitude with a star at set distance of 10pc.

M- m = -2.5 log10(d2) - (-2.5 log10102)

Using the rules of logarithms to make some simplifications.

M = m -2.5 log10(d2/102)

M = m - 5 log(d/10)(5)

M = m - 5 [log(d) - 1]

M = m - 5 log(d) + 5(6)

Distance Modulus
Starting from equation (6) we can calculate the distance d from the Earth if we know the absolute magnitude. In practice we don’t know the absolute magnitude because we cannot travel 10 parsecs from the star in question. We can use several indirect methods to determine its absolute magnitude. If the star is on the main sequence of stars then we can determine the brightness from its parallax.

If we know the apparent magnitude m and the absolute magnitude then we can find the distance in parsecs to the star.

m - M = 5 log10(d) + 5

Rearranging for d

d = 10((m-M)+5)/5

scienceisbeauty:

The Brain on Music. Does Music Education Enhance the Developing Brain and Academic Achievement? (The Jane and Harry Willson Center for Humanities and Arts)

propaedeuticist:

At NASA’s Drawing Board - J R Eyerman

mypubliclands:

In honor of Women’s History Month, we are sharing the stories of women who work in BLM science, technology, engineering and math-related positions (STEM) or positions that are as unique as our multiple-use mission…

Did you know that the Amarillo Field Office employs BLM’s only two Chemists at the Cliffside Helium Plant? While we are proud of both our Chemists, we are highlighting the work of Roya Mortazavi. Roya’s degree in Organic Chemistry is unusual in the BLM workplace. Her work as a Chemist for BLM includes analysis of routine and non-routine samples for mass spectrometry and gas chromatography for helium, natural gas, and atmospheric samples. Roya has made presentations as well as cryogenic demonstrations to different schools and the local state fair, encouraging young girls to pursue careers in science.

scinerds:

Largest Prime Number Discovered

The largest prime number yet has been discovered — and it’s 17,425,170 digits long. The new prime number crushes the last one discovered in 2008, which was a paltry 12,978,189 digits long.

The number — 2 raised to the 57,885,161 power minus 1 — was discovered by University of Central Missouri mathematician Curtis Cooper as part of a giant network of volunteer computers devoted to finding primes, similar to projects like SETI@Home, which downloads and analyzes radio telescope data in the Search for Extraterrestrial Intelligence (SETI). The network, called the Great Internet Mersenne Prime Search (GIMPS) harnesses about 360,000 processors operating at 150 trillion calculations per second. This is the third prime number discovered by Cooper.

“It’s analogous to climbing Mt. Everest,” said George Woltman, the retired, Orlando, Fla.-based computer scientist who created GIMPS. “People enjoy it for the challenge of the discovery of finding something that’s never been known before.”

In addition, the number is the 48th example of a rare class of primes called Mersenne Primes. Mersenne primes take the form of 2 raised to the power of a prime number minus 1. Since they were first described by French monk Marin Mersenne 350 years ago, only 48 of these elusive numbers have been found, including the most recent discovery.

After the prime was discovered, it was double-checked by several other researchers using other computers.

While the intuitive way to search for primes would be to divide every potential candidate by ever single number smaller than itself, that would be extremely time-consuming, Woltman told LiveScience.

“If you were to do it that way it would take longer than the age of the universe,” he said.

Instead, mathematicians have devised a much cleverer strategy, that dramatically reduces the time to find primes. That method uses a formula to check much fewer numbers.

The new discovery makes Cooper elligible for a $3,000 GIMPS research discovery award.

matthen:

The smooth motion of rotating circles can be used to build up any repeating curve even one as angular as a digital square wave. Each circle spins at a multiple of a fundamental frequency, and a method called Fourier analysis shows how to pick the radiuses of the circles to make the picture work. Decomposing signals like this lies at the heart of a lot of signal processing. [more] [code]

jtotheizzoe:

How to defeat a dragon with math

In the mighty land of Pi, the Musketeers of PEMDAS must come together to defeat an evil math dragon! You’ll never forget order of operations again.

(via TED-Ed)

quantumaniac:

How Big Would a Coin Made of $1 Trillion Worth of Platinum Be?

Of course this isn’t what is being considered, but what if the U.S. Treasury minted a coin from $1 trillion worth of platinum?

Based on the fact that platinum is worth $1,593 per troy ounce (a troy ounce is roughly equal to 31 grams), such a coin would weigh 42,778,918 pounds — the equivalent of nearly seven Saturn V rockets — and occupy 31,947 cubic feet.

What would this coin look like?

If it had the same proportions as the U.S. dollar coin, we calculated it would be roughly 80 feet wide and 6 feet thick. Though not a very practical coin, it would have the benefit of being really difficult to steal. And you could see it from space.

But commodity money disappeared a long time ago, so let’s say the government decides to mint an actual trillion-dollar coin, and makes it out of pure platinum at the same size as the U.S. silver dollar; though the coin would be worth $1 trillion, the platinum itself would only be worth a bit more than $1,200.

Image: Alchemist-hp/Wikimedia commons

Source: Wired

theworstmathematician:

When two bodies orbit around each other in space, we know exactly what happens. The bodies trace out conic sections, they do so in accordance with Kepler’s laws, and that’s it, more or less.

When three or more bodies orbit around each other in space, things can be more complicated. In the general case, no explicit formula for the orbits exists, and we have to rely on numerical simulations. As the first two animations illustrate, these can get messy. (These animations by my friend poulenque.)

Among all these possible orbits, though, there exist some which repeat after some time.  These are called n-body choreographies (with n = the number of bodies), small islands of order in a large chaotic space of ways-things-can-be. That’s what all those other animations are. (These animations are by Chris Moore, from here, where he has some others too.)

Most of these are completely unstable, in that the slightest nudge or imbalance in their masses will get amplified until they go flying. However, the one that traces out a figure 8 above is only somewhat unstable, in that (apparently) it will resist small nudges or variations in mass. It is estimated that between 1 and 100 naturally-occurring such figure 8 configurations exist in the entire observable universe.

In all of the animations above except for the second, the masses of all the objects are the same. This is important if you want to wonder about them.

.‿.

(via twocubes)

memeengine:

In case it ever comes up.

ikenbot:

Speed of light

The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact because the length of the metre is defined from this constant and the international standard for time.

In imperial units this speed is approximately 186,282 miles per second. According to special relativity, c is the maximum speed at which all energy, matter, and information in the universe can travel. It is the speed at which all massless particles and associated fields (including electromagnetic radiation such as light) travel in vacuum.

It is also the speed of gravity (i.e. of gravitational waves) predicted by current theories. Such particles and waves travel at c regardless of the motion of the source or the inertial frame of reference of the observer. In the theory of relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence E = mc2.

mothernaturenetwork:

Finding the Fibonacci sequence in Hurricane Sandy
It’s amazing how closely the powerful swirls of Hurricane Sandy match the Fibonacci sequence.