How To Draw A Regular Pentagon [x]

Neutron Stars Are Even Weirder Than We Thought

Let’s face it, it’s hard for rapidly-spinning, crushed cores of dead stars NOT to be weird. But we’re only beginning to understand how truly bizarre these objects — called neutron stars — are.

Neutron stars are the collapsed remains of massive stars that exploded as supernovae. In each explosion, the outer layers of the star are ejected into their surroundings. At the same time, the core collapses, smooshing more than the mass of our Sun into a sphere about as big as the island of Manhattan.

Our Neutron star Interior Composition Explorer (NICER) telescope on the International Space Station is working to discover the nature of neutron stars by studying a specific type, called pulsars. Some recent results from NICER are showing that we might have to update how we think about pulsars!

Here are some things we think we know about neutron stars:

Pulsars are rapidly spinning neutron stars ✔︎

Pulsars get their name because they emit beams of light that we see as flashes. Those beams sweep in and out of our view as the star rotates, like the rays from a lighthouse.

Pulsars can spin ludicrously fast. The fastest known pulsar spins 43,000 times every minute. That’s as fast as blender blades! Our Sun is a bit of a slowpoke compared to that — it takes about a month to spin around once.

The beams come from the poles of their strong magnetic fields ✔︎

Pulsars also have magnetic fields, like the Earth and Sun. But like everything else with pulsars, theirs are super-strength. The magnetic field on a typical pulsar is billions to trillions of times stronger than Earth’s!

Near the magnetic poles, the pulsar’s powerful magnetic field rips charged particles from its surface. Some of these particles follow the magnetic field. They then return to strike the pulsar, heating the surface and causing some of the sweeping beams we see.

The beams come from two hot spots… ❌❓✔︎ 🤷🏽

Think of the Earth’s magnetic field — there are two poles, the North Pole and the South Pole. That’s standard for a magnetic field.

On a pulsar, the spinning magnetic field attracts charged particles to the two poles. That means there should be two hot spots, one at the pulsar’s north magnetic pole and the other at its south magnetic pole.

This is where things start to get weird. Two groups mapped a pulsar, known as J0030, using NICER data. One group found that there were two hot spots, as we might have expected. The other group, though, found that their model worked a little better with three (3!) hot spots. Not two.

… that are circular … ❌❓✔︎ 🤷🏽

The particles that cause the hot spots follow the magnetic field lines to the surface. This means they are concentrated at each of the magnetic poles. We expect the magnetic field to appear nearly the same in any direction when viewed from one of the poles. Such symmetry would produce circular hot spots.

In mapping J0030, one group found that one of the hot spots was circular, as expected. But the second spot may be a crescent. The second team found its three spots worked best as ovals.

… and lie directly across from each other on the pulsar ❌❓✔︎ 🤷🏽

Think back to Earth’s magnetic field again. The two poles are on opposite sides of the Earth from each other. When astronomers first modeled pulsar magnetic fields, they made them similar to Earth’s. That is, the magnetic poles would lie at opposite sides of the pulsar.

Since the hot spots happen where the magnetic poles cross the surface of the pulsar, we would expect the beams of light to come from opposite sides of the pulsar.

But, when those groups mapped J0030, they found another surprising characteristic of the spots. All of the hot spots appear in the southern half of the pulsar, whether there were two or three of them.

This also means that the pulsar’s magnetic field is more complicated than our initial models!

J0030 is the first pulsar where we’ve mapped details of the heated regions on its surface. Will others have similarly bizarre-looking hotspots? Will they bring even more surprises? We’ll have to stay tuned to NICER find out!

And check out the video below for more about how this measurement was done.

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com.

Interesting submission rk1232! Thanks for the heads up! :D :D

Six stages of debugging

Everyone who reblogs this will get a pick-me-up in their ask box.

Every. Single. One. Of. You.

The 21 Card Trick created in Python.

See how it works and read a little more about it here: [x]

Feel free to ask any questions you may have. :)

New Research Heading to Earth’s Orbiting Laboratory

It’s a bird! It’s a plane! It’s a…dragon? A SpaceX Dragon spacecraft is set to launch into orbit atop the Falcon 9 rocket toward the International Space Station for its 12th commercial resupply (CRS-12) mission August 14 from our Kennedy Space Center in Florida.

It won’t breathe fire, but it will carry science that studies cosmic rays, protein crystal growth, bioengineered lung tissue.

Here are some highlights of research that will be delivered:

I scream, you scream, we all scream for ISS-CREAM! 

Cosmic Rays, Energetics and Mass, that is! Cosmic rays reach Earth from far outside the solar system with energies well beyond what man-made accelerators can achieve. The Cosmic Ray Energetics and Mass (ISS-CREAM) instrument measures the charges of cosmic rays ranging from hydrogen to iron nuclei. Cosmic rays are pieces of atoms that move through space at nearly the speed of light

The data collected from the instrument will help address fundamental science questions such as:

Do supernovae supply the bulk of cosmic rays?

What is the history of cosmic rays in the galaxy?

Can the energy spectra of cosmic rays result from a single mechanism?

ISS-CREAM’s three-year mission will help the scientific community to build a stronger understanding of the fundamental structure of the universe.

Space-grown crystals aid in understanding of Parkinson’s disease

The microgravity environment of the space station allows protein crystals to grow larger and in more perfect shapes than earth-grown crystals, allowing them to be better analyzed on Earth. 

Developed by the Michael J. Fox Foundation, Anatrace and Com-Pac International, the Crystallization of Leucine-rich repeat kinase 2 (LRRK2) under Microgravity Conditions (CASIS PCG 7) investigation will utilize the orbiting laboratory’s microgravity environment to grow larger versions of this important protein, implicated in Parkinson’s disease.

Defining the exact shape and morphology of LRRK2 would help scientists to better understand the pathology of Parkinson’s and could aid in the development of therapies against this target.

Mice Help Us Keep an Eye on Long-term Health Impacts of Spaceflight

Our eyes have a whole network of blood vessels, like the ones in the image below, in the retina—the back part of the eye that transforms light into information for your brain. We are sending mice to the space station (RR-9) to study how the fluids that move through these vessels shift their flow in microgravity, which can lead to impaired vision in astronauts.

By looking at how spaceflight affects not only the eyes, but other parts of the body such as joints, like hips and knees, in mice over a short period of time, we can develop countermeasures to protect astronauts over longer periods of space exploration, and help humans with visual impairments or arthritis on Earth.

Telescope-hosting nanosatellite tests new concept

The Kestrel Eye (NanoRacks-KE IIM) investigation is a microsatellite carrying an optical imaging system payload, including an off-the-shelf telescope. This investigation validates the concept of using microsatellites in low-Earth orbit to support critical operations, such as providing lower-cost Earth imagery in time-sensitive situations, such as tracking severe weather and detecting natural disasters.

Sponsored by the ISS National Laboratory, the overall mission goal for this investigation is to demonstrate that small satellites are viable platforms for providing critical path support to operations and hosting advanced payloads.

Growth of lung tissue in space could provide information about diseases

The Effect of Microgravity on Stem Cell Mediated Recellularization (Lung Tissue) uses the microgravity environment of space to test strategies for growing new lung tissue. The cells are grown in a specialized framework that supplies them with critical growth factors so that scientists can observe how gravity affects growth and specialization as cells become new lung tissue.

The goal of this investigation is to produce bioengineered human lung tissue that can be used as a predictive model of human responses allowing for the study of lung development, lung physiology or disease pathology.

These crazy-cool investigations and others launching aboard the next SpaceX #Dragon cargo spacecraft on August 14. They will join many other investigations currently happening aboard the space station. Follow @ISS_Research on Twitter for more information about the science happening on 250 miles above Earth on the space station.  

Watch the launch live HERE starting at 12:20 p.m. EDT on Monday, Aug. 14!

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com

Regarding Fractals and Non-Integral Dimensionality

Alright, I know it’s past midnight (at least it is where I am), but let’s talk about fractal geometry.

Fractals

If you don’t know what fractals are, they’re essentially just any shape that gets rougher (or has more detail) as you zoom in, rather than getting smoother. Non-fractals include easy geometric shapes like squares, circles, and triangles, while fractals include more complex or natural shapes like the coast of Great Britain, Sierpinski’s Triangle, or a Koch Snowflake.

Fractals, in turn, can be broken down further. Some fractals are the product of an iterative process and repeat smaller versions of themselves throughout them. Others are more natural and just happen to be more jagged.

Fractals and Non-Integral Dimensionality

Now that we’ve gotten the actual explanation of what fractals are out of the way, let’s talk about their most interesting property: non-integral dimensionality. The idea that fractals do not actually have an integral dimension was originally thought up by this guy, Benoit Mandelbrot.

He studied fractals a lot, even finding one of his own: the Mandelbrot Set. The important thing about this guy is that he realized that fractals are interesting when it comes to defining their dimension. Most regular shapes can have their dimension found easily: lines with their finite length but no width or height; squares with their finite length and width but no height; and cubes with their finite length, width, and height. Take note that each dimension has its own measure. The deal with many fractals is that they can’t be measured very easily at all using these terms. Take Sierpinski’s triangle as an example.

Is this shape one- or two-dimensional? Many would say two-dimensional from first glance, but the same shape can be created using a line rather than a triangle.

So now it seems a bit more tricky. Is it one-dimensional since it can be made out of a line, or is it two-dimensional since it can be made out of a triangle? The answer is neither. The problem is that, if we were to treat it like a two-dimensional object, the measure of its dimension (area) would be zero. This is because we’ve technically taken away all of its area by taking out smaller and smaller triangles in every available space. On the other hand, if we were to treat it like a one-dimensional object, the measure of its dimension (length) would be infinity. This is because the line keeps getting longer and longer to stretch around each and every hole, of which there are an infinite number. So now we run into a problem: if it’s neither one- nor two-dimensional, then what is its dimensionality? To find out, we can use non-fractals

Measuring Integral Dimensions and Applying to Fractals

Let’s start with a one-dimensional line. The measure for a one-dimensional object is length. If we were to scale the line down by one-half, what is the fraction of the new length compared to the original length?

The new length of each line is one-half the original length.

Now let’s try the same thing for squares. The measure for a two-dimensional object is area. If we were to scale down a square by one-half (that is to say, if we were to divide the square’s length in half and divide its width in half), what is the fraction of the new area compared to the original area?

The new area of each square is one-quarter the original area.

If we were to try the same with cubes, the volume of each new cube would be one-eighth the original volume of a cube. These fractions provide us with a pattern we can work with.

In one dimension, the new length (one-half) is equal to the scaling factor (one-half) put to the first power (given by it being one-dimensional).

In two dimensions, the new area (one-quarter) is equal to the scaling factor (one-half) put to the second power (given by it being two-dimensional).

In three dimensions, the same pattern follows suit, in which the new volume (one-eighth) is equivalent to the scaling factor (one-half) put to the third power.

We can infer from this trend that the dimension of an object could be (not is) defined as the exponent fixed to the scaling factor of an object that determines the new measure of the object. To put it in mathematical terms:

Examples of this equation would include the one-dimensional line, the two-dimensional square, and the three-dimensional cube:

½ = ½^1

¼ = ½^2

1/8 = ½^3

Now this equation can be used to define the dimensionality of a given fractal. Let’s try Sierpinski’s Triangle again.

Here we can see that the triangle as a whole is made from three smaller versions of itself, each of which is scaled down by half of the original (this is proven by each side of the smaller triangles being half the length of the side of the whole triangle). So now we can just plug in the numbers to our equation and leave the dimension slot blank.

1/3 = ½^D

To solve for D, we need to know what power ½ must be put to in order to get 1/3. To do this, we can use logarithms (quick note: in this case, we can replace ½ with 2 and 1/3 with 3).

log_2(3) = roughly 1.585

So we can conclude that Sierpinski’s triangle is 1.585-dimensional. Now we can repeat this process with many other fractals. For example, this Sierpinski-esque square:

It’s made up of eight smaller versions of itself, each of which is scaled down by one-third. Plugging this into the equation, we get

1/8 = 1/3^D

log_3(8) = roughly 1.893

So we can conclude that this square fractal is 1.893-dimensional.

We can do this on this cubic version of it, too:

This cube is made up of 20 smaller versions of itself, each of which is scaled down by 1/3.

1/20 = 1/3^D

log_3(20) = roughly 2.727

So we can conclude that this fractal is 2.727-dimensional.