Numbers within Physics

Friday, June 13, 2014

Harmony of Spheres

Harmony of Spheres, also known as Music of Spheres or Musica Universalis, comes from ancient times. It is mathematical and philosophical concept that expresses tones of energy resulting from numbers, angles, and shapes within pattern of proportion.

The Pythagoras were the first to identify that pitch of musical note is proportional to length of string that makes it and intervals between frequencies form numerical ratios. Back in these ancient times, musical notes were assigned to seven heavenly bodies in symbolic arrangements. It was thought that sun, moon and planets have orbital resonance due to their orbits.

Then Kepler came along, interested in Harmony of Spheres and wanted to calculate them. He noticed that ratios between planets’ extreme angular velocities were all harmonic intervals. He wrote book called Musica Universalis that showed relationships between geometry, cosmology, and harmonics.

I thought this topic was cool because it combines geometry, physics and music. Three things I enjoy.

Sources:
http://en.wikipedia.org/wiki/Harmony_of_the_Spheres
http://en.wikipedia.org/wiki/Harmonices_Mundi

Thursday, June 12, 2014

Dust in interstellar atmospheres

Dust affects our view of the distant universe!

The red ring around the galaxy is dust

How and why does dust matter?

Stars convert hydrogen into heavier elements and release them into the interstellar medium (via supernova, etc). These particles absorb light at certain wavelengths, which creates a big problem to the study star forming regions.

Dust particles will absorb high energy light that is emitted from star forming regions (the H-alpha regions). The luminosity that we receive is the luminosity from star formation - the absorption by dust. It is important to correct for the dust affects. It helps us correctly calculate the initial mass function and star formation rates. If we knew how much dust is in the interstellar atmosphere, then we could calculate the true luminosities of star forming regions. This data could help theorists better approximate the initial mass function and star forming rates.

How to measure the amount of dust?

Dust emits light in IR range. Here is a plot of luminosity of distant star forming galaxies.

As you can see, our IR detectors are not sensitive enough to calculate the luminosity from dust. This doesn't mean that we have to give up. There is a very interesting method to estimate the amount of dust know as stacking method.

We use stacking method to cancel out the effects of random disturbances to see any peaks (in IR) in star forming regions. Basic idea is to average luminosities from different IR images to see any peaks.

Procedure:
Look at different regions of sky and find as many star forming regions as you can from H(alpha) break from UV/Visible pictures.
Take IR images of these regions and cut out star forming areas. Now average fluxes from these cutouts and hope that you see some peak. Doing this should make all the disturbances cancel out, and reveal the small peak in the flux.

Special Thanks to Dr. Naveen Reddy

Wednesday, June 11, 2014

Asteroid Belt

Beyond Mars, which marks end of inner solar system, lies a particularly huge space. On the other side is massive planet Jupiter. It is in this huge space that Asteroid Belt exists. Thousands of large and small tumbling rocks is what Asteroid Belt is made up of. There are four types of asteroids that current Asteroid Belt consists of, carbonaceous asteroids, silicaceous asteroids, metallic asteroids and rare basaltic asteroids.

Carbonaceous asteroids are most common type and make up large percentage of Asteroid Belt and its outer regions. They are carbon rich and consist of organic compounds. An interesting article can be found at http://www.psrd.hawaii.edu/April11/amino_acids.html

Silicaceous asteroids are second most common type and make up majority of inner region” of Asteroid Belt. These types asteroids are mainly composed of iron and magnesium silicates and a very few even show hint of organic compounds. This tells us that their “materials have been significantly modified from their primordial composition, most likely through melting and reformation”.

Metallic asteroids are third most common type of asteroids. Their compositions are not fully known, but many consist of nickel, iron and a little stone. This class of asteroids is not fully understood and it appears there may be several different types.

Basaltic asteroids are considered rare and are mystery in Astrophysics. They are composed of extrusive volcanic rock and mineral olivine, which is magnesium iron silicate. If you are interested, you can read more about these mysterious types of asteroids here.

There are main-belt comets that orbit within Asteroid Belt which tend to stay in outer part of belt. There are also spaces, known as Kirkwood Gaps, cleared where orbital resonances with Jupiter occur. Orbital Resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on one another.” The largest gap is at orbital distance which would correspond to period of one third that of Jupiter.

The most massive of all the asteroids is Ceres , comprising over one third of total mass of all of asteroids. It is considered a dwarf planet, smallest one in our solar system, and only dwarf planet to exist in Asteroid Belt.

Asteroid Belt is highly unlikely to be remains of a small planet because no sizeable body could ever have formed so close to Jupiter.

Sources:

http://en.wikipedia.org/wiki/Asteroid_belt

http://www.psrd.hawaii.edu/April11/amino_acids.html

Tuesday, June 10, 2014

Magnetic Field of a Neutron Stars

A neutron star is stellar remnant that results from the gravitational collapse of a massive star (between 8 to 20 solar masses). Even though neutron stars are composed of almost entirely neutrons, they have very strong magnetic fields.

To understand why a neutron star has a huge magnetic field, let's look at its structure.

The structure

This model hasn't been proven, but it gives very good understanding of neutron stars and reveals many known properties of neutron stars. The surface of a neutron star is composed of ordinary nuclei with a sea of free electrons flowing around them. Most of the nuclei are left over hydrogen, helium and iron. The atmospheres of these stars, according to recent hypothesis, could be at most several micrometers. This is because of the intense gravity on the surface. A calculation of gravity is here. This is approximately 10^12 times stronger than earth's gravity.

A little deeper into the star, the gravity gets strong enough so that neutrons leak out of nuclei and become free neutrons. As we dig dipper and dipper, the nuclei becomes smaller and smaller until the core is reached where nuclei disappear. The composition of the super dense core remains uncertain.

Angular velocity

To get a rough estimate of angular velocity, we can assume that angular velocity is conserved.
Here is a sample calculation. We can get something like several rotations per second!!!

Magnetic Field

Here is a rough calculations of neutron stars' magnetic field assuming charge density is uniform in spherical shell shape. This shell can have a lot of surface charge density since there is a sea of electrons. If we estimate the magnetic field of rotating charged sphere, then the below picture shows that neutron stars can have magnetic fields like 50,000 Tesla. Compare that to earth's magnetic field (0.0001 Tesla) or maximum magnetic field produced on earth (100 Tesla).

Here is a link to the interactive CDF file to explore magnetic field of neutron star with different parameters.
Click here to download

Sources
Wikipedia Neutron Star
Magnetic Field of a rotating Sphere Estimates

Monday, March 17, 2014

Last minute studying

Binary System (This one is not so great. I haven't finished making it.)

http://dl.dropbox.com/u/58867372/Astrophysics/Binary%20Systems.cdf

http://dl.dropbox.com/u/58867372/Astrophysics/Binary%20Systems.nb

http://dl.dropbox.com/u/58867372/Astrophysics/Binary%20Systems.pdf

Tuesday, February 4, 2014

Spectral Lines and Classification of Stars

Do you know how to interpret Hertzsprung-Russell Diagrams?
Do you know why do spectral lines have widths?
Do you know why we see strong hydrogen absorption in certain stars and not other?

All of these questions are answered in Chapter 8 (30 pages) of our book. I have written detailed, interactive, notes about this chapter that I would like to share. I have included interactive plots and diagrams to help us understand and explore these questions. It also includes small applications to solve for saha, boltzmann, and other equations.

Hopefully this information helps you.

Here are links to the files. I highly recommend you use Wolfram CDF (Its free, click here). PDF version is dull and boring. CDF player will let you interact with plots.

PDF version
Wolfram CDF version
Wolfram Mathematica version

Tuesday, December 17, 2013

Declination and Right Ascension

Here is the link to the Word document I created
Here is the link to the Google Docs page.
I could not insert all the equations and formatted text into blogger.

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