6. RXTE

Rossi X-Ray Timing Explorer (RXTE) was a spacecraft in low-earth circular orbit of 90 minutes.

wikipedia.org

RXTE was launched on December 30, 1995. Its mission was to study time variation of astronomical X-ray sources. The spacecraft was named after an Italian physicist Burno Benedetto Rossi.
The mission was deactivated on 5th January, 2012 after working for 16 years and 6 days.

RXTE solved one of the deepest mysteries in Astronomy.

It was known through observations that the galactic plane glows in X-rays whose brightness increases towards the galactic center.

Other observatories like Chandra and XMM-Newton were not able to give details of what's causing the glow. So, it was assumed by astronomers that the X-rays were coming from hot, diffuse Interstellar gas.

RXTE had mapped the X-ray background for 10 years since February, 1996. And NASA's another satellite COBE (Cosmic microwave Background Explorer) in early 1990s had also mapped the near-Infrared glow from our galaxy. The data from two satellites were matched.

Credit: NASA/RXTE-COBE/Revnivtsev et al.

As lots of individual stars glow in near-Infrared, it was suggested that X-ray emission in the galactic plane came from cataclysmic variables (a binary system with a star and a white dwarf).

White dwarfs are cores of dead stars and if they are in a binary, they will accrete gas from their companion star. Due to this process very high energy X-rays are released.

(New Map of Milky Way Reveals Millions of Unseen Objects - March 2006. heasarc.gsfc.nasa.gov)

5. INTEGRAL

ESA's INTEGRAL (INTErnational Gamma Ray Astrophysics Laboratories) is orbiting in a highly elliptical orbit around Earth. And it takes three days to orbit once around Earth.

Credit: ESA/ D. Ducros

INTEGRAL was launched on 17th October, 2002. Its mission is to study black holes, neutron stars, pulsars, active galactic nuclei, Supernovae, Gamma Ray Bursts etc.

It's the most sensitive gamma-ray Observatory ever launched. To detect Gamma rays from the objects in the universe an instrument needs to go in space because Earth's protective layer prevents them from reaching the ground.

INTEGRAL can observe objects in gamma-rays, X-rays and visible light. There are two detectors on INTEGRAL to detect gamma rays from space - an imager (IBIS - Imager on-board INTEGRAL) and an spectrometer (SPI - Spectrometer on INTEGRAL). Other two instruments are JEM-X (Joint European X-ray Monitor) and OMC (Optical monitoring Camera). OMC can detect stars with visual magnitude up to 19.7. It's a standard optical refractor with 5-cm lens and a CCD of 2055×1056 pixels in the focal plane.

On 14th August, the merger of two neutron stars that triggered the LIGO detectors fifth time also triggered the instruments on board INTEGRAL. And It was recorded as a 2 second gamma-ray-burst prior to the gravitational wave detection.

It became the first event to be observed in gravitational waves and in electromagnetic spectrum by lots of ground based and space based Telescopes in addition to the LIGO detectors.

4. Chandra X-ray Observatory

Chandra X-ray Observatory (CXO) is orbiting around Earth in a highly elliptical orbit of 64 hours.

Artistic image of CXO: wikipedia.org

Chandra Observatory was launched on the space shuttle Columbia in July 23, 1999.

There are lots of objects which emit X rays, for example Stars, Supernovae, Supernova remnants, gases falling into neutron stars and black holes etcetera.

But the mirrors used in Chandra Observatory are not like in any optical telescope where parabolic mirrors are used. If the X rays fall directly on a mirror they'll be absorbed. So the mirrors are shaped like a hollow cylinder which narrows the X rays until they are focused on an electronic detector, as shown in the video.

Last year in December Chandra released a new image of the 11 thousand light years distant Supernova remnant named Cassiopeia A. In this image different colours show different elements. Silicon is shown in red, Sulfur in yellow, Calcium in green and Iron in purple.

chandra.harvard.edu

A similar but more colorful composite image was also released using the data from Spitzer Space Telescope, Hubble Space Telescope and Chandra X ray Observatory.

The best thing about these images is that you can see the remaining core of the star as a dot (white or blue) in the center which is a neutron star.

3. XMM-Newton

XMM-Newton is a space telescope that is orbiting around Earth in an elliptical orbit of 48 hours.

Artistic Image of XMM-Newton - ESA - D. Ducros

It was launched on December 10, 1999.  

Later on February 9, 2000 European Space Agency (ESA) presented the first image taken by XMM and also announced its new name : XMM-Newton after the originator of the field of spectroscopy - Issac Newton. It's now called X-ray Multi-Mirror mission. One of its goals was to identify black hole candidates. 

Some of its major instruments are-

1. European Photon Imaging Cameras (EPIC) : It has two MOS-CCD cameras of total resolution 2.5 MegaPixel to detect low energy X-rays and a single pn-CCD camera to detect high energy X-rays.

2. Reflection Grating Spectrometers (RGS)

3. Optical Monitor 

XMM-Newton and NASA's NuSTAR measured the spin rate of a Supermassive Black Hole for the first time which is at the center of galaxy NGC 1365.

Last year in December the mission was extended for two years and is expected to operate till the end of 2020.

2. Keck Telescopes

W.M. Keck Observatory has two Telescopes in the Hawaii Island which lies in the middle of the Pacific Ocean.

The red dot shows the position of Keck Telescopes on Earth

The two Keck telescopes can see both infrared and visible light. Each telescope has a diameter of 10m and weigh 300 tons. The mirror used is made of 36 Hexagonal segments and a single segment is 1.8m in diameter which is only a little bit greater than the average human height.

Keck Telescopes

Keck1 telescope started observing in May 1993 and Keck2 telescope in October 1996.

A recent science news released by Keck Observatory tells us about a star orbiting the supermassive black hole at the centre of our galaxy, which was thought to be binary. The star named S0-2 is now proved to be single.

The orbit of S0-2 is shown in blue in the image below.

CREDIT: S. SAKAI/A.GHEZ/W. M. KECK OBSERVATORY/ UCLA GALACTIC CENTER GROUP

There are several theories which describe how S0-2 can form near the black hole and the theory that S0-2 should be a binary is one of them.

But the news that S0-2 does not have a companion deepens the mystery of its formation.

1. Very Large Telescope Array (VLT)

European Southern Observatory has advanced observational facilities at three sites in northern Chile - La Silla, Paranal and Chajnantor.

The red dot shows the position of VLT on Earth

Very Large Telescope (VLT) at Paranal has four 8.2m telescopes and four 1.8m telescopes.
These telescopes can work together to form a giant interferometer.
The 8.2m telescopes are mostly used individually but the 1.8m telescopes are available to allow VLTI to operate every night.

The large 8.2 telescopes are named Antu, Kueyen, Melipal, Yepun. Out of four Antu was the first telescope to begin routine observations from 1st April, 1999.

There are many discoveries and scientific firsts by VLT.

1. The accelerating expansion of the universe.

For this discovery Nobel Prize in physics was awarded in 2011. ESO's two observatories also contributed to the discovery and VLT was one of them.

Hubble's observation of red shifted galaxies led to the theory of expanding universe and the observation of Type1a Supernova led to the theory of accelerating expansion of the universe.

2. First image of an extrasolar planet.

3. Tracking of individual stars that are moving around Supermassive Black Hole at the center of Milky Way.

Transcendental Numbers

"...Pi wasn't the only transcendental number. In fact there was an infinity of transcendental numbers. More than that, there were more transcendental numbers than ordinary numbers, even though pi was the only one of them she had heard of. In more ways than one, pi was tied to infinity."

These beautiful lines are from the book, Contact by Carl Sagan.

Even though there are infinite transcendental numbers most of us have heard of only e and pi.
e = 2.718281828459045...
Pi = 3.1415926535...

Transcendental numbers are irrational. That is, they cannot be expressed as the ratio of two integers.

The abc book of e : mathwithbaddrawings.com

But all irrational numbers are not transcendental.

Its because, transcendental numbers cannot be expressed as a solution of a polynomial equation. In other words they are not the solution of any polynomial equation with integer coefficients.

So square root of 2 is an irrational number but not transcendental.

In this Numberphile video a simple proof is shown that pi is transcendental. The proof was given by Ferdinand von Lindemann in 1882.

1. He first proved that e^a is transcendental where a is nonzero. In 1873 Charles Hermite had already proved that e is transcendental.

2. Next, he used Roger Cotes' identity (famously but inaccurately known as Euler's identity). And using proof by contradiction he proved that i(pi) and pi are transcendental.

mathwithbaddrawings.com

There is a conjecture in transcendental theory which indirectly implies that above equation is the only nontrivial relation between e, pi and i.

Hilbert's seventh problem is also about transcendental numbers:

If a is an algebraic number such that a>1 and b is an irrational algebraic number, is a^b necessarily transcendental?

It was eventually proved and now known as Gelfond-Schrieder theorem in 1934.

Here are some of the numbers and functions that are proved to be transcendental.

wikipedia.org