**Gravitational collapse** is the contraction of an astronomical object due to the influence of its own gravity, which tends to draw matter inward toward the center of mass. Gravitational collapse is a fundamental mechanism for structure formation in the universe. Over time an initial relatively smooth distribution of matter will collapse to form pockets of higher density, typically creating a hierarchy of condensed structures such as clusters of galaxies, stellar groups, star-sand planets.

# Gravitational Collapse

# The formulation of the Solar System

The **formation of the Solar System** began 4.6 billion years ago with the gravitational collapse of a small part of a giant molecular cloud. Most of the collapsing mass collected in the center, forming the Sun, while the rest flattened into a proto-planetary disk out of which the planets, moons, asteroids, and other small Solar System bodies formed.

# A brief maths for gravitational field

In physics, a **gravitational field** is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenomena, and is measured in newtons per kilogram (N/kg). In its original concept, gravity was a force between point masses. Following Newton, Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century explanations for gravity have usually been taught in terms of a field model, rather than a point attraction.

# The most massive black hole

**S5 0014+81** is a distant, compact, hyperluminous, broad-absorption line quasar or blazar located near the high declination region of the constellation Cepheus, near the North Equatorial Pole.

## Characteristics

The object is a blazar, in fact an FSRQ quasar, the most energetic subclass of objects known as active galactic nuclei, produced by the rapid accretion of matter by a central supermassive black hole, changing the gravitational energy to light energy that can be visible in cosmic distances. In the case of S5 0014+81 it is one of the most luminous quasars known, powering up light equivalent to over 10^{41} watts, equal to an absolute bolometric magnitude of -31.5. If the quasar were at a distance of 280 light-years from earth it would give as much energy per square meter as the Sun despite being 18 million times more distant. The quasar’s luminosity is therefore about 3 x 10^{14} (300 trillion) times the Sun, or over 25 thousand times as luminous as all the 100 to 400 billion stars of theMilky Way Galaxy combined, making it one of the most powerful objects in the universe. However, because of its huge distance of 12.1 billion light-years it can only be studied by spectroscopy . The central black hole of the quasar devours an extremely huge amount of matter, equivalent to 4000 solar masses of material every year.

# Human mission to Mars

A **human mission to Mars** has been the subject of science fiction, engineering, and scientific proposals since the 19th century. The plans comprise proposals to land on Mars, eventually settling on and terraforming the planet, while utilizing its moons, Phobos andDeimos.

# Basic maths for black holes

The basic idea of a black hole is simply an object whose gravity is so strong that light cannot escape from it. It is black because it does not reflect light, nor does its surface emit any light.

Before Princeton Physicist John Wheeler coined the term black hole in the mid-1960s, no one outside of the theoretical physics community really paid this idea much attention. In 1798, the French mathematician Pierre Laplace first imagined such a body using Newton’s Laws of Physics (the three laws plus the Law of Universal Gravitation). His idea was very simple and intuitive. We know that rockets have to reach an escape velocity in order to break free of Earth’s gravity. For Earth, this velocity is 11.2 km/sec (40,320 km/hr or 25,000 miles/hr). Now let’s add enough mass to Earth so that its escape velocity climbs to 25 km/sec…2000 km/sec…200,000 km/sec, and finally the speed of light: 300,000 km/sec. Because no material particle can travel faster than light, once a body is so massive and small that its escape velocity equals light-speed, it becomes dark. This is what Laplace had in mind when he thought about “black stars.” This idea was one of those idle speculations at the boundary of mathematics and science at the time, and nothing more was done with the idea for over 100 years.

# Superstring theory

**Superstring theory** is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings.

‘Superstring theory’ is a shorthand for **supersymmetric string theory** because unlike bosonic string theory, it is the version of string theory that incorporates fermions and supersymmetry.

# Lorentz transformation – the mathematical connection between space and time

In physics, the **Lorentz transformation** (or **transformations**) are coordinate transformations between two coordinate frames that move at constant velocity relative to each other.

Frames of reference can be divided into two groups, inertial (relative motion with constant velocity) and non-inertial (accelerating in curved paths, rotational motion with constant angular velocity, etc.). The term “Lorentz transformations” only refers to transformations between *inertial* frames, usually in the context of special relativity.

In each reference frame, an observer can use a local coordinate system (most exclusively Cartesian coordinates in this context) to measure lengths, and a clock to measure time intervals. An observer is a real or imaginary entity that can take measurements, say humans, or any other living organism—or even robots and computers. An event is something that happens at a point in space at an instant of time, or more formally a point in spacetime. The transformations connect the space and time coordinates of an event as measured by an observer in each frame.

They supersede the Galilean transformation of Newtonian physics, which assumes an absolute space and time (see Galilean relativity). The Galilean transformation is a good approximation only at relative speeds much smaller than the speed of light. Lorentz transformations have a number of un-intuitive features that do not appear in Galilean transformations. For example, they reflect the fact that observers moving at different velocities may measure different distances, elapsed times, and even different orderings of events, but always such that the speed of light is the same in all inertial reference frames. The invariance of light speed is one of thepostulates of special relativity.

Historically, the transformations were the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame, and to understand the symmetries of the laws of electromagnetism. The Lorentz transformation is in accordance with special relativity, but was derived before special relativity. The transformations are named after the Dutch physicist Hendrik Lorentz.

Continue reading Lorentz transformation – the mathematical connection between space and time

# Solutions of Einstein field equations

**Solutions of the Einstein field equations** are spacetimes that result from solving the Einstein field equations (EFE) of general relativity. Solving the field equations actually gives a Lorentz manifold. Solutions are broadly classed as *exact* or *non-exact*.

The Einstein field equations are

# Let me hear your ideas

# Proof of Fermat’s Last Theorem

Link 1:Proof of Fermat Last Theorem – University of Visconsin

Link 2: Proof of Fermat Last Theorem – University of Vd

In number theory, **Fermat’s Last Theorem** (sometimes called **Fermat’s conjecture**, especially in older texts) states that no three positiveintegers *a*, *b*, and *c* satisfy the equation *a*^{n} + *b*^{n} = *c*^{n} for any integer value of *n* strictly greater than two. The cases *n* = 1 and *n* = 2 have been known to have infinitely many solutions since antiquity.

# “Article for conservative people” Mr.Do

If you think we are the only species in this universe, then you should give up those thoughts. Don’t you know that there are approximately 600 of billions of visible galaxies in the present universe. Moreover, 600 billions is also the average number of present stars in each galaxy. Now, you can imagine an extremely huge amount of stars out there. So should we stop here?

No, we have not discussed anything about the planets yet. How many planets are there in a typically stellar system?

The answer could be 0 or up to hundred or thousand. Let’s make a little calculation here. Assume that 30 is the average amount of planets inside a stellar system.

Pln(x) = 600 billion x 600 billion x 30 = 10.8 of million of billion of billion planets. That value is something very small when compared to the whole universe. It is due to the effect of hidden part of the cosmos. Obviously, we know nothing about it. Based on research, it can be noticed that the amount of discovered planets in the Milky Way is 11000. It is a “huge” number.

**k = 1.08e+25 / 11000 = 9.81e+20**

So what does the number 9.81e+20 tell us?

For each 981 billions of billions of planets in this universe, we had discovered “one”. If my calculation included the invisible cosmos, (which accounts more than 90% of the total universe), then … what do you think?

So, let’s come back the main problem. It is Drake equation.

The **Drake equation** is a probabilistic argument used to arrive at an estimate of the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy.

# A Chronology of Mars Exploration

**No name (retroactively named Marsnik 1)(Mars 1960A)** – 480 kg – USSR Mars Probe – (October 10, 1960)

- Failed to reach Earth orbit.

**No name (retroactively named Marsnik 2)(Mars 1960B)** – 480 kg – USSR Mars Probe – (October 14, 1960)

- Failed to reach Earth orbit.

**Sputnik 22 (Mars 1962A)** – USSR Mars Flyby – 900 kg – (October 24, 1962)

- Spacecraft failed to leave Earth orbit after the final rocketstage exploded.

# What if you fell into a black hole?

*Let’s say you happened to fall into the nearest black hole? What would you experience and see? And what would the rest of the Universe see as this was happening?*

Let’s say you decided to ignore some of my previous advice. You’ve just purchased yourself a space dragon from the Market on the Centauri Ringworld, strapped on your favorite chainmail codpiece and sonic sword and now you’re going ride head first into the nearest black hole.