Great number

The Large Numbers hypothesis asserts that all the large dimensionless numbers occurring in Nature are connected with the present epoch, expressed in atomic units, and thus vary with time. It requires that the gravitational constant G shall vary, and also that there shall be continuous creation of matter. The consistent following out of the hypothesis leads to the possibility of only two cosmological models. One of them, which occurs if one assumes that the continuous creation is a multiplication of existing matter, is Einstein’s cylindrical closed Universe. The other, which occurs if one assumes the continuous creation takes place uniformly through the whole of space, involves an approximately flat Minkowski space with a point of origin where the Big Bang occurred.

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Dirac, P. A. M. (1974). Cosmological models and the large numbers hypothesis. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 338(1615), 439-446. doi:10.1098/rspa.1974.0095

The distance from the Moon

The method currently used to evaluate the distance from the Moon dates back to 1962, when a team from MIT (Massachusetts Institute of Technology) in collaboration with soviet astronomers from the Crimean Astrophysical Observatory carried out an experiment to measure the round-trip time of a laser pulse reflected on the surface of the Moon. The evolution of this experiment was completed thanks to the Apollo missions of 1969, when the astronauts placed reflective mirrors on the lunar surface in order to improve the accuracy of the measurement. Lasers traveling to the Moon involve multiple structures and are part of the Lunar Laser Ranging.
The distance measurement from this project is 384402 km with an error of 1.1 millimeters⁽¹⁾, which in terms of light time corresponds to just under 1.3 seconds.
The pre-laser method is also inspired by the same principle: in 1957 the US Naval Research Laboratory sent 2 μs radar pulses from a radio antenna with a diameter of about 15 meters. After the echo produced by the waves on the surface of the Moon, the experiment detected the return signal and measured the delay time, from which to derive the distance from our satellite. Unfortunately, this experiment was subject to an excessively high error with respect to the signal and therefore the result produced was not considered reliable⁽²⁾.
The experiment was repeated the following year, in 1958, by the Royal Radar Establishment in Great Britain. In that case, radar pulses of 5 μs were sent with a maximum power of 2 megawatts and a frequency of 260 pulses per second⁽³⁾.

The road to reality

The discussion around what we know about the universe is in continuous development. If we take the infographic below, for example, we are faced with three possible scenarios: an accelerated expanding universe that will conclude is run in a big rip, in which the universe eventually turns completely black; a universe in which expansion is in balance with gravity, but nevertheless destined to make the skies of planets black and starless; a universe where expansion is blocked and reversed to a big crunch.

Source: visual.ly

The cosmological un-constant

Just a couple of abstract:

A general line element and a general metric tensor are defined as functions of two parameters $\alpha$ and $\alpha'$. The related Einstein's field equations of a gravitational potential field in a vacuum, including parameter $\Lambda$, have been derived. The parameters $\alpha$ and $\alpha'$ are identified in a gravitational field by the solution of the Einstein's field equations. Parallel with this, it has been find out that the so‐called cosmological constant $\Lambda$, is not really constant, but a function of gravitational radius, $\Lambda = f(r)$. This discovery is very important, among the others, for cosmology. One of the consequences is the new form of the acceleration equation of the universe motion that can be attractive (negative) or repulsive (positive). According to the observations, the repulsive acceleration gives rise to accelerating expansion of the universe at the present time. The obtained solution of the diagonal line element can be applied in a very strong gravitational field. Besides, this solution gives the Ricci scalar equal to zero, $R=0$. This is in an agreement with the current observation that our universe is flat.

from Novakovic B.M., Novakovic D.B. & Novakovic A.B. (2004). The Cosmological Constant $\Lambda$ is not Really Constant but the Function of a Gravitational Radius, AIP Conference Proceedings, 718 133. DOI: 10.1063/1.1787318

Extracting energy from a black hole

The Penrose process is a process theorised by Roger Penrose wherein energy can be extracted from a rotating black hole. That extraction is made possible because the rotational energy of the black hole is located, not inside the event horizon of the black hole, but on the outside of it in a region of the Kerr spacetime called the ergosphere, a region in which a particle is necessarily propelled in locomotive concurrence with the rotating spacetime. All objects in the ergosphere become dragged by a rotating spacetime. In the process, a lump of matter enters into the ergosphere of the black hole, and once it enters the ergosphere, it is split into two. The momentum of the two pieces of matter can be arranged so that one piece escapes to infinity, whilst the other falls past the outer event horizon into the hole. The escaping piece of matter can possibly have greater mass-energy than the original infalling piece of matter, whereas the infalling piece has negative mass-energy. In summary, the process results in a decrease in the angular momentum of the black hole, and that reduction corresponds to a transference of energy whereby the momentum lost is converted to energy extracted.
The process obeys the laws of black hole mechanics. A consequence of these laws is that if the process is performed repeatedly, the black hole can eventually lose all of its angular momentum, becoming non-rotating, i.e. a Schwarzschild black hole. Demetrios Christodoulou calculated an upper bound for the amount of energy that can be extracted by the Penrose process.

And Reva-Kay Williams used the Penrose process to explain the collimated and asymmetrycal jets from some space objects, like rotating black holes:

Over the past three decays, since the discovery of quasars, mounting observational evidence has accumulated that black holes indeed exist in nature. In this paper, I present a theoretical and numerical (Monte Carlo) fully relativistic 4-D analysis of Penrose scattering processes (Compton and $\gamma \gamma \rightarrow e^+ e^-$) in the ergosphere of a supermassive Kerr (rotating) black hole. These model calculations surprisingly reveal that the observed high energies and luminosities of quasars and other AGNs, the collimated jets about the polar axis, and the asymmetrical jets (which can be enhanced by relativistic Doppler beaming effects), all, are inherent properties of rotating black holes. That is, from this analysis, it is shown that the Penrose scattered escaping particles exhibit tightly wounded coil-like cone distributions (highly collimated jet distributions) about the polar axis, with helical polar angles of escape varying from 0.5o to 30o for the highest energy particles. It is also shown that the gravitomagnetic (GM) field, which causes the dragging of inertial frames, exerts a force acting on the momentum vectors of the incident and scattered particles, causing the particle emission to be asymmetrical above and below the equatorial plane, thus breaking the reflection symmetry of the Kerr metric (above and below the equatorial plane). When the accretion disk is assumed to be a two-temperature bistable thin disk/ion corona, recently referred to as an advection dominated accretion flow (ADAF), energies as high as 54 GeV can be attained by these Penrose processes alone; and when relativistic beaming is included, energies in the TeV range can be achieved, agreeing with observations of some BL Lac objects. When this model is applied specifically to quasars 3C 279 and 3C 273, their observed high energy luminosity spectra can be duplicated and explained. Moreover, this Penrose energy extraction model can be applied to any size black hole, irrespective of the mass, and, thus, suggests a complete theory for the extraction of energy from a black hole.

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Williams, R.K., High Energy-Momentum Extraction from Rotating Black Holes Using the Penrose Mechanism. American Astronomical Society, 195th AAS Meeting, #134.02; Bulletin of the American Astronomical Society, Vol. 32, p.881
Reva Kay Williams (2002). The Gravitomagnetic Field and Penrose Processes, arXiv: astro-ph/0203421v2
Penrose, R., Gravitational Collapse: the Role of General Relativity. Rivista del Nuovo Cimento, Numero Speziale I, 252 (1969) (pdf)

The birth of a planet

partially translated by @ulaulaman from a post by @_starblogger_

When I write about the Nice model, I explain how a group of researchers try to explain the birth of our Solar System. The approach of the group is to design some simulations about the dynamics of the whole Solar System. This approach is very used in physics, in particular when calculation by hand are too complicated. So, today I would propose you a video with the interview to a new group that perform some simulations in order to explain how a planet could born. The group, leaded by Sally Dodson-Robinson is

(...) carrying out a series of computer simulations of the proto-stellar disks. The simulations provide some important parameters, such as the turbulence and the temperature of the disc, which influence how and where the planets are formed. In a disk with a high percentage of turbulence, the particles forming the planetesimals move very quickly and go away from each other. At the other hand, in a less turbulent situation, there will be a much more probability that the particles collide and are aggregated together in order to give rise to future planets. In 1988, it was known only an extrasolar planet, and today almost 2400 waiting to be confirmed. Therefore, understanding those favorable conditions for the formation of a planet will allow astronomers to discover more and more of them and, at the same time, will provide important new clues about the birth and evolution of the Earth and then of the Solar System.⁽¹⁾

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(1) Translated from AstronomicaMens

The void theory

On tumblr, one of my reader, frankietwohats, ask me the following question:

Can I ask you a random question? I can't remember the name of a theory that argued that the universe wasn't expanding, but instead was stretching. Do you happen to know of it/it's name? It came up in conversation today (well, universe expansion did) and I want to look into it more.

I don't know if this is the theory that you intend, but after a briefly research on Google, i find th Void theory. About it, Esther Inglis-Arkell writes on io9:

There was a time that the earth was considered the center of the universe. Then it got knocked out of the way by the sun, and ever since then the astronomer's mantra was, "We are nothing special." The part of the universe the earth resides in can't be any different than any other part. It's not unique, or remarkable, or even out of the ordinary. Void Theory contradicts all that. Instead of sitting in a typical part of the universe, the earth sits in an unusually empty part; a void. The universe isn't expanding due to some mysterious force. It's just that when light comes from a denser part of the universe and trips across the void, it is altered to make it look like the universe is expanding. Since this exansion is the same when observed from any part of the earth, the earth has to be roughly at the center of this void. Suddenly, the observable universe is geocentric again.

But... what is the void theory?

This diagram reveals changes in the rate of expansion since the universe's birth 15 billion years ago. The more shalow the curve, the faster the rate of expansion. The curve changes noticeably about 7.5 billion years ago, when objects in the universe began flying apart as a faster rate. Astronomers theorize that the faster expansion rate is due to a mysterious, dark force that is pulling galaxies apart.

First of all, following Clifton, Ferreira and Land⁽¹⁾, we must remember that our picture of the universe is based on the following two principles: the spacetime is dynamical, obeying to the Einstein's equations; the Universe is homogeneous and isotropic on large scales, that is a generalisation of the Copernican Principle that the Earth is not in a central, specially favored position.
Now, the exact solution of Einstein's equations was provided by Lemaitre-Tolman-Bondi spacetime \[\text{d} s^2 = -\text{d} t^2 + \frac{Y'^2}{1-K} \text{d} r^2 + Y^2 \text{d} \Omega\] In this model there are four free parameters: the density at the origin, the density and radius at the midpoint, and the radius at which we match to Einstein-de Sitter spacetime⁽²⁾. Instead the void model:

is completely specfied by the radial profile, the Hubble rate at the void centre today, $H_0$, the radiation density today, which is fixed by the CMB mean temperature, $T_0 = 2.725 K$, and the baryon fraction $f_b = \frac{\rho_b}{\rho_m}$. Outside the void we asymptote to EdS.

The curvature for three different types of voids

Super-Nobel in Physics 2011

The first observation of a supernova is dated 1572 by Tycho Brahe, but the hystorically most important supernova's observation is the Galilei's observation in 1604:

The supernova of 1604 caused even more excitement than Tycho's because its appearance happened to coincide with a so-called Great Conjunction or close approach of Jupiter, Mars and Saturn.⁽¹⁾

The Galilei's discover was revolutionary for one important reason:

Galileo's observations and those made elsewhere in Italy and in Northern Europe indicated that it was beyond the Moon, in the region where the new star of 1572 had appeared. The appearance of a new body outside the Earth-Moon system had challenged the traditional belief, embodied in Aristotle's Cosmology, that the material of planets was unalterable and that nothing new could occur in the heavens.⁽¹⁾

About the new star

Galileo states that [it] was initially small but grew rapidly in size such as to appear bigger than all the stars, and all planets with the exception of Venus.⁽¹⁾

We can confrount the observation with modern definitions:

Novae are the result of explosions on the surface of faint white dwarfs, caused by matter falling on their surfaces from the atmosphere of larger binary companions. A supernova is also a star that suddenly increases dramatically in brightness, then slowly dims again, eventually fading from view, but it is much brighter, about ten thousand times more than a nova.⁽¹⁾

These dramatical events became soon a good tools in order to observe the expansion of the universe:

Type Ia supernovae are empirical tools whose precision and intrinsic brightness make them sensitive probes of the cosmological expansion.⁽⁵⁾

And observing a series of supernovae the team of Brian Schmidt (1967) and Adam Riess (1969) in 1998⁽³⁾ and the team of Saul Perlmutter (1959) in 1999⁽⁴⁾ found an important consmological observation: Universe is accelerating!

Review: Death from the skies

#SciDoom

The universe is trying to kill you.
Philip Plait, Death from the skies

The Universe is the most dangerous place that you can imagine. There are a lot of perils: asteroids and comets, supernavae, gamma ray bursts and finally our star, the Sun. Every source of danger is examined in nine chapters introduced by a fictional short story, that is scientifically correct. In these introductory stories, Plait describes a possible scenario in which Earth is shotted by, for example, a comet o a great asteroid, like the one that leaves the Meteor Crater in Arizona

(Commons)

or the ones that probably caused the dinosaurs extintion.
In order to prevent a bad encounter with a great object, physicists describe a lot of possible solutions: in the list there are a nuclear bomb, an impact against an artificial object (like Deep Impact with Tempel 1) or try to change the bullet's trajectory using the gravitational force of an ather astetoids. This last solution is proposed by B612 Foundation and, like the others, present a lot of difficulties, but is technically realizable now!
Some possible problems are, for example with shot solutions, that the object is broken into too big pieces, while for the gravitational solution we must demonstrate a very precise control of the gravity. These are the only enemies we can prevent, but against the others we could realize some particular protection, like radiations from Sun or from supernovae explosions. In this last case, the probability to be shot is 1/10000000, against 1/700000 of an asteroid shot, that is a probability actually higher than terrorism!
Another danger from outer space is an... alien attack! Don't worry! I don't mean the little green men from Mars, but simply eventually microscopic life present in asteroids or comets. An attach like this has a very low probability, first of all because the aliens must survive at Earth atmosphere, and after because they have a low probability to interact with DNA developed in our environment: following our knowledge, we must remeber that in the Universe our planet is unique!
I don't know if we are alone or not, but in this moment it is so...
In the last part of the post I spend some words about Sun:

Brian May, astrophysicist

Brian May is the famous guitarist of the Queen, Freddie Mercury's rock band (and one of my favourite band!), but is also an astrophysicist!
He wasborn 19 July 1947 in Twickenham, London. He studied mathematics and physics at Imperial College, where he started also the PhD program, but he abandoned when Queen became a succesful band in the world. He completed his PhD in 2007⁽⁵⁾, but he did not forget his research activity, indeed he written with Patrick Moore and Chris Lintott Bang! – The Complete History of the Universe (2006)... but... just a moment... research activity? Yeah!
In 1972 and 1973 two papers signed by Mr.May are be published: Mg_I Emission in the Night-Sky Spectrum and An Investigation of the Motion of Zodiacal Dust Particles (Part I), written with Mr.Hicks and Mr.Reay.
May and collegues are interestend in zodiacal light, in particular in Mg_I spectrum, near the 5183.62 Å wavelength.
The importance of this kind of studies is that the Mg_I and Mg_II formation is one feature in the interaction between atmosphere and star radiations^{(2, 3)}.
But go to the papers: in order to determine the absorbtion lines from zodiacal light, Brian and friends used the Fabry-Perot interferometer:

The method was to sample, for 48 s, each of up 18 points acrossthe spectral interval. Pulse counting electronics and a line printer recordedthe signal levelat each sample point. A second channel of pulse counting monitored the overall sky background over a widewaveband, thus allowing correction forfluctation in sky transparency. The resolving power of the interferometer was 3500, corresponding to an instrumental profile width of 1.5 Å.

Obesrvation time is September, October 1971 and April 1972 from the observatory at Izana on Tenerife, Canary Islands.

The Nice model of Solar System

When I see the previous video (via Keplero) I immediatly thought to the Nice model, a simulation model about our Solar System developed by Rodney Gomes, Harold F. Levison, Alessandro Morbidelli, Kleomenis Tsiganis in three papers published on Nature vol.235
First of all a little resume about Solar System formation thoery. Following Kant-Laplace model, our Solar System was born from massive and dense clouds of molecular hydrogen—giant molecular clouds. In this nebula occurs planets formation. In particular theory supposed that giant planets formed on circular and coplanar orbits^{(3, 5)}. In this picture, all planets aresubstantially formed in the same position of the actual System. The Nice model suggests that all Solar System objects are formed in a different position and a perturbation in orbits forced the actuall more stable orbits.
The original model's core was developed by Gomes, Morbidelli and Levison in 2004⁽⁷⁾

We study planetary migration in a gas-free disk of planetesimals. In the case of our Solar System we show that Neptune could have had either a damped migration, limited to a few AUs, or a forced migration up to the disk’s edge, depending on the disk's mass density. We also study the possibility of runaway migration of isolated planets in very massive disk, which might be relevant for extra-solar systems. We investigate the problem of the mass depletion of the Kuiper belt in the light of planetary migration and conclude that the belt lost its pristine mass well before that Neptune reached its current position. Therefore, Neptune effectively hit the outer edge of the proto-planetary disk. We also investigate the dynamics of massive planetary embryos embedded in the planetesimal disk. We conclude that the elimination of Earth-mass or Mars-mass embryos originally placed outside the initial location of Neptune also requires the existence of a disk edge near 30AU.

In this first paper there's an analytic toy model for migration process. First of all they calculate the variation in time of the semi-major axis $a_P$ of the planet:
\[\frac{\text{d} a_P}{\text{d} t} = \frac{k}{2 \pi} \frac{M(t)}{M_P} \frac{1}{\sqrt{a_P}}\]
where $M(t)$ is the amount of material in orbits that cross the orbit of the planet, $M_P$ the mass of the planet, $k$ a parameter of the distribution of those orbits.
The evolution of $M(t)$ is described by the following equation:
\[\dot M (t) = -\frac{M(t)}{\tau} + 2 \pi a_P |\dot a_P| \sigma (a_P)\]
where $\tau$ is decay time of planetesimals, $\sigma$ the surface density of not yet scattered planetesimals, $\dot a_P$ the planetary migration rate, $\dot M (t)$ the decay of the planetesimal population due to the planetesimal's finite dynamical lifetime.
Sobstituting the first equation in the second, it can obtain:
\[\dot M (t) = \left ( \frac{1}{\tau} + |k| \sqrt{a_P} \frac{\sigma(a_P)}{M_P} \right ) M(t)\]
And the solution of this equation is given by
\[M(t) = M(0) \text{e}^{\alpha t}\]
where
\[\alpha = \frac{1}{\tau} + |k| \sqrt{a_P} \frac{\sigma(a_P)}{M_P}\]
that is time independent.
We can have two different situations: $\alpha$ negative, $\alpha$ positive.
In the first case the migration speed is too low to compensate the loss of planetesimals: the migration mode is called damped migration.
In the second case $M(t)$ grows exponentially, and migration, called forced migration, is self-sustained.

After the giant planets were formed and the circumsolar gaseous nebula was dissipated, the Solar System was composed of the Sun, the planets and a debris disk of small planetesimals.

Planets' migration so is caused by the change of angular momentum during the scattering with planetesimals.

Numerical simulations⁽⁴⁾ show that Jupiter was forced to move inward, while Saturn, Uranus and Neptune drifted outward.

An example of the output produced by Nice simulations is the following plot: