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Does the Perseid peak cause enough light pollution to be a problem?
The annual Perseid peak occurs between August 9-14. During this time, about one meteor burns up in the atmosphere per minute.
When these meteorites burn up, they generate light. When you have one of these per minute, does it produce enough light pollution to be a problem for those making astronomical observations?

Tought to answer, because the amount of airborne dust due to meteor showers and its stability in the upper atmosphere will vary significantly enough. We had many meteor showers, Perseids included, in the past that were a bit of a letdown and didn't produce as many shooting stars as initially predicted, and also the other way around of course.
But here's the thing tho, that discounting for any additional atmospheric glow during a few crucial hours of dusk and dawn, this airborne meteor dust might even improve the average atmospheric refraction with mostly extremely fine powder silicate dust settling onto the lower atmosphere and dispersing water molecules and binding to other solids (read: decrease humidity and pollutants), by being highly electromagnetically charged from the atmospheric reentry and electrostatically binding to larger atmospheric or pollution molecules, or simply for being hygroscopic and binding really good to water molecules, making them heavier enough to fall in a light spray back on the ground and remove the pollutants from the lower atmosphere in the process, too.
There might be other physical phenomena going on that I'm not aware of, but what I wanted to illustrate is, that there might even be positive side-effects in terms of light pollution vs increase in meteors, which is how we call meteoroids entering Earth's atmosphere.


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What are practical considerations for backyard radio-astronomy detection of black holes?
Evidently, direct observation of a black hole for an amateur astronomer, such as described for what professionals do in the question "How are black holes found?" would be nigh on impossible, so the observations would be based on their effects of the surrounding matter (specifically, accretion disks and jets) and more likely detecting the radiation signals.
Given that the locations of many black holes are known, what practical considerations would a backyard radio-astronomer need to consider to attempt to do detect black holes?
Amateur radio-astronomy detection of pulsars and gamma ray bursts are discussed practically in Introduction to Radio Astronomy (Society of Radio Astronomers), this question is to see what practical considerations would be needed to extend those techniques to detecting black holes.

I would say that the error boxes are too large to see any of the interesting behavior that BHs show. For example, Cyg A would probably just be a big radio-emitting blob, and the lobes would not be distinguishable.

@Manishearth can you get references and write that as an answer?

The resolution/error box. Radioastronomy has always been hindered by the resolution, because it is inversely proportional to the size of the telescope and making larger telescopes (even with interferometry) is not always easy. No amount of modern technology can substitute for a large effective diameter.  (When I say effective I'm including interferometry here; either way one needs a large area to build on).
Let's take a look at Reber's initial paper1 where he first mapped the sky:

In the diagram on the left, from top down, the three peaks in the contour map are Cas A, Cyg A, and finally Sgr A. The latter two have black hole origins, the former is a supernova remnant.
The resolving power of Reber's telescope here seems to have been 6 degrees, and it was 31.4 feet in diameter (and he focused on a 1.9m wavelength).
Now, by the Rayleigh criterion, the angular resolution is proportional to the wavelength divided by the diameter. As mentioned before, this is the major limiting factor for radioastronomers, and will be what holds amateur radioastronomers from making great telescopes — amateurs usually don't have acres or land in which to build a good interferometer (let alone the precision), and single-dish telescopes can't be made too large by an amateur. One may notice that I'm citing rather old observations here, on old telescopes; however given that radioastronomy technology has not changed nearly as much as size has, it should be OK to compare amateur telescopes with the smaller telescopes of the past.
Now, Cyg A was the first to be identified as a black hole, even though the radio-brightness of Sgr A was discovered at the same time. I'm focusing the rest of my analysis on Cyg A for this reason, as it stands to reason that the first confirmed BH out of the brighter radio sources would have more prominent indicators that it is a black hole.
Let's have a look at Cyg A with a better resolution:

(From this paper2, using the 5km array)
Note that the black blob in the center is the actual galaxy (probably an optical photograph superimposed on the contour map).
We can see that the lobes are less than a minute wide. (The actual galaxy is around 50 arcseconds wide)
To me, the most interesting thing that one would like to see here are the gas jets coming from the central galaxy. As mentioned in my answer here, these radio-emitting gas jets are in a steady line over thousands of light years, indicating that they come from some sort of cosmic gyroscope which has been steady for very long. However, even with the Ryle telescope the 1969 people could not get a picture of them; just a slight hint of their existence from the shape of the lobes.
Alright, so no gas jets. What else can indicate a black hole? They could try to look at the lobes themselves. They do not directly indicate the existence of a black hole, but their shape hints towards them being formed from jets (this is pretty much in retrospect).
However, with lobe dimensions of less than an arc minute, there's not much an amateur can get here, either. It's possible that a really good amateur telescope would just manage to notice that there are two lobes, but not much else as far as I can tell.
The other interesting bits would be the central galaxy itself, but it's too small. In the optical region one may have a chance of seeing Baade's "colliding galaxies" (it only looks like a pair of colliding galaxies). The gravitational effects (lensing, etc) are really only visible in the optical and beyond, for it to be visible in the radio we would need to be very lucky and have a huge radio source pass behind Cyg A — not happening anytime soon.

I'm pretty sure that a similar analysis would work for Sgr A or any other black hole candidate; the gas jets would be too small for an amateur radiofrequency resolution, and the gravitational effects of the black hole would only work well in the optical and X ray frequencies.
1. Reber, G. (1944). Cosmic Static. The Astrophysical Journal, 100, 279.
2. Mitton, S., & Ryle, M. (1969). High resolution observations of Cygnus A at 2. 7 GHz and 5 GHz. Monthly Notices of the Royal Astronomical Society, 146, 221.

another problem for an amateur looking for black holes is that the telltale signature of a black hole, coming in the form of continuous or bursts of X-rays and gamma rays, cannot be observed from the surface of the Earth, because the atmosphere (thankfully) protects us from that sort of stuff.

So that is why you need to go in space, or on the surface of a planet without atmosphere (the Moon would be suitable, Mars should do as well, since the atmospheric pressure is 6 millibars there and space rays come all the way to the surface, compared to 700-1000 millibars on Earth at sealevel), or send up your own space telescope, such as the likes of
http://xmm.esac.esa.int/ XMM Newton
http://chandra.harvard.edu/
and especially
http://www.nasa.gov/mission_pages/nustar/main/index.html
Nustar - delivering the X-ray goods.

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How can the orbit of a Kuiper Belt Object be differentiated from the transit of a rogue planet?
Related to the question "Are any Pluto-sized objects remaining to be discovered in the Kuiper Belt?" and the fact that most of the Kuiper Belt objects have very elliptical orbits, the question begs, what observational techniques are used to confirm that the object being viewed is an orbiting Kuiper Belt Object, as opposed to the transit of a rogue or 'orphan' planet?

I'm not speaking from an informed position here, but two things come to mind.
First is that a rogue planet is likely to be traveling very fast, relative to our solar system. An object from within our solar system (a Kuiper/Oort object) is going to have an orbital velocity. Something that isn't a part of the system at all could be traveling much, much faster.
Secondly, if a rogue planet somehow slowly drifted into our system at almost no speed, and then got pulled into a sort of orbital speed by the sun, the direction of its orbit might give it away. For example, it's orbital inclination could be way off--even perpendicular to the normal orbital plane. It also might be orbiting in the wrong direction--that is--clockwise, instead of ante-clockwise.
That being said, there's no reason that some disturbed Kuiper belt object might not have an eccentric orbital inclination or even an anti-clockwise orbit. But the larger the object, the less likely this is, because it would need a larger and larger disturbance to throw it so out of whack.

No special techniques are required that I am aware of, but several observations must be taken to make a reasonable estimate of the orbit. Once a sufficient number of observations are made so that the orbital elements can be determined, then anything that has an elliptical orbit (eccentricity >0 but >1) can be assumed to be orbiting as part of the solar system and thus not a transiting rogue object.
An object with an eccentricity to its orbit greater than 1 is following a hyperbolic escape trajectory, and, unless substantially perturbed by the gravity of another planet, is on its way out of the solar system. I am not aware of any such objects that are thought to have originated from outside the system, but comets have been known to have been flung from the system along hyperbolic paths from the influence of Jupiter.

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Jupiter FM - What are practical and inexpensive ways for the amateur detection of signals from Jupiter, especially of the transit of her moons?
What modifications to a standard AM/FM or shortwave radio are needed in order to be able to detect radio-wave signals emitted from Jupiter?
Would it be possible to detect the transit of the major moons and even minor planets (maybe even Ceres and Mars) using this method?

@Arne is right in his answer about two things, that the most suitable frequency for Jovian amateur radio is 20.1 MHz, and that this is a 15 meter wavelength. However, the antenna can actually be half the wavelength, and amateur radio astronomers have had good results listening to all kinds of Jovian sounds, including detecting occultations of its many moons as they produce change in frequency due to the Doppler shift when passing in front of it, amplification due to echo of Jupiter's own radio wave signature when close beside it from the observer's vantage point, and other effects causing radio wave frequency and amplitude changes with a simple dual dipole array that might look something like this:

        The Jove dual dipole array. Dipoles are suspended between PVC masts. Signals from the dipoles go to a power combiner and        then to the receiver. Source: Amateur Radio Astronomy Projects — Radio Signals from Jupiter (PDF)
Now this dual dipole antenna is more or less a simple two-piece of roughly half the wavelength of coaxial cable, stripped of insulation at the dipole ends and run dipoles parallel to each other at roughly 6.1 meters (20 ft) apart suspended over PVC masts. That is perfectly acceptable for nearly any amateur radio astronomer in both space and the price of the parts needed. There are also ways to help oneself with a lot smaller antenna, which I'll mention a bit later. Let's first clear the frequency range discussion with this really informative quote from Radio Receiver for Jupiter webpage (based on NASA's Radio JOVE project):

The peak of Jupiter signals occur around 10 MHz. Still this frequency
  is not that suitable, as it is very near to Ionospheric cutoff. The
  best suitable frequencies are in between 18 to 22 MHz, as the chances
  of getting emissions are more. In practice 18.7 MHz, 20.1 MHz, 22.3
  MHz are common. The frequencies above 30 MHz are not suitable because
  of less strength. The frequency of 20.1 MHz is used for this project,
  as the probability of getting emission is high. So the entire receiver
  is designed considering 20.1 MHz as the operating frequency.

Antenna is of course merely one part of the story. Second thing that is required is the receiver. NASA is sponsoring Radio JOVE project with an assembly manual for roughly 100 electronic components and pieces of hardware worth RJ1.1 Receiver (Radio Jove 1.1 Receiver) that can be almost completely assembled out of parts ordered from Radio Shack (it even includes RS part numbers). I'll add a photograph and a few other links, and you'll have to be on your own then:

   Self-assembled Radio Jove Receiver's front plate with two turning knobs for volume and tuning. Source: KB0LQJ Observatory
Some relevant links for building Radio Jove (or Jupiter FM, if you like, it will be your own receiver so name it as you wish), starting with already mentioned ones:

Amateur Radio Astronomy Projects — Radio Signals from Jupiter (PDF)

Ten years ago a group of (mostly)
  University of Florida graduates working at
  NASA conceived an educational outreach
  program known as Radio Jove. The idea was
  to build an inexpensive radio telescope kit
  suitable for detecting signals from Jupiter.
  The Jove receiver (Figure 2) is a simple
  direct-conversion design operating over a
  few hundred kilohertz range centered at
  20.1 MHz.

NASA's Radio JOVE project (PDF)

The site is currently down due to US government shutdown, so here's a Google cached version that sadly doesn't come with in-document images

KB0LQJ Observatory Amateur Radio Astronomy — Radio Jove observations

For my home observatory, I started with the Radio Jove receiver from NASA’s Radio Jove Project. This was a fairly easy-to-build kit with great directions, not just for the receiver but also the antenna setup and installation.  Unfortunately, I don’t have enough space to put up a phased antenna array.  Also, I’m bordered by power lines on the north and south sides of my property.   Also, since I’m in an urban area, I knew that I’d pick up a lot of noise.   Not to worry.   Solar observations are also quite interesting, and since the Sun is such a good signal source (especially so far this year), I opted for an antenna in my attic.

Radio Receiver for Jupiter

This website contains the Technical details of the antenna and receiver used for receiving natural radio emissions from Jupiter at 20.1MHz. The antenna and receiver discussed in this site is based on the design given by NASA Radio Jove Program.
  Natural radio emissions from Jupiter or from Sun are detected by using a dual dipole array as an antenna and with a sensitive receiver. The RF voltage developed at the antenna terminals is amplified with the RF amplifier and converted in to audio frequencies using a mixer. The audio signal thus generated is recorded on PC through a sound card in ‘wav’ format. Also a strip-chart recorder software is available to generate the strip-chart of data coming through sound card.

So there are indeed many ways to build your own antenna and receiver out of affordable and easily obtainable electronic parts, and some of these websites listed above will help you through the process of self-assembly, even providing some tricks how to do it easier, like for example assembling a smaller, in-house antenna array.
Now, one other thing that all these websites mention is also using various PC software that lets you analyze through computer's sound card received Jovian radio sounds, but since there's many different and free solutions out there, including NASA's own that runs on Windows PCs, I'll let you discover those on your own. Here's one page listing many links, to get you started. More computer savvy of you might even write your own software for this purpose, this is Stack Exchange afterall.
And if anyone is wondering what such self-assembled radio receivers and antennas are capable of, here's a link to a collection of various Jovian sounds in the radio wavelengths on Astrosurf.com, and another one as a collection of solely amateur radio astronomy sounds of Jupiter and its moons (scroll a bit down to the list of recordings). And here's a short description of various sound types one might hear:

Chorus (quote source: The University of Iowa Department of Physics and Astronomy)

Chorus consists of brief, rising-frequency tones that sound like the chorus of birds singing at sunrise, hence the name "chorus" or "dawn chorus." Chorus at Earth is generated by electrons in Earth's Van Allen radiation belts. Once generated, the chorus waves affect the motions of the electrons through a process called a wave-particle interaction. Wave-particle interactions disturb the trajectories of the radiation belt electrons and cause the electrons to hit the upper atmosphere.

Decametric noise storms (quote source: Radio-Jupiter Central on RadioSky.com)

The emissions we can hear are often referred to as decametric noise storms, because the waves are tens of meters long. Okay, it is possible to hear Jupiter from 15 to 38 MHz, but what are the optimal frequencies?  The consensus seems to be that 18 MHz up to about 28 MHz is a good place to listen.  A good rule would be to pick the lowest frequency in this range which was not being hindered by ionospheric refraction.

Whistlers (quote and image source: Wikipedia):

A whistler is a very low frequency or VLF electromagnetic (radio) wave generated by lightning.1 Frequencies of terrestrial whistlers are 1 kHz to 30 kHz, with a maximum amplitude usually at 3 kHz to 5 kHz. Although they are electromagnetic waves, they occur at audio frequencies, and can be converted to audio using a suitable receiver. They are produced by lightning strokes (mostly intracloud and return-path) where the impulse travels along the Earth's magnetic field lines from one hemisphere to the other.

Auroral Radio Emissions  (quote source: Wikipedia)

Auroral radio emissions from giant planets with plasma sources such as Jupiter's volcanic moon Io could be detected with radio telescopes.

And so on. The last two on the list are probably a bit of a stretch for amateur astronomers, with auroral radio emissions average frequency range at 100 to 500 kHz, and whistlers cutoff at usually around 30 kHz, and both requiring too big antennae, but I wouldn't bet against it being possible with smaller antennae either, although bow frequency cutoffs might prevent identification of actual aural events. But there are many other sounds to listen to both from Jupiter, as well as it's many moons, mostly though the bigger and closer ones.
Good luck tuning in to your own Jupiter FM and happy hunting for rare radio frequency events!

I would never have guessed that it might be possible with such an easy setup. Very good answer!

Same here.  15m is such a busy terrestrial band that I'm amazed that a dipole (not terribly directional) would pick up Jupiter without being swamped by all the local signals!

There are many fine detail points to making this all work, essentially a lot of fine tweaking, but that's already something an amateur astronomer should enjoy greatly. Antennae can be even smaller than half-wave dipoles (e.g. Hertzian dipole) but they won't achieve dBi (decibels relative to isotropic radiator) as high, so other factors will play a major role, like use of narrow band and low pass filters. But that could stretch several more pages long to properly answer, so I thought to just let readers find their own answers, or perhaps ask new questions. It would IMO make a great blog topic.

The StarGazers lounge featured a radio kit article for Jupiter radio astronomy. The same article is also featured over at the Radio Group of BritAstro.
It seems that 20.1 MHz is the suitable frequency for amateurs observing Jupiter. I am far from being an expert for radio astronomy, but for a small source such as Jupiter, I would assume that you need a big parabolic dish (for antenna gain and directionality), and a proper feed antenna, suited for 20.1 MHz. You will probably also need to have a motorized mount for the antenna, to track the motion of Jupiter across the sky.
I will post more info, after I have asked a friend, who's an expert on antenna design, which configuration may be suitable.
Edit: Ok, the infos are in. A parabolic dish is out of the question -- 20 MHz corresponds to about 15m wavelength. And dishes need to be many multiples of a wavelength. So we could use a dipole antenna, but those are not very directional. Also, the dipole needs to be rather large, for good gain. To make it directional, you need an array of steerable dipole antennas.
Summary: I think it is not really feasible to do this on an amateur scale. Of course, I am gladly being proven wrong!

There are posts mentioning it not being practical for amateurs because of the size of the antenna (generally) required combined with the need to "point it" in the right direction.
One answer to this is -- if you can just point a static antenna structure toward the sky (front poles supporting the forward-most element higher than the real-most support poles supporting it, thereby angling the beam toward space) then you simply let Earth be your antenna motor. The excitement comes from waiting for the precise time that Jupiter naturally moves through your window of opportunity.
This is a wonderfully feasible method of aiming huge wire antennas toward space for pretty low frequency signals of all kinds.
As far as "never knowing if it's just a terrestrial signal", for one thing, man's signals are not super-ultra-wide band like that. Receiver parameters should be set before being aimed at Jupiter, and results compared before and after. Plus there are all sorts of other tests and identification factors. With enough know-how, which is the free and laborless aspect of it, one can rule out man and extraneous natural interference.

At a minimum, you'll need a highly directional antenna appropriate for the frequencies in question (I do not know what they are).  The radio would also have to able to detect the frequencies that you expect to hear signals on.

-1 No research effort demonstrated. Other answers found specific frequencies.

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Why did the Comet Shoemaker-Levy-9 fragments cause such large explosions on Jupiter?
In July 1994, the comet Shoemaker-Levy 9 (D/1993 F2) tidally fragmented and these fragments collided into Jupiter, as per the image below.

Image source
The question is, what mechanisms resulted in these small fragments causing such large explosions in the Jovian clouds?

Shoemaker Levy 9 was estimated to have released kinetic energy equivalent to 300 gigatons of TNT. That is $1.255 \times 10^{21} {\rm J}$. This release through friction and compression was sufficient to heat the atmosphere to 4000K at first. That in turn should probably be enough to break down the molecular hydrogen and methane, releasing further energy. But that's only my guess. The heating from the impact alone should make a huge fireball.
Sources:
Fragment Size and Mass Estimates
Galileo observations

An important factor is that the comet had fallen through Jupiter's gravitational field, picking up Jupiter's escape velocity of about 60 ${\rm km/s}$ in addition to whatever velocity it had as it approached the Jupiter system. A paper by D. A. Crawford from the Sandia National Laboratories gives detailed estimates of the sizes of all the fragments at impact. Three of them are estimated at 1km diameter or more, so they were not really small.

It's also important to remember kinetic energy scales with the square of velocity. As Jupiter escape velocity is nearly 6x that of Earth, the potential gravitational energy for a given mass is about 6*6 = 36 times larger in Jupiter.

FWIW, the kinetic energy density of material at 60 km/s is 1800 MJ/kg. Chemical explosives only have around 10 MJ/kg or so of explodable chemical potential energy.

@The_Sympathizer: I remember the pre-collision estimates suggesting induced fusion. NASA also planned to turn approaching Galello spacecraft to try to catch any reflections of the Jovian moons but never heard word of any result thereof.


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Which galaxy is receding from the Milky Way the fastest? What is known of the mechanism behind its recession?
Galaxies are always in motion relative to the Milky Way. My question is, which galaxy is receding the fastest from our viewpoint?
What is the theorised mechanism that causes this?

How are you claiming gravity as the cause of the expansion of the universe when almost nothing is known about dark energy? Its not even known if dark energy is a real thing, a result of a theory of gravity which we have not yet discovered (just as general relativity helped explain the orbit of mercury over newtonian gravity), or even just the result of our patch of the universe being situated in an unlikely but nevertheless possible gigantic void which would cause it to expand in all directions because of the gravitational pull of objects we can't yet detect.

There are a lot of unknowns about dark energy. However, typically, it is included into Einstein's field equations through the addition of a term called "the cosmological constant". If it is in fact supposed to be included in GR in this particular way (which it is absolutely not clear that it is supposed to be), then the interpretation is that it must have a negative equation of state. That's all I was saying below. Secondly, we have mapped out the large scale universe out to a fair distance - we do not live at the center of a void (unless the size of the void is that of the entire universe).

This question may be a duplicate to: On what scale does the universe expand?
The mechanism for the expansion of the universe is gravity, manifested through what's known as Dark Energy. Dark Energy is a component to the universe which today, composes 68.3% of the energy density of the universe. You may be confused as to how gravity could be responsible for the expansion of the universe, but the equation of state of DE,
w = pressure/density

is negative (w_DE = -1), which means that it has anti-gravitational properties. Additionally, its density remains constant as the coordinates of the universe change, which is the reason why it dominates later on in the universe's history (while all other components, matter (dark or otherwise) and radiation/relativistic matter, become diluted with the expansion of the universe).
To answer your question, because the expansion of the universe is happening at all points in space, it looks like the "center" of expansion is at every point in space (see: Space expansion in layman terms), the galaxies furthest away (highest redshift), are the ones moving quickest away from the Milky Way Galaxy.

Is there a specific galaxy receding the fastest?

Whatever the furthest one discovered so far - that's the one receding the fastest. Until we discover a further one. So the question to ask is "what is the furthest galaxy discovered"

@RoryAlsop yes, something like that

Well in that case: I think it's MACS0647-JD

http://www.space.com/18502-farthest-galaxy-discovery-hubble-photos.html

Expansion is not the only mechanism causing galaxies to move away from us. Galaxies have their own momenta, otherwise they would not collide. The galaxies of the Local Group orbit a center of mass between Milky Way and Andromeda (though their orbits may not be radial). See http://arxiv.org/ftp/arxiv/papers/1101/1101.2821.pdf

This momentum you describe is motion relative to the expansion of the universe (the "Hubble Flow"), and it's deemed peculiar velocity. Yes, it does dictate how galaxies of the same group/cluster move with respect to one another, however his question is asking about galaxies which move the fastest away from the MW. These are certainly non-local galaxies, and the reason is because of the expansion of the universe, not peculiar velocity.

@astromax If expansion is discounted, would it be possible to calculate the galaxy moving away from the Milky Way the fastest in peculiar velocity only?

@called2voyage Sure, if the universe didn't expand, and the motions of galaxies had only to do with orbiting about local centers of mass, then the redshift of all galaxies would be telling you about their peculiar velocities. When we measure redshifts, we're measuring the speed of both the peculiar velocity of its motion about local influences and the bulk flow of the universe. It just so happens that the bulk flow trumps local gravitational influences on large scales.

The galaxy that is receding away from us fastest is whichever galaxy currently holds the record for the highest measured redshift.
This galaxy obviously changes as more and more discoveries are made. This web page that describes redshift, may keep an up-to-date record of this. It lists UDFy-38135539, discovered in the Hubble Ultra Deep Field, as a previous record holder (see below), with a spectroscopically confirmed redshift of $z=8.5549 \pm 0.0002$.  That is, lines in the spectrum appear at wavelengths that are a factor of $(1+z)=9.55$ times longer (redder). But there is apparent controversy over the claimed detection of spectral features in this galaxy. (e.g. Bunker et al. 2013).
Bramnmer et al. (2013) report the "tentative detection" of a possible Lyman alpha emission line at $z=12.12$ for UDFj-39546284, another ultra deep field galaxy.
Either way it seems only a matter of time before $z>9$ galaxies are confirmed, since there are many candidates that have so far been selected only by virtue of their peculiar colours (Lyman break galaxies at near infrared wavelengths, including MACS0647-JD mentioned in comments to other posts). e.g. Bouwens et al. (2014).
Update Oesch et al. (2016) report HST grism spectroscopy of a high redshift galaxy candidate, GN-z11, identified in the CANDELS/GOODS survey. They confirm the presence of a Lyman break indicating a spectroscopic redshift of 11.1. This appears to be the current record holder.
The reasons that these galaxies are receding from us is simply the expansion of the universe. Galaxies that are further away appear to recede faster. The galaxies discussed above must be $>13$ billion light years away according to the current "concordance" cosmological model.
Translating a redshift to a recession velocity requires knowledge of the cosmological parameters. Fig.2 of Davis & Lineweaver (2004) shows the relationship. For our current best estimates of cosmological parameters, a redshift of 11 corresponds to a recession velocity of 2.3c. That is, this galaxy is currently receding from us at 2.3 times the speed of light.

How fast, in km/sec, are these galaxies with redshifts around 9 receding?

@john see new last paragraph.

@john : 2.3c is roughly 690,000 km/sec.


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What theories are there in explaining the formation of the Pluto-Charon system?
After reading the question and answer to Effect of Charon on Pluto, a further question is this: how is the Pluto-Charon relationship explained?
Specifically, what theories are there in how did the Pluto-Charon system was formed?
Additionally, does this explain the presence of other moons (Nix, Hydra etc)?

The favored theory is a giant impact, at the end of the final stage of planetary formation (Canup, 2005). A "giant impact" is a collision with an object of a comparable size of the planet. That is also the most probable scenario for lunar formation (Canup, 2004).


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How long would it take for a rogue planet to evaporate in the late stages of the Universe?
I've read once a popular science book, in which the author calculated how long would it take for the most massive black holes to evaporate because of Hawking radiation. He claimed that after that time the Universe will be the soup filled only with elementary particles.
However, what would happen with celestial bodies that aren't black holes? For example, a rogue planet of the size of Earth, drifting somewhere in deep space, in an extremely cold Universe? What known effects would cause that planet to evaporate? How long would it take?

Assuming that you're talking about Hawking Radiation affecting black holes, no know phenomenon affects planets, stars, or other celestial non-black hole objects.

Before the evaporation of black holes that you mention, our universe will enter what is known as the Black Hole Era. About $10^{40}$ years from now, all the protons and neutrons in the universe will have decayed into positrons and neutrinos. This is how the last of the planets will pass away.
The Black Hole Era is so named because at this point only black holes and elementary particles will remain.
It should be noted that there is currently no evidence for proton decay, and so this phase of the Universe is strictly theoretical.
Source:

The Decay of Heaven - DeepAstronomy.com

This page by physicist John Baez explains what will happen in the long term to bodies that aren't massive enough to collapse into black holes, like rogue planets and white dwarfs, assuming they don't cross paths with preexisting black holes and get absorbed. Short answer: they'll evaporate, for reasons unrelated to Hawking radiation. It's apparently just a thermodynamic matter, presumably due to the internal thermal energy of the body periodically causing particles on the surface to randomly get enough kinetic energy to achieve escape velocity and escape the body (the wiki article here mentions this is known as 'Jeans escape'). Here's the full discussion:

Okay, so now we have a bunch of isolated black dwarfs, neutron stars, and black holes together with atoms and molecules of gas, dust particles, and of course planets and other crud, all very close to absolute zero.
As the universe expands these things eventually spread out to the point where each one is completely alone in the vastness of space.
So what happens next?
Well, everybody loves to talk about how all matter eventually turns to iron thanks to quantum tunnelling, since iron is the nucleus with the least binding energy, but unlike the processes I've described so far, this one actually takes quite a while. About $10^{1500}$ years, to be precise. (Well, not too precise!) So it's quite likely that proton decay or something else will happen long before this gets a chance to occur.
For example, everything except the black holes will have a tendency to "sublimate" or "ionize", gradually losing atoms or even electrons and protons, despite the low temperature. Just to be specific, let's consider the ionization of hydrogen gas — although the argument is much more general. If you take a box of hydrogen and keep making the box bigger while keeping its temperature fixed, it will eventually ionize. This happens no matter how low the temperature is, as long as it's not exactly absolute zero — which is forbidden by the 3rd law of thermodynamics, anyway.
This may seem odd, but the reason is simple: in thermal equilibrium any sort of stuff minimizes its free energy, E - TS: the energy minus the temperature times the entropy. This means there is a competition between wanting to minimize its energy and wanting to maximize its entropy. Maximizing entropy becomes more important at higher temperatures; minimizing energy becomes more important at lower temperatures — but both effects matter as long as the temperature isn't zero or infinite.

[I'll interrupt this explanation to note that any completely isolated system just maximizes its entropy in the long term, this isn't true for a system that's in contact with some surrounding system. Suppose your system is connected to a much bigger collection of surroundings (like being immersed in a fluid or even a sea of cosmic background radiation), and the system can trade energy in the form of heat with the surroundings (which won't appreciably change the temperature of the surroundings given the assumption the surroundings are much larger than the system, the surroundings being what's known as a thermal reservoir), but they can't trade other quantities like volume. Then the statement that the total entropy of system + surroundings must be maximized is equivalent to the statement that the system alone must minimize a quantity called its "Helmholtz free energy", which is what Baez is talking about in that last paragraph--see this answer or this page. And incidentally, if they can trade both energy and volume, maximizing the total entropy of system + surroundings is equivalent to saying the system on its own must minimize a slightly different quantity called its "Gibbs free energy" (which is equal to Helmholtz free energy plus pressure times change in volume), see "Entropy and Gibbs free energy" here.]

Think about what this means for our box of hydrogen. On the one hand, ionized hydrogen has more energy than hydrogen atoms or molecules. This makes hydrogen want to stick together in atoms and molecules, especially at low temperatures. But on the other hand, ionized hydrogen has more entropy, since the electrons and protons are more free to roam. And this entropy difference gets bigger and bigger as we make the box bigger. So no matter how low the temperature is, as long as it's above zero, the hydrogen will eventually ionize as we keep expanding the box.
(In fact, this is related to the "boiling off" process that I mentioned already: we can use thermodynamics to see that the stars will boil off the galaxies as they approach thermal equilibrium, as long as the density of galaxies is low enough.)
However, there's a complication: in the expanding universe, the temperature is not constant — it decreases!
So the question is, which effect wins as the universe expands: the decreasing density (which makes matter want to ionize) or the decreasing temperature (which makes it want to stick together)?
In the short run this is a fairly complicated question, but in the long run, things may simplify: if the universe is expanding exponentially thanks to a nonzero cosmological constant, the density of matter obviously goes to zero. But the temperature does not go to zero. It approaches a particular nonzero value! So all forms of matter made from protons, neutrons and electrons will eventually ionize!
Why does the temperature approach a particular nonzero value, and what is this value? Well, in a universe whose expansion keeps accelerating, each pair of freely falling observers will eventually no longer be able to see each other, because they get redshifted out of sight. This effect is very much like the horizon of a black hole - it's called a "cosmological horizon". And, like the horizon of a black hole, a cosmological horizon emits thermal radiation at a specific temperature. This radiation is called Hawking radiation. Its temperature depends on the value of the cosmological constant. If we make a rough guess at the cosmological constant, the temperature we get is about $10^{-30}$ Kelvin.
This is very cold, but given a low enough density of matter, this temperature is enough to eventually ionize all forms of matter made of protons, neutrons and electrons! Even something big like a neutron star should slowly, slowly dissipate. (The crust of a neutron star is not made of neutronium: it's mainly made of iron.)


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How often does Earth cross the galaxy regions with higher supernovae activity?
According to Summa Technologiae, a book by a Polish author Stanisław Lem that based his science fiction novels on scientific research of the era, the Earth crossed in the moment of forming of life the arms of the Galaxy, with high supernovae activity, which triggered life creation. Afterwards, it moved to regions with low supernovae activity, which enabled the preservation of existing life.
I'd like to test the validity of this claim against current research. How often does the Earth cross regions with higher concentrations of stars (and therefore, much greater chance of gamma burst wipe)? Additionally, how many times the probability of nearby supernova explosion is higher in that regions?

Have you read the relevant Wiki article? It has some information on this that cites some reliable sources, though I have no idea how accurate their citation of the material is. If you've already read this and are satisfied with it, what additional information are you looking for beyond this?

@called2voyage I'm more interested in Earth movement through galaxy and changing density of supernovae candidates connected with it

The paper "Frequency of nearby supernovae and climatic and biological catastrophes" by Clark, McCrea, and Stephenson published in Nature estimates (at 50% probability) that the Solar System passes within 10 parsecs of a supernova every 100 million years. This supernova would be part of a 20-parsec strip in which an estimated 50 supernovae occur.
They do speculate that a connection between the Solar System passing through these regions and climatic and biological events (such as ice ages) is possible.
You can read the paper yourself for more details. It's only two pages and you can purchase 48 hour access for $5 from Readcube.
Source:

"Frequency of nearby supernovae and climatic and biological catastrophes" - Clark, McCrea, and Stephenson

Do this paper deals with varying probability of meeting supernova depending on in which region of galaxy is the Solar System in given moment of its history?

@ŁukaszL. In brief, yes. It does not get into a lot of detail and there is no solid density/time information. You might, however, find their discussion of how they got to their estimate interesting.

Basically they figure Type II supernovae are usually localized to the arms of the Milky Way.

OK, but do they provide any calculations or estimations, how much more probable is to meet nearby supernova there?

I've given you all the end results: 50% probability of passing within 10 parsecs of one supernova every 100 million years, a supernova which is in a group of 50 supernovas in a 20-parsec region. The rest of the detail in in their methods, not their results.

Actually i read some where that in the entire time of humankind on earth, the earth has just covered 1/10th of a percent around the milky way galaxy, so assuming earth would survive that long and humankind would survive to witness it, i would say it would take billions-billions of year, before earth would move to closer to giant stars.
As for the supernova activity, humankind hasn't seen a supernova (excluding some theories), but our best bet to witness on would be Betelgeuse, it is already old for its size class and is expected to explode relatively soon (it may explode tomorrow or after a million years nobody knows exactly when) compared to its age.
So, i would say, we would be lucky if we witness a supernova in our lifetime.

This question was not asking about within the human lifetime but within the entire lifetime of the Earth. Also, it would be helpful if you could give a better reference for where you got your information. Do you think you could track down where you read this?

Humankind has seen several supernovae in historical times.  See https://en.wikipedia.org/wiki/History_of_supernova_observation  The last observed supernova in the Milky Way was Kepler's Star in 1604, but since the rise of telescopy our observational capabilities have risen to the point of being able to observe them in other galaxies.  Phil Plait, the Bad Astronomer gives the most likely next supernova as SBW1.  See http://www.slate.com/blogs/bad_astronomy/2014/01/13/sbw1_a_star_on_the_verge_of_supernova.html


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What is the standard reference point for measuring speed?
Speed, as we know, doesn't exist without first having a reference point. We then say that the reference point isn't moving at all, and speed is then measured in relation to the reference point.
What is the standard reference point when determining the speed of objects in astronomy? Earth?

The rest frame for measuring (astronomical) speeds and velocities depends on the context and purpose.
A geocentric frame, based on the Earth's centre of mass might be appropriate for objects in orbit around the Earth.
A heliocentric reference frame, centred on the Sun, is often used when describing the line of sight velocities of astronomical objects, but more usually, a barycentric frame at the solar system centre of mass is used. For example, this is how the radial velocities measurements of exoplanet host stars or components of eclipsing binaries would be quoted. It would also be appropriate for the motion of objects in the solar system.
Motions in the Galaxy are commonly defined in two ways. One is the Local Standard of Rest (LSR), which measures velocities with respect to the average motion of stars near the Sun. The second attempts to measure velocities with respect to the Galactic plane and radially and tangentially in the plane with respect to the Galactic centre. These are the so-called $U,V,W$ velocities. The position and motion of the LSR with respect to the Galactic centre are uncertain at the level of a few km/s, whereas the solar motion with respect to the LSR is more precisely known.
The Galactic centre can also be used as a reference frame for the motion of galaxies in our local group. e.g. when talking about the motion of the Andromeda Galaxy.
Finally, we can determine a cosmic standard of rest - the co-moving stationary frame of the Hubble flow - using precise measurements of the cosmic microwave background (CMB). In other words, we can determine our peculiar motion with respect to the Hubble flow by observing the dipole doppler signature in the CMB.

As Einstein realized and like you correctly state, you indeed can't measure the speed of an object by itself since it has to be measured relative to something else.
As a logic result, if you ask the question "How fast is X moving?", you will have to specify that you want the speed with respect to another object because motion cannot be measured without a reference point.
Some examples:

If you ask how fast Earth is moving with respect to its own axis, the center of the Earth will be your reference point.
If you want to know how fast the Earth orbits the Sun, the Sun will be your reference point.
If you want to know how fast the Moon's distance from Earth increases, Earth will be your reference point.
If you want to know the speed of our solar system in the milky way galaxy, the center of the Milky Way will be your reference point.

"standard" reference point
If no reference point is given, it could be assumed that the "standard reference point" is the location of the observer. In the realms of astronomy, that would be the location of the astronomer.
It should be noted that the astronomer could well be on an space mission outside Earth's atmosphere, or he/she could be using a telescope in Earth's orbit. Therefore, "Earth" can not generally be assumed to be a standard reference point for astronomy because, depending on the precision of the measurements and the location of (for example) the telescope, assuming "Earth" may result in inexact measurements.
EDIT
As @TidalWave correctly commented, there's also the International Celestial Reference Frame (ICRS) which can help you find reference points, calculate distances, etc. according to a celestial reference system, which has been adopted by the International Astronomical Union (IAU) for high-precision positional astronomy. The origin of ICRS resides at the barycenter of the solar system.
Wrapping it up:
If no reference point is defined and if we can assume that the astronomer works according to the rules and definitions of the International Astronomical Union (which would be the regular, if not ideal case), the International Celestial Reference Frame provides you with a "standard reference point" at it's center (which is the barycenter of the solar system).
In rare cases where IAU compliance can not be assumed (something that "might" happen in amateur realms), it has to be assumed that the reference point is the point of observation.

The last part is a bit off considering IAU adopted standards, plus it's impossible to determine one's speed by moving with the reference point. You might also wanna mention the International Celestial Reference Frame (ICRS) to also answer the last part of the question. It's all there... ;)

Well, when making measurements of the cosmic microwave background radiation, one has to subtract off the dipole moments associated with the movement of the satellite in orbit around the Earth, the Earth's motion due to it revolving around the sun, and the motion due to the sun about the center of the galaxy. I would imagine that this would always need to be a step whenever high accuracy observations (from telescopes in space) are made of distant objects. See: http://ned.ipac.caltech.edu/level5/March05/Scott/Scott2.html

@astromax Exactly. That's why I said it's not correct to assume Earth as a standard reference point.

@astromax True that as well, though for academic reasons, we can boil it all down to determining Inertial Frame of Reference, which might of course be different depending on yours and your object of observations common parameters that would describe time and space homogeneously, isotropically, and in a time-independent manner for both. So yes, with respect to background radiation, what you say is absolutely correct.


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What was the greatest spatial extent of the Asteroid Belt prior to the Late Heavy Bombardment?
Reading the article On the asteroid belt’s orbital and size distribution (Gladman et al. 2009), there is an interest point made:

asteroids a
  few kilometers and smaller in size are recent collisional shards of
  larger objects since their lifetime against collisional destruction is
  much less than the age of the Solar System. As such, these bodies preserve information about collisional breakup, the dominant
  physical process that has shaped the present asteroid belt.

This suggests that there would have been a lot more asteroids etc in the main belt at the time prior to the Late Heavy Bombardment (~4 billion years ago) - which is after the major planets had formed.
My question is what was the greatest spatial extent of the Asteroid Belt in the period just before the Late Heavy Bombardment?
(I am after peer reviewed resources).

There have been some studies based on observations on the best preserved impact craters of that time in the inner solar system, namely those on Mercury and the Moon.  In the paper, Impact-induced compositional variations on Mercury (Edgard et al. 2014), state that based on the nature of Mercury's craters, they have developed a

New dynamical simulations of the early evolution of the asteroid belt hint at the presence of additional
  asteroids in a region interior to the present-day belt, known as the “E-belt”.

Through their modelling and simulations, they have determined that the 'E-belt'

The recent reevaluation of the early history of the inner Solar System suggests the primordial asteroid belt could have originally extended well into the Mars-crossing zone

The 'Hungarias' are thought to be a remnant of this belt - as shown in the diagram below

Image attribution:
By Agmartin (Own work) [CC-BY-3.0], via Wikimedia Commons

authors: ʇolɐǝz ǝɥʇ qoq


text:
How do we detect if a planet has a liquid core?
In case of Earth, we have many hints about the internal structure of our planet, from what I know, the most important of which is analyzing seismic waves.
Do we have any instruments to detect if other solid planets, such as Mars or Venus, have solid or liquid core? Is it possible using remote sensing?

A good way to show how this is achieved is to show you a case study, below I will detail how we came to make the theory that Mercury has a liquid core.
It is first important to note that we are never definite of the properties but we are able to use the data to infer and create a theory that we believe to be an accurate representation of the truth.

The MESSENGER spacecraft was launched for the purpose of analyzing MErcuries Surface, Space ENvironment, GEochemistry and Ranging (hence MESSENGER).
Messenger had a number of pieces of equipment on board to allow it to conduct it's experiments, as detailed in the below image:

Mercury Laser Altimeter
So how does the MLA aide us in determining if Mercury has a liquid core? Well the purpose of the MLA is to:

track the planet’s slight, forced libration – a wobble about its spin axis – which will tell researchers about the state of Mercury’s core.

How does a Laser Altimeter work?

A laser altimeter is operated from a plane, a helicopter or a satellite. It determines the distance to the [Planet's] surface by measuring the time-of-flight of a short flash of infrared laser radiation. The instrument emits laser pulses which travel to the surface, where they are reflected. Part of the reflected radiation returns to the laser altimeter, is detected, and stops a time counter which was started when the pulse was sent out. The distance is then easily calculated by taking the speed of light into consideration.

Using this technology one can build up a 3D visualization of a planets surface
What scientists discovered from this mapping is that:

The planet's crust is thicker in low latitudes and thinner at the poles, a distribution that suggests the planet could have a liquid outer core. Its core is also large relative to the planet, comprising 85 percent of the planet's radius, much more than Earth.

How did they come to this conclusion? This paper explains in depth. (The full version is free, but requires signing up to the site, signing up is also free and has no costs and has the ability for you to turn off receiving emails and newsletters from them)
The most notable part is this excerpt and image:

Resulting moment of inertia parameters for more than 1 million Monte Carlo models that include a silicate crust and mantle, as well as an Fe-rich core that may contain solid and liquid layers are shown in

(A) Outer radius of Mercury’s liquid core. (B) Average density of the solid shell that overlies the liquid core
Conclusion
Essentially, specific readings taken by a Laser Altimeter allow us to map out the three dimensional shape of a planets surface. Analysis of the shape shows us that the crust is thinner at the poles which is likely due to a liquid core.
On top of this, Mercury is believed to have a small magnetic field (1% of our own) and this might be due to a liquid outer core circulating a solid inner core, acting like a dynamo. Though there is still much speculation given over what causes the magnetic field so this is unreliable to use for a solid footing.
Aside from that there is the logical thought process that larger planets are capable of creating huge amounts of heat and pressure at their cores which create a molten core, or at least a molten layer. This is why there is much skepticism over Mercury because it is such a small planet that its core should have solidified long ago.


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Have we observed any rogue/wandering stars?
Do we know (have we observed and cataloged) any rogue star, being not part of galaxy, but drifting somewhere in inter-galactic space?
I know that determining if a star is a part of galaxy or not is a matter of definition, but let's take those, that inter-galactic space is where the gravitational influence of any galaxy isn't dominating.

There's a whole wikipedia page devoted to them http://en.wikipedia.org/wiki/Intergalactic_star

Different types of observations have been made:

hypervelocity stars: there are stars in the halo of our Galaxy (it is kind of the suburbs of the Milky Way) with such velocity that they are escaping it, and aiming to the intergalactic medium (IGM). There not yet fully in the IGM, but the're on their way. (Reference)
molecular clouds in the IGM: there are molecular clouds detected in the IGM, that are forming stars. Stars are not directly observed, but these star forming molecular clouds are proof of their existence. (Reference)

It's hard to do better, because it is hard to observe directly stars outside of the Milky Way.

+1 I completely forget about molecular clouds in the IGM. It would be really wild to find an entire planetary system that developed in the IGM. Maybe one day we will find a way to observe them.

Well, most of the time you can expect to have a planetary system when you form a star, whatever the environment. Basically, all you need is a protostellar (and later protoplanetary) disk to form, and disks are a quite common feature of star formation (and they form by angular momentum conservation so you don't really care of the environment). So, ISM or IGM, as soon as you form stars, you should form planets as well!

Right that is what is so exciting...to imagine a world that formed completely outside of a galaxy. Could such a world form life? What would it be like? So many possibilities.

It would partly depends on the composition of your molecular clouds. I don't know much about it, but it seems that most of these clouds result from galaxies interaction (and are therefore made of gas from galaxies, not just H and He, the main components of IGM), so you could expect to have planets in habitable zone with enough oxygen, carbon, and all those elements you'd need to see life forms poping out.

Intergalactic stars are well established http://en.wikipedia.org/wiki/Intergalactic_star#Discovery


text:
What reason is there to doubt the existence of the hypothesised planet Tyche in the far distant solar system?
Please note, I do not necessarily believe in its existence, just after a scientific (hence, non-Wikipedia) reasoning to doubt the planet's existence, other than the "we would have seen it" argument.  I am, nor are the articles below, referring to the alleged 'Nemesis' planet, as in the question What are the current observational constraints on the existence of Nemesis?
According to the article Astronomers Doubt Giant Planet 'Tyche' Exists in Our Solar System (Wolchover, 2011), the planet Tyche is a hypothesised massive planet

by John Matese and Daniel Whitmire of the University of Lousiana-Lafayette, is not new: They have been making a case for Tyche since 1999, suggesting that the giant planet's presence in a far-flung region of the solar system called the Oort cloud would explain the unusual orbital paths of some comets that originate there.

Further information is found in the scientists' research paper Persistent Evidence of a Jovian Mass Solar Companion in the Oort Cloud (Matese and Whitmire, 2010), describe the hypothesised planet to be

of mass  1 − 4 M(Jupiter) orbiting in the
  innermost region of the outer Oort cloud. Our most restrictive prediction is that the orientation
  angles of the orbit normal in galactic coordinates are centered on
  , the galactic longitude of
  the ascending node = 319 and i, the galactic inclination = 103 (or the opposite direction)
  with an uncertainty in the normal direction subtending  2% of the sky.

They posit that the elongated orbit of Sedna is a result of the presence of this planet.
So, the question, what reason is there to doubt the existence of Tyche?

Disproving the existence of or proving the non-existence of an object is practically impossible, so I'm going to rephrase the question a little bit. It might also get you better answers because they won't just be aimed at disproving Tyche but questioning the methods that suggest Tyche in the first place.

As an example of the practical impossiblity I suggested, someone could say that Tyche existed at one point but got pulled out of orbit (in the case that Tyche were not where it should be observed).

Now, to progress toward answering your question, the livescience article that you linked in the body of your question refers to several astronomers questioning the methods employed by Matese and Whitmire in the first place. It would be interesting to see someone actually debunk their statistics from their paper, if possible.

@called2voyage yes, that is pretty much what I am after.  Good edit by the way.

@called2voyage while you said practically impossible, that's not precisely true.   We know there are no stars in the inner solar system apart from the sun because we'd have seen it if there was one.   Some things can effectively be proven within all reason to not be there.   I know for a fact that there are no tigers in my room as I type this.  It's often true that proving a negative is impossible, but it's not always true.   A large orbiting object can be ruled out within a certain distance because of surveys.  An object passing through is possible, but that's not a theorized planet.

@userLTK First, this was about planets. Second, it is not about within the inner solar system. I think you took my general tone a little too literally. Yes, a large orbiting object can be ruled out within a certain distance, but it is beyond that distance that is in question.

@userLTK You may have confused Nemesis and Tyche. Despite the mention of both, this question is about the latter.

@called2voyage I don't mean to argue, and I think it's safe to include a theoretical undiscovered planet (Tyche or otherwise) as a large orbiting object - my words chosen specifically to include Tyche.   In either case, it is possible to disprove the existence of a planet in the outer solar system within a certain distance.  Surveying the entire sky makes that possible.    That might be a minor point, but I wanted to make it.

@userLTK Possible to disprove its current existence in that location, yes. Has it been done yet? No. (Edit: Seems that it has been done now, but it wasn't at the time the question was originally posed.) Might be informative for others, though, so I'll leave it up.

Generally it would be that peers of Matese and Whitmire looking at the statistics and viewing that the results are not conclusive enough to indicate the existence of Tyche.  There can also be alternative reasons to explain the results mentioned in the paper other than a Jupiter sized planet in the Oort Cloud. As was mentioned in the comments, it is almost impossible to prove the non-existence of something.
At this time, the results from WISE are the best bet for locating Tyche if it exists.  As it will not be visible in the visible light spectrum but more likely in the infrared and the WISE mission scanned the entire sky which means that it won't have been missed due to looking in the wrong place.
http://www.jpl.nasa.gov/news/news.php?release=2011-060
http://www.nasa.gov/mission_pages/WISE/main/index.html#.UnJb3xCJ5fs
There isn't any hard science to show that Tyche doesn't exist.  It is skepticism that this is the explanation for observations to date.  These are the same reasons that Nemesis isn't thought to exist, the data isn't strong enough to support its existence.

"... it is almost impossible to prove the non-existence of something." -- Not always. We know there's no Jupiter-sized planet between the orbits of Mercury and Venus. We just don't yet have enough information about the Oort cloud.

@KeithThompson He did say "almost".

@called2voyage: Good point. But I expect that at some time in the future, we will have examined the Oort cloud closely enough to be confident that there's no Jupiter-sized planet out there, once we have enough data to be sure that we would have seen it if it existed. (Either that, or we will have found it.)

@KeithThompson I agree, good point of clarification.

@called2voyage: That happened sooner than I expected. See my answer. (I did the research, such as it was, after I posted the above comments.)

Several months after the accepted answer was posted:

In 2014, NASA announced that the WISE survey had ruled out any object with Tyche's characteristics, indicating that Tyche as hypothesized by Matese, Whitman, and Whitmire does not exist.

The quotation is from the Wikipedia article on Tyche. The article gives the following references for the statement:

http://www.jpl.nasa.gov/news/news.php?release=2014-075
https://arxiv.org/PS_cache/arxiv/pdf/1004/1004.4584v1.pdf
http://norwalk.dailyvoice.com/news/does-solar-system-have-giant-new-planet

Note that Tyche is not the same as the (currently) hypothetical Planet Nine.

Good to finally have confirmation.


text:
Is there any evidence that the Gas Giant planets in our solar system are experiencing orbital migration?
Planetary migration is defined by Lubow and Ida (2010) in their article Planet Migration as

the process by which a planet’s orbital radius changes in time. The
  main agent for causing gas giant planet migration is the gravitational interaction of the young
  planet with the gaseous disk from which it forms.

Relevant, it is believed by some that the gas giant planets in our solar system experienced orbital migration.  According to the article Wandering Gas Giants and Lunar Bombardment (Taylor, 2006), as an example,

Outward migration of Saturn might have triggered a dramatic increase in the bombardment rate on the Moon 3.9 billion years ago, an idea testable with lunar samples.

So my question is is there any evidence (not opinions) to suggest any form of migration occurring with our solar system's gas giants?

There is no direct evidence of change of orbits of the gaseous planets of the Solar System. But one could wonder about the stability of the Solar System, and if such events could happen again.
Theory:
The Solar System is a chaotic system, as most of gravitational systems involving $N$ bodies. The KAM theorems (for Kolmogorov, Arnold and Moser, the three authors of the theory) show that, for non-degenerate Hamiltonian systems, quasiperiodic trajectories exist, that could ensure the stability of the system. But unfortunatly the KAM theorems cannot be applied to the Solar System, because the planets are too massive.
Simulations:
It leaves us with numerical simulations, that show that the Solar System is indeed chaotic, and that planetary collisions, ejection and migration can happen. But if it is true for the telluric planets, it is not the case for the gaseous planets: one reason could be that they are not much perturbated by the inner planets.
Sources:

Laskar (1994)
Laskar (2012)


text:
How old is our Sun in Galactic years?
A year is measured as the amount of time it takes Earth to orbit the Sun once, a Galactic year is the time it takes our sun to make one full orbit of the center of the Galaxy.
In Galactic years, how old is our Sun?

According to the blog How old is the Sun in Galactic years? (Siegel, 2008), a Galactic year is about 223 million Earth years.
The age of the Sun, according to the Stanford Solar Centre's page How old is the Sun? is approximately 4.57 billion years.
This would put the sun at approximately 20.5 galactic years old.

Almost old enough to buy a galactic beer!

In some places, it already could.

@astromax Mmm...galactic beer. - Homer Simpson

The Galactic rotation period at the Sun's Galactocentric radius is about 230 million years (with a five percent uncertainty) and the Sun, as stated in user8's answer is 4.57 billion years old - giving $\sim 20\pm 1$ orbits.
However, the idea of a Galactic year is misleading.  For instance, the Milky Way rotation curve is quite flat between 1 and 10 kpc from the centre (see picture), so the "year" also varies by a factor of 10 over this range, with the year being much shorter in the inner part of the Galaxy.
Therefore to know how many rotation periods the Sun has executed requires us to know at what Galactocentric radius it has spent its life. It is an ongoing debate as to whether the Sun has migrated to its position from outside or inside its current radius, or whether it has been where it is all along. As a result, how many "Galactic years" our Sun has experienced is still quite uncertain.
eg. see
http://adsabs.harvard.edu/abs/2015MNRAS.446..823M
http://adsabs.harvard.edu/abs/2002MNRAS.336..785S
http://adsabs.harvard.edu/abs/2013A%26A...558A...9M

Our sun takes about 225-250 million years to complete one galactic year (also called a cosmic year),so from the age of the sun it has completed approximately 19 galactic years.

This answer adds nothing not already covered by the other answers.


text:
How much of an effect does the moon have on Earth's liquid mantle?
The gravitational pull of the moon is enough to create tidal forces of large bodies of liquid, i.e the sea.
I was having a conversation the other day about how to terraform Mars, and someone suggested that if Mars was to have a moon artificially placed there then its gravitational effects would help keep a liquid core flowing.
Does the moon therefore also have an effect on other large bodies of liquid on Earth? Does the moons gravitational pull affect in any way the flow of Earths liquid mantle?

I've always wondered the same thing. The next google result after this question was the following article: https://astronomynow.com/2016/04/01/moon-thought-to-play-major-role-in-maintaining-earths-magnetic-field/

Not even near a proper answer, but related: Earth tides run about 384mm diurnal: https://en.wikipedia.org/wiki/Earth_tide

The mantle is solid. The outer core of the Earth is liquid

Interesting question. I would say from an energy standpoint, it almost certainly it has no effect.
Of course, the extreme case is Io, one of the Galilean moons whose heat source comes from the gravitational tidal stretching as it orbits very closely to the planet Jupiter. The heat that sustains the core of the Earth, however, is left over from its formation and also comes from radioactive decay of heavy elements.
The differential potential energy (and hence the tidal force) over the planet Io due to Jupiter, which is approximately 1300 times more massive than the Earth, is much larger than that of the Earth due to the moon. The relationship between force and differential potential energy is:
$$ F = - \nabla U $$
At a given location on the potential energy curve, the strength of the force is determined by its steepness (derivative) at that same location. Below is a quick plot I've generated for the Earth-Moon system, where the vertical red line represents the average Earth-Moon distance over a one-year period. As you can see it doesn't appear to be very 'steep', though keep the scales of the x- and y-axes in mind.

Admittedly this isn't that exciting of a plot. But, for comparison one could be made for the Jupiter-Io system, and numerical derivatives could be taken for both to calculate the magnitude of the tidal force in each situation.
To answer the question:
If the difference in the gravitational potential energy of object A on B over the scale of B is comparable to the self-gravitational energy of object B, then tidal forces will become important. This self-gravitational energy is the amount required to completely pull apart all massive particles infinitely far away. Formally, this limit is called the Roche Limit.

As per @edward-furey link https://astronomynow.com/2016/04/01/moon-thought-to-play-major-role-in-maintaining-earths-magnetic-field/ - this response is out of date.  "The Earth continuously receives 3,700 billion watts of power through the transfer of the gravitational and rotational energy"


text:
Does Ceres have an exosphere similar to the Moon?
Thinking about the question and answers for Does the Moon have any oxygen in its atmosphere? begs the question, despite being considerably smaller than the Moon and further away from the sun, does Ceres have a similar atmosphere as the Moon?

We'll probably find out soon.

In general, asteroids experience the same fundamental processes as the moon: solar wind, micrometeorites  and photons from the sun are striking them and sputtering material off to form an exosphere.  So there must be some sort of exosphere, but its density and composition will vary with distance from the sun, as well as the gravity and composition of the asteroid.
A 1992 ultraviolet study of Ceres found $OH$ emission, consistent with escaping water, and suggesting a ice cap.
But a more recent study with the more sensitive VLT  did not detect $OH$, limiting the maximum amount of water produced  per second to $7 \times 10^{25}$ molecules per second at the time of the observation.

So equivalent to somewhat less than 2 liters liquid water per second .

This is an old question but I thought it good to add an update since more information has become available.
Ceres has indeed been confirmed by Dawn to have a tenuous atmosphere created by ice sublimating off the surface.


text:
Can moon set after being up when due north? (pseudo circumpolarity)
I'm in the northern hemisphere, facing north, and notice that the moon
is due north (azimuth 0) and is still above the horizon, albeit barely.
Does this mean the moon is necessarily circumpolar (doesn't set), at
least for the next few hours?
As the moon moves away from due north, it's altitude/elevation
normally increases. However, it's possible that the moon's declination
is decreasing so rapidly that the moon's elevation actually decreases,
and the moon sets.
Is this possible?
This question is tangentially related to my question "libnova odd behavior for 89.5 degrees north latitude" on Stack Overflow.
EDIT to answer questions: I am facing true north. I am referring to the Earth's true moon, but not necessarily in any given time frame. In other words, if something like this happens 10,000 years from now, that's fine.
EDIT: OK, I believe the moon CAN set even if it's up when due north. Example:

You are at latitude 89.5N
The moon's declination when due north is +0.5N. This means the
moon grazes the horizon when due north.
If the moon's declination were constant, it's highest elevation
for the day would be 1 degree.
Since the moon's declination can change more than one degree per
day (average of 1.5 degrees/day), it's quite possible for the moon's
declination to go below -0.5N, at which point it would have set (it
will actually set before this point unless it happens to reach due
south).

In theory, this could happen with any object whose declination
changes, provide you're close enough to the North Pole.
I'll leave this update open for critiques.
EDIT: Actually, this whole question is just asking whether the midnight sun/moon can set at any position other than due north, which is fairly obviously true. Reasoning: once the moon/sun finally sets not due north, it was obviously still up the last time it was due north.

Clarify if you are facing true north or magnetic north?

Are you asking about a hypothetical moon, or The Moon as in Earth's moon?

re your edit - you're right that the moon could set after being visible at due north in an extreme case such as in your example - in my prior comment I neglected to mention the small daily declination changes which enable the borderline case. But yes, the rare borderline case could enable rising and setting very close to due North. Now that the question is clearer, hopefully the answer is too.

Answering my own question: yes, the moon can set after being up
while due north, and this situation occurs quite frequently at far
northern/southern latitudes.
Example: On 2013-08-03 21:45:21 at 72N, 0E, the moon is due north and up:

Less than 24h later, at 2013-08-04 at 20:51:08, the moon sets:

This situation is typical. If the moon has been up for more than 24 hours:

It will almost always set at a location other than due north.
In the 24 hours prior to moonset, it will have been due north and
above the horizon.

Note: I used stellarium for dramatic effect, even though it tends to
give inaccurate results compared to other libraries (
https://stackoverflow.com/questions/16293146/ ).
Other libraries give similar, but nonidentical results.
The general case is the same, however: if the moon's been up for over
24 hour and sets, it will have been up and due north some time in the
last 24 hours.
I am downvoting and not accepting Moriarty's answer because:

He originally answered the wrong question.
He later answered the right question incorrectly.
He later claimed that this is a "rare borderline case". In fact,
this happens almost anywhere/anytime the moon is up for more than 24
hours.

EDIT: it turns out this is known. All planets (incl the Sun and Moon) do NOT reach maximum elevation when they culminate: http://www.geoastro.de/TransitCulm/index.html

http://www.geoastro.de/TransitCulm/index.html explains why this can happen

Yes - here is a good explanation of the situation. Just as it's possible to have continuous daylight for days or weeks on end, you can have continuous moonlight too.
The Moon's orbit is tilted at (a maximum of) just over 5 degrees to the ecliptic, however this tilt has an oscillatory precession with a period of 18.6 degrees. This precession means that our "lunar arctic circle" will vary in latitude over time.
For example, if the moon is sitting exactly on the ecliptic (latitudinally speaking), it would remain above the horizon until it is at a sufficiently low phase of illumination that its current ecliptic longitude is below the horizon. Of course in reality the moon only crosses the ecliptic twice during each lunar cycle (it's these two points that precess). Stellarium is a cool program to visualize this on if you turn on the ecliptic grids.
One important thing to note is that this phenomenon is dependent on both the time of year and the phase of the moon. In the summer months, new and near-new moons are the ones that can remain visible for days or weeks on end. Conversely, at the North pole, you might not see a full moon at all for a few months!

I think this just answers the question "can the moon be cirumpolar", to which I already knew the answer (yes). My question is about a much more specific case.

@barrycarter If you are in the Northern hemisphere and the moon is due north and you can still see it, it will not set for at least 24 hours due to my explanations above. The turning points of all celestial objects, when they go from increasing to decreasing altitudes (or vice versa) are always true North and South. That's just the way the Earth rotates. Any differences due to the fact that the Moon slowly moves along the ecliptic are inconsequentially small.

"Any differences due to the fact that the Moon slowly moves along the ecliptic are inconsequentially small"... that's what I'd like to see proof or explanation of. The moon's declination can change quite rapidly.

@barrycarter "The moon's declination can change quite rapidly." - no, it cannot. The equatorial co-ordinate system is independent of Earth's rotation. Perhaps you are confusing declination with altitude. The Stellarium program (linked above) will help you visualize the situation.

OK, can you put an upper limit on the moon's change in declination so we can have some numbers to work with?

Here you go - look especially at the plots on the right. The superposed periods of declination do not change the observed altitude of the Moon over a short enough timespan such that the observed maximum and minimum altitudes deviate significantly from true North and South. The JPL Horizons web interface will provide you with all the data you could ever want. I cannot prove the Moon's orbit any more than I can prove that the Earth exists. It just is what it is.


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Can I see comet ISON from Saudi Arabia?
I live in western Saudi Arabia, I am trying to see the comet ISON, reading here and there tells that I can see it by naked eye somewhere next to the constellation leo, I used an app to tells me where constellation leo is but I could not see the comet.
Is it visible from Saudi Arabia? if so, in which direction (west, east, etc.) and what time is the best to see it?

You could test this out by installing Stellarium (free night sky application: http://www.stellarium.org/). Input your location and you should be able to see whether or not you could possibly see it.

I also highly recommend Stellarium.

I'm not far from you (Israel) and I am also waiting to see comet ISON.
Comets are very unpredictable, and comet ISON has not yet reached the critical part of its journey which will determine visibility for us. Comet visibility is usually due to reflection of the Sun's rays on the coma and tails of the comet, as the nucleus is to small to see directly. So ISON's visibility (and all comets for that matter) depend on how much gas, water, and other materials that it outgasses. This in turn depends on how much volatiles it has, how much the Sun melts them, how much the slingshot around the sun and tidal forces fracture the nucleus, and other factors. So the actual visibility that will occur is very difficult to determine in advance. That said, ISON has all the markings of this being its first trip around the Sun. Thus, we assume that it has many volatiles to release and we assume that ISON will be exceptionally bright.
In any case, ISON will be most visible when it is closest to Earth, near the end of December. It should be most visible in the early morning sky, I'm guessing at about 4:00 AM or so. This is because ISON will be close to the Sun (thus visible close to the time that the Sun becomes visible). Like all celestial bodies, it will rise in the East. Each day the comet will move farther from the Sun and thus will be visible earlier and earlier in the night, until it disappears from view probably sometime in mid January.
You are welcome to visit Beersheba and have a peak through my binoculars!

I think the term "most visible" is somewhat vague.  Early (~5th of) December may be more favourable than later in the month, even though you'll have to observe it in twilight.  As the days go by, you can indeed see the comet earlier, against a darker sky background and higher above the horizon, but the object itself will also be dimmer.  You may therefore always need binoculars to see "ISON".

By 'most visible' I infer the greatest visual magnitude difference between light originating from the comet components (nucleus, coma, tail) to between sunlight reflected from out atmosphere or direct from the Sun.

Good, and I was wrong. I wrote a small program to compute exactly that: the "excess magnitude" defined as  - , where positive values indicate you may see the object with the naked eye. I get (for Riyadh):
Nov:
Day time Exc.mag
15 4:56 -0.2
17 4:59  0.1
19 5:03  0.3
21 5:08  0.2
23 5:17 -0.4
25 5:53 -1.3
27 6:10 -2.2
(28 17:06 -50.7 - never visible)
Dec:
01 6:15 -3.4
03 6:04 -2.3
05 5:57 -1.8
07 5:29 -1.3
09 5:23 -0.4
11 5:21  0.1
13 5:18  0.3
15 5:17  0.3
17 5:15  0.4
19 5:16  0.3
21 5:15  0.3
23 5:16  0.2
25 5:13  0.1
27 5:14 -0.0

@AstroFloyd: Please put that up on Github! I would love to see that, no matter what language it is written in.

I apologise for the loss of format above (paste it into your text editor to restore the three columns).  Summarised, the table indicates you could see ISON with the naked eye on Nov 17-21 and Dec 11-25, best around Dec 17 at 5:15 AST.  The computer code is very simple and while I think that the best dates and times are roughly correct, the magnitudes are probably not and you may well need binoculars to see ISON as the original answer indicates.

On what basis do you calculate the absolute magnitude of the cometary system? Surely not as a rocky object I hope! Don't forget that the coma and tail are mostly empty space, thus there is no crescent and the light is very diffuse. You would need to know the amount of particles in the material as well, which we don't know. Even the albedo of the particles we don't know as we don't know which type of particles there will be (ice, methane, etc.).

I use elements and magnitude data from the MPC - not perfect, especially for "first-time" comets.  Still, the best moment for observation may suffer relatively little from systematic effects.

I added the code to libTheSky. This link points to github and my contact data in case you have questions. Check the functions best_planet_xsmag() and pl_xsmag() in the file visibility.f90 (it's in Fortran, sorry ;-)).


text:
Is lunar elevation at a given location for a given day unimodal?
Is lunar elevation at a given location for a given day unimodal:
Unimodal function
In other words, once the moon's elevation reaches a minimum (which may
be above or below the horizon depending on if the moon is
circumpolar), does it increase continuously to its maximum, or can it
decrease briefly and then increase again (resulting in a local minimum
that's not a global minimum) before reaching the maximum.
And also similar to the above as it goes from the maximum elevation
(which may also be above or below the horizon depending on whether the
moon rises at all on a given day).
Why this is important: I think I found a bug in libnova that assumes
the moon is circumpolar if it is above the horizon when it's due
north. This is untrue
My fix
does not assume this, but does assume that lunar elevation is
unimodal.
If that's untrue, I'll need to further fix my fix.
EDIT: Here's how far I've gotten:

The moon's declination and hour angle (at a given location) are
both functions of time. Thus, we can implicitly consider the moon's
declination to be a function of its hour angle. This only works
because the moon never experiences retrograde motion. Bodies that
experience retrograde motion could have two declinations for a given
hour angle, so the declination would no longer be a function of the
hour angle.
Using the standard formula, we see the moon's elevation is:

$$
   \sin ^{-1}(\sin (\text{lat}) \sin (\text{dec}(\text{ha}))+\cos (\text{ha})
    \cos (\text{lat}) \cos (\text{dec}(\text{ha})))
$$
where dec(ha) is the declination at hour angle, ha is the hour angle,
and lat is the latitude.

Since the moon's elevation is a differentiable function (except
potentially at the poles and equator), we find the derivative with
respect to the hour angle:

$$
   \frac{\text{dec}'(\text{ha}) (\sin (\text{lat}) \cos
    (\text{dec}(\text{ha}))-\cos (\text{ha}) \cos (\text{lat}) \sin
    (\text{dec}(\text{ha})))-\sin (\text{ha}) \cos (\text{lat}) \cos
    (\text{dec}(\text{ha}))}{\sqrt{1-(\sin (\text{lat}) \sin
    (\text{dec}(\text{ha}))+\cos (\text{ha}) \cos (\text{lat}) \cos
    (\text{dec}(\text{ha})))^2}}
$$

The moon's elevation will reach a min/max (in the sense of
unimodality) when this derivative is 0. That occurs when:

$
   \sin (\text{ha})\text{ = } \text{dec}'(\text{ha}) (\tan (\text{lat})-\cos
    (\text{ha}) \tan (\text{dec}(\text{ha})))
$
So the question becomes: can this equation have more than two
solutions for 0 < ha < 2*Pi
Which I hope someone answers at: https://math.stackexchange.com/questions/587136/

Yes, it is unimodal.
Earth's movement is a simple rotation, thus if the Moon were fixed on sky it will describe a circumference like the fixed stars.
From that basic movement we need to introduce Moon's own movement on the fixed stars sphere, which makes Moon not to complete the circumference in 1 day. Instead, Moon performs an arc similar to that of the fixed stars but shorter.
This circumference-like movement does not wobble, so it has just one maximun and one minimum in elevation.

Could you provide a more mathematical explanation? I agree the circumference-like movement (fixed declination) doesn't wobble, but, what if, combined with the moon's own declination change, it does wobble?

I never said fixed declination. In fact, it is not, due to the Moon's proper motion on the orbit. But since that is a movement on a great circle (the orbit's projection on sky sphere) and is composed with a movement on a constant declination circle (the Earth's rotation) you get a wavy movement. If the sky sphere were projected into a plane that movement would be a trocoid. There is no wobbling there, besides the own's of the Moon moving.

Even after looking at https://en.wikipedia.org/wiki/Trochoid I'm not sure I understand. Could you provide some mathematical formulas to confirm this?

I'm sorry but I can not. I have my degree notes buried deeply under a ton of other papers

Bummer. After what happened with the "circumpolar" answer, I'm suspicious of any verbal arguments that aren't backed up with math.


text:
What might cause a planet to have a significant tilt in their orbit?
Most of the planets in our solar system all orbit along the same plane, supposedly because of the almost flat dust clouds that formed the planets.
But some planets, such as the one featured below, have a significant tilt in their orbits that separates them from the normal plane of orbit for that star.

Image courtesy of Science Daily
What might cause a planet to have such a tilt? Is this the star capturing a wandering body into orbit or is this a phenomena caused by the formation of these systems?

Orbital tilts are almost certainly an effect of the formation and evolution of the protoplanetary disk (at least in the majority of cases). They could also be captured rogue planets.
Consider the eccentricity of Pluto. Like Pluto's eccentric orbit, it's probable that its current inclination is the result of orbital resonances with Neptune. This paper (unpublished grad student research) describes some such scenarios.
It is likely these resonances are between the Jupiter-induced precession frequencies of the ascending nodes of Pluto and Neptune. Pluto's inclination could either be relatively stable now, or it may still oscillate on the timescale of several million years.
I wish I could give a more definitive and detailed explanation - it's just one of these cases where no one knows for sure.


text:
How can I safely observe a Solar Flare?
Solar Flares obviously release extreme amounts of energy and extend thousands of miles out into space.
Because they are so big I would like to be able to observe some of these events through a telescope but I am wary of damaging both my eyes or the sensitive telescopic equipment.
How might I safely observe a solar flare through an amateur telescope? Might this be solved by using light filters to dim the amount of light entering the telescope or is a more specialist piece of equipment required?

You can always look at the freely available SDO dataset, which is not an amateur telescope modification but they have hundreds of TBs of observations.

One truly safe way of solar flare observations is to not directly observe them (with your eyes or imaging technology) at all, such is the case with radio-astronomy.  There are a number of examples of how this could be done, for example, the Sudden Ionosphere Disturbance Monitor, this device measures disturbances in the ionosphere that includes the effects of solar flares.  This operates in the VLF (3-30kHz) range.
From the Society of Amateur Radio Astronomers, the advice is

For VLF solar flare observations you will need a strip chart recorder and a radio receiver capable of operating in the noisy 20 to 100 kilohertz radio band. These receivers are quite simple and may be home constructed.

(Plans for these can be obtained from that group)
A repository of further links (far too many to list here) can be found on the website Amateur Radio Astronomy on the Internet.

Apologies for having to point this out, but the OP isn't asking how to observe a flare with a radiotelescope. If someone lands on this part of the page: it's worth to look at the other two answers.

Yes, there are filters which do block out the vast majority of light from the sun. I think it's actually only a very small (~1 angstrom) wavelength band of light which gets through. You can see some pretty amazing features, including sunspots, and solar flares. Here's a composite image as an example (taken through a Hydrogen alpha filter):

Those smallish looking edge features are solar prominences which are large enough to swallow up multiple Earth's. This is not too far off from what you could observe with a solar scope.

Solar flares are explosive events that last not too long, so actually, your bigger problem will be to be able to see them when they are happening.
Normally they are classified by their X-ray flux, and they can be either X, M, C, B or A class which corresponds to the logarithmic scale of $Watts/m^2$ ($10^{-4}, 10^{-5}, 10^{-6}, 10^{-7}, 10^{-8}$ respectively).
You can understand better what I mean by looking at the real time lightcurves obtained from GOES satellite
These peaks have different duration depending of the flare, there are some records of flares lasting few hours where the shortest can be shorter than a minute.
All the above applies to X-ray flares, which we cannot seen from Earth, we need to put some instrument on board spacecraft or rocket so we go above the part of the atmosphere that absorbs them.
Now, if you want to see them by using an optical telescope you have two options, either using the whole visible range by projection or through an Hydrogen alpha filter.  In this case the flare classification is different than in the X-ray case.  Where the flare class in X-ray is measured by the enhanced of flux produced, the optical class is based by the area it covers. The Solar Influence Data Analysis Center offers a table with their properties and the corresponding X-ray flare type:

Area(sq deg)
Area ($10^{-6}$ solar A)
Class
Typical corresponding SXR Class

<= 2.0
<= 200
S
C2

2.1-5.1
200-500
1
M3

5.2-12.4
500-1200
2
X1

12.5-24.7
1200-2400
3
X5

>24.7
>  2400
4
X9

For example, the famous Carrington's event (Sept. 1, 1859) was observed and hand-drawn from Carrington by projection.  But, as this article says: "He was lucky enough to be in the right place at the right time..." you need too to be quite lucky to observe one of these.


text:
How can I clean my lenses without causing scratching or damages to the lens surface?
Sometimes you can be trying to observe very faint or very small objects in the sky and it wouldn't pay to have these obscured or marred by a scratch or dust on the lenses.
I keep to good practices and make sure to replace the cap on the lenses when finished in order to stop dust buildup but inevitably it will get a little dusty and dirty, taking this into consideration:
What steps do I need to take to ensure that my lenses are kept in top condition?
Can I simply use a damp cloth or sponge and dab the lenses or should I use a softer material, like someone with glasses might have a softer lens cleaner?
Do I require a special cleaning fluid or can a good quality clean be done without any additional cleaning agents?

Honestly, I would go with compressed air. Even with a damp cloth you can risk either scratching the surface, or you could leave residue as the moisture dries from the surface. I'll leave the answer to this question to a more knowledgable person.

I wouldn't use a compressed air canister as I'd be worried that it might play too rough. Get a photographic air blower bulb instead.

Clean your eyepieces in the same way you would clean a camera lens. An air blower, soft (i.e. camel hair) brush, lens tissue or microfibre cloth, and a solvent or alcohol will do the trick.
When I was an undergraduate I did some work with lasers and very expensive dielectric coated mirrors. The techniques here will show you how to carefully clean optics. Never completely wet your lens tissue or cloth. One drop on a lens tissue is usually enough, or a couple of drops on a microfibre cloth.
Essentially, you need to:

Use a blower to blow off as much dust as you can.
Then use a soft brush.
Dampen a small square of lens tissue with pure alcohol or acetone (see warning below). Gently draw or wipe the tissue across the surface once, and then discard. Repeat if necessary.
You may need to fog the lens with your breath to help remove water-soluble gunk.

Be insanely careful if you are using a solvent such as acetone. Although a good for cleaning optics, it's not very nice to paint and plastic so it should be a last resort for very stubborn marks well away from the edges of the lens (so you'll never touch the paint with it). Methyl or isopropyl alcohol are safer but less effective, or a generic lens cleaner from a camera store.

...and while damage to the paint done by acetone will be merely an insignificant matter of aesthetics, acetone-diluted paint smeared over the lens will be a problem.

Indeed that is even worse. Solvents are something to use only when you really know what you're doing and you are aware of the risks.


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Dealing with damp and dew whilst stargazing at night or in the early morning
Sometimes when using my telescope late at night or early in the morning, especially in the more humid of seasons, I notice i sometimes get dew buildup on the lenses.
How can I minimize damp buildup whilst using my telescope?
Simply dabbing away the liquid with a dry cloth doesn't seem to do the trick as I am still left with some water tracks and residue that I just can't soak up, this then means that all of the light is refracted providing a very fuzzy and blurry image.
What preventative measures can i take to stop damp build up in the first place?

Condensation will build up because the temperature of your optics has fallen below the dew point.
You simply have to keep the temperature your telescope above the dew point, which can be quite difficult on humid nights. Dew shields can help, as can dew heaters (which literally just gently heat your telescope and/or eyepiece).

Hypothetical: "I'm looking at the graph of dew point vs air temperature on the link above. I don't understand how my optics can get colder than the air temperature!

At night, our source of heat (the Sun) has disappeared. The unlit side of the Earth (and everything on it) begins radiating its latent heat away into space (which has a temperature of ~3 Kelvin). Your telescope is trying to get into thermal equilibrium with outer space.

+1 for "Your telescope is trying to get into thermal equilibrium with outer space."