earth - How many planets have we discovered that can support human life?

There is currently only one planet known to be capable of supporting human life, and you're on it.

Several planets have been found in the region in which we expect water to be liquid on much of the planet. Of these, only one fits the criteria of being Earth-sized and well placed in the habitable zone: Kepler 186-f

However we know nothing about it's atmosphere (or lack of one). The star is a red dwarf, so it could be subject to dramatic solar flares. The planet is rather colder than earth, so could be in a perpetual "snowball world" state, depending on the composition of the atmosphere and the strength of the greenhouse effect. The atmosphere would be very unlikely to be even close to breathable, and it is nearly 500 light-years from Earth, so could not be reached in a reasonable amount of time, even with much more advanced propulsion.

At the moment we can't usually detect most Earth-like planets in the habitable zone of brighter stars like the sun, though the probably do exist and may be common.

stellar evolution - How is the age of a star on the Henyey track calculated?

I was reading Stellar Evolution in Early Phases of Gravitational Contraction, by Chushiro Henyey, where he writes,

If $L propto R^{-alpha}$ along the path, the age of a star from the time when $R=infty$ is given by
$$t=C/(1-alpha), C=GM^2/RL=10^{7.20}left(frac{M}{M_{odot}}right)^2frac{R_{odot}}{R}frac{L_{odot}}{L}text{ years}$$
where $R$ and $L$ are the present values.

This seems to be just for stars on the Hayashi track (and treated here just for Population 1 stars). Is there a similar expression for stars on the Henyey track, or is the same expression valid in both scenarios?

Is there any hard evidence that rogue planets exist?

Giant planets when first formed are big and hot. They radiate their own light, mostly in the infrared. So young isolated planets can be seen directly.

There have been various claims in the literature that objects as small as a few Jupiter masses have been identified in young star forming regions. See various papers by the IAC brown dwarf research group

http://adsabs.harvard.edu/abs/2000Sci...290..103Z

http://adsabs.harvard.edu/abs/2002ApJ...578..536Z

http://adsabs.harvard.edu/abs/2014A%26A...568A..77Z

http://adsabs.harvard.edu/abs/2013MmSAI..84..926Z

Another object that is part of the beta Pic moving group, recently discovered by Liu et al. (2013), has an estimated mass of about 8 Jupiter masses (Biller et al. 2015).

http://arxiv.org/abs/1510.07625

These claims are open to criticism - sometimes it is hard to tell whether a faint object really belongs to the star forming region observed, rather than being an unassociated background object. The claimed masses also depend heavily on models for the luminosity-mass relation as a function of age, and the ages of these objects are not easily constrained. The likelihood is that at least some of these objects are below 10 Jupiter masses and would rank as planets by some definitions; though none of the individual objects could be said to be proven beyond any doubt.

Nevertheless it would not be surprising if, in the maelstrom of the formation of a cluster of stars, some planetary systems were stripped from their parent stars by close encounters with other objects and indeed numerical simulations of planetary systems in dense star clusters show that this process occurs (e.g. Davies 2011).

http://adsabs.harvard.edu/abs/2011IAUS..276..304DD

The chances of seeing older, isolated, planetary mass objects are slim, but microlensing appears to be the only technique presently available. The microlensing signature of a free-floating planet is of course unrepeatable so a discovered planet could not be followed up in any way. However, surveys of microlensing events could be a way of saying something statistically about how common such objects are. See for example http://astrobites.org/2011/05/24/free-floating-planets-might-outnumber-stars/

It is also worth noting that the whether these things really are "planets" at all is disputed. They could either be genuine planets, formed in the same way that is hypothesised for most giant planets - that is by accretion onto a rocky core that formed around a star. They could then have been displaced from their parent star by dynamical interactions with other bodies in their system or with a third body. As I said above, N-body simulations do predict that this will happen (e.g. Liu et al. 2013).

On the other hand they could represent the very lowest mass gas fragments that are able to form during the collapse and fragmentation of a molecular cloud and that for some reason were unable to accrete further gas (i.e. they are really more like low-mass brown dwarfs). This so-called "fragmentation limit" is of order 10 Jupiter masses, but if it were a little lower it might explain the free-floating "planets" that have been seen so far.

software - What are the most popular computer programming languages in observational astronomy?

As an observational astronomer, most of your programming will be to perform data analysis, data exploration, and possibly image manipulation. Previously much of this was done with IDL, and the analysis pipelines for several/many/all(?) telescopes still rely on IDL. As GreenMatt points out though, IDL is on its way out. Since you have to buy a license to use it, you can only share code with other IDL users, it's not open source, etc.

The community is in the process of switching to Python, which is absolutely what I would recommend first for a new entry into the field. Python is free, open source, etc, etc. Since you'll be using python for data analysis and numerics, it is vital that you learn the NumPy package as well. With NumPy array operations in python are almost as fast as C or Fortran. SciPy and MatPlotLib are also incredibly useful, you don't need to learn the entire library, but you should be familiar with the basics.

The astronomy community is collaborating on some python packages to make more analysis techniques common. These are the AstroPy and AstroML packages. Once you get a handle on things, both would be good to be familiar with.

C is great to know, but not vital for day-to-day observational astronomy. We use it a lot in theoretical astronomy to write numerical simulations. Mainly I see C codes used in observational either for one-off calculations from a large dataset, or used to write fast modules for Python :) If that sounds up your alley, you should give it a shot too!

What is meant by "short lived" in the duration of a planetary nebula?

In the case of planetary nebulae we are talking of ~10,000 years (follow the link to the main article on Planetary Nebulae).

In general a short lifetime for a phenomena means a time short compared to the total life of the entity it is related to. It is an informal term and does not have a fixed maximum value, but 10,000 years is a short time on most astronomical scales.

astrophysics - How to calculate the mean molecular weight of the Sun

I have a homework question in which I need to estimate a parameter known as $beta_{P}$ and also the core temperature, both for the Sun.

However, prior to doing this I need to know the mean molecular weight of the Sun.

First question is, how would I go about doing this.

Second question is, can I assume that it is about 70% hydrogen and 30% Helium?

Is there a connection between black holes and dark matter/energy?

No, not really.

As Stan Liou hints at in his comment, massive objects such as black holes (BHs) were previously a candidate to dark matter (DM). But it can be shown that in order to explain the various problems that the existence of DM needs to solve, there would have to be so many, that their gravitational effect ("microlensing") on background sources would be much larger than what is observed. Today, most people think that DM is simply a particles with an extremely small interaction cross section, such that it virtually doesn't interact with other particles, except through gravitational attraction.

You also ask if there's any spatial relationship, and in a way you could say there is. Most, if not all, galaxies sport a supermassive BH, and these tend to lie in the center of the gravitational potential wells created by the galaxies' DM. "Normal" BHs, however, just float around like stars.

BHs also tend to grow by accretion of matter onto them, and of course they can also eat DM, so to some extend BHs also consist of DM. But since the DM doesn't interact, a DM particle would need to fly directly toward the BH, lest it would simply be deflected and escape. Normal matter, on the other hand, is slowed down by friction and spirals toward the BH. Thus, BHs consist mostly of normal matter. It doesn't really matter, though, since after something has fallen into a BH, everything but its mass, charge, and angular momentum will be forgotten.

Dark energy is something completely different, better described as a negative pressure which is a property of space itself. I think. Or we think. Nobody really knows. But it presence doesn't correlate with that of BHs or DM. Ten years ago, there was a hypothesis that a collapsing star should be converted into dark energy rather than a BH, causing a so-called dark-energy star, but I don't think anybody believes this anymore.

orbit - Precessing of the Earth

Based on what I can access right now, the precession of Earth's axes are in a cone shape, so there isn't much wobble. But with all of those Near-Earth Objects, and nearby planets, there is probably some wobble (I'm no professional).

There's also this thing called the Milankovitch Cycle, which shows how the combined effects of precession, external forces, and etc. affect climate. It also affects the eccentricity, or the circularity, of Earth's orbit in a cycle of 430,000 years. This affects seasonal length and season intensity. It also changes orbit orientation, so the perihelion and aphelion move to different locations. If you want to learn more, read https://en.wikipedia.org/wiki/Milankovitch_cycles.

the sun - How old is our Sun in Galactic years?

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 $sim 20pm 1$ 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

orbit - How much light does Jupiter project onto the surface of Ganymede?

How much? Well how accurately do you need it? How do you want it quantifying? And in what wavelength range?

Jupiter scatters a fraction of its incident sunlight. It also has its own luminosity (predominantly in the infrared).

A quick calculation:

The solar constant (flux at 1 au) is about 1370 W/m$^{2}$. Jupiter is situated about 5.2 au from the Sun (it varies by about +/- 5%) and has a radius of 70,000 km. The albedo is about 0.34.

Thus it receives about $7.8times 10^{17}$ W from the Sun and radiates about $2.6times 10^{17}$ W back into space. Assuming this is done more-or-less isotropically into a hemmisphere, then Ganymede, at a distance of 1,070,000 km from Jupiter, receives a flux of only 0.1 W/m$^2$ multiplied by the fraction of the sunlit hemisphere that can be seen.

This compares with the $sim 50$ W/m$^2$ it receives from the Sun!

This surprising result (to me) puts into perspective all the simulations you see of things in orbit around Jupiter. The planet is still pretty faint compared to the Sun.

I'd be grateful if someone could double-check the sums!

[The intrinsic infrared luminosity of Jupiter is less than a fifth of what it receives from the Sun, so this would increase, but not double the received power.]

Is Higgs Boson mass equal to the missing mass of dark matter?

To answer this question, we need to understand what dark matter and a Higgs Boson are.

Higgs Boson

A Higgs Boson is an elementary particle in the standard field of quantum physics. It was theorised by a few people, namely Peter Higgs. The Higgs Field is a field which we can now believe exists, as we can detect it through its excitations, which become Higgs Bosons. The quantum excitations of the Higgs Field create Higgs Bosons.

A Higgs Boson is a particle with no spin, infact, it is the only particle with no spin, electric charge or colour charge. It's also extremely unstable and decays into other particles almost instantly.

Dark matter

Dark matter is a heavily researched topic in physics at the moment. Out of all matter in the universe, dark matter makes up about 80% of it!

One example of a theorised candidate for a dark matter particle is a WIMP. These are abbreviations of 'Weakly Interacting Massive Particles'. These particles are not normal matter, therefor we can't detect them. Our efforts to detect them include trying to look at the annihilation of WIMP particles.

The main characteristics of WIMPS are that they only interact through the weak nuclear force or gravity. They also larger than standard particles (a dark matter particle with mass less than a electronvolt is classified as light dark matter)

Wimps move slowly and are therefor cold, making them one of the main candidates for cold dark matter.

Think of dark matter as a 'skeleton' for normal matter.

Conclusion

From looking at both types of particles, we can clearly tell that Higgs Bosons are completely different from dark matter. We are still trying to find out about them both, as both of them can answer fundamental questions in physics.

Does the shape of a supernova remnant depend on the progenitor star's magnetic field?

Not really, the shape of the supernova remnant is mainly caused by the structure and biometry of the star. At the time of explosion the layers of the star expands
and high speeds which result in a supernova remnant. A good example is the crab nebula in constellation Taurus.

astrophysics - Why are the magnetic poles of a pulsar so far off the rotational axis, yet stable?

The magnetic field of a star is not entirely a result of the global spin of the star. The global spin is part of it, but there are other mechanisms as well. Within the star, there are convection zones, meridional flow, etc.

http://solarscience.msfc.nasa.gov/dynamo.shtml

All these flows generate their own field components. The overall field is simply the sum of all little fields. Its general orientation might be close to the global spin, if the strongest components are aligned to it, but there are many smaller components with different orientations. Therefore, the total field of the star can be somewhat slanted.

And then the star collapses into a neutron star, and its field is compressed. The collapse itself may be slightly asymmetrical, and may further deviate the magnetic field axis.

As a result of all of the above, it's by no means unusual that the magnetic field of the neutron star is not aligned with the spin.

planet - Questions about terminology used for Mars and its moons

Deimos is, like our own moon, tidally locked to Mars, so one hemisphere of Deimos faces the planet, and the faces away. The Sub-Martian hemisphere faces Mars.

Since Deimos is locked, there is a point on its surface that always faces in the direction of orbital motion, that point is the leading apex. It is an apex in the sense of a "leading point"

A meridian is a line of longitude, running from the North to the South pole. One of Deimos's meridians goes through the centre of its hemisphere that faces away from Mars, this is the anti-Mars Meridian. As you say, the "meridian on the side of Deimos facing away from Mars.

The image here shows a map of Deimos:

The leading face is the left side of the image, and the trailing face is on the right. The central 50% is the sub-martian hemisphere and the anti mars meridian is the line on the left and right edge, where the 3D image of Deimos has been cut to make a 2D map