What is the closest star to us?

The nearest star to us (besides our Sun, of course) is Proxima Centauri. It is actually part of the triple star system Alpha Centauri. It is about 4.3 light-years away. A light year is the distance that light travels in one year at a speed of 186,000 miles per second.
How many stars are in our galaxy?
Our galaxy contains about 200 billion stars.
What percentage of stars have warm disks around them?
This is one of the primary science goals of the new Spitzer Space Telescope. Right now, we don't know the answer to that question. I'm not sure exactly how many stars have been found to have excess infrared emission (which is how they found the first of these systems), but my guess would be well under 10%. The real number is probably quite a bit higher than that, but no large-scale survey has yet been completed.
Can a rotating neutron star hold planets in its orbits? What would the orbits look like?
To begin with, yes, a neutron star would definitely be able to hold planets in orbit. In fact, if for some reason our Sun became a neutron star (with the same mass it has now), our orbit would be unaffected, at least to any accuracy we could measure. Neutron stars do indeed warp both space and time, but the distortion is vanishingly small at the distance that planets orbit. I don't think you'd really notice the effects until you were maybe 1000 miles away from the neutron star, too close for a stable planetary orbit anyway.
As for the second focus of Earth's orbit, that is inside the Sun as well. The very center of the Sun is the location of one focus, but the other one is inside the Sun too, just off-center. Earth's orbit is very nearly perfectly circular, so the foci are quite close together. Even if our orbit was very elliptical (like a comet), there wouldn't have to be anything at the other focus. It's really just a mathematical construction -nothing has to be there at all.
How many stars can you see at night? How does ambient light affect this?
The number of stars that you can see on a clear (moonless) night in a dark area (far away from city lights) is about 2000. Basically, the darker the sky, the more stars you can see. Moonlight brightens the night sky and reduces the number of stars you can see. A full moon brightens the sky more than a crescent moon or half moon. Ambient light also reduces the number of stars you can see. In a large city, which has a lot of bright lights at night, you may only be able to see the brightest dozen stars. As the night sky gets brighter, the faintest stars disappear from view first. A major problem for ground based astronomers is what we call "light pollution" - the increase in man-made light sources which affects observations of the night sky.
Where are the daytime stars? Why can't we se them?
You definitely do see the "day time" stars six months later. Take Orion, for example. Orion is visible in the night time sky starting in the autumn, through the spring. The reason you can't see Orion in the summer is that it's up during the day. If you were looking at the Earth from Orion, you'd have a hard time seeing the Earth in the "summer," as the Earth would be on the opposite side of the Sun (behind the Sun), spinning happily on its axis once a day, unable to see Orion due to the sunlight. During the winter, however, you'd have a clear view of our planet, as it would be on the near side of the Sun.
What are constellations?
A constellation is a group of stars that make an imaginary shape in the night sky. They are usually named after mythological characters, people, animals and things.
What is a naked-eye double star?
A naked-eye double is a double star or binary star system which can be seen with the naked eye (no telescopes or binoculars needed). An example is the double star Epsilon Lyrae in the constellation Lyra, although this is sometimes difficult to see. An easier system to view is the pair Mizar and Alcor in Ursa Major (near the big dipper).
What are binary stars?
Stars often form in pairs. Binary stars are pairs of stars which orbit around their common center of gravity.
What is a brown dwarf?
Brown dwarfs are objects which are too large to be called planets and too small to be stars. They have masses that range between twice the mass of Jupiter and the lower mass limit for nuclear reactions (0.08 times the mass of our sun). Brown dwarfs are thought to form in the same way that stars do - from a collapsing cloud of gas and dust. However, as the cloud collapses, it does not form an object which is dense enough at its core to trigger nuclear fusion. The conversion of hydrogen into helium by nuclear fusion is what fuels a star and causes it to shine. Brown dwarfs were only a theoretical concept until they were first discovered in 1995. It is now thought that there might be as many brown dwarfs as there are stars.
Who can officially name stars?
The International Astronomical Union ( is the only organization which can officially name stars.
What is a supernova? How does it happen?
A supernova is the death explosion of a massive star, resulting in a sharp increase in brightness followed by a gradual fading. At peak light output, supernova explosions can outshine a galaxy. The outer layers of the exploding star are blasted out in a radioactive cloud. This expanding cloud, visible long after the initial explosion fades from view, forms a supernova remnant.
What would a neutron star look like if it where reasonably close to us? i.e. it would be a perfect sphere, no surface features due to the high gravity, would it have a color temperature and would it radiate?
Although the intense gravity of a neutron star crushes the stellar remnant into tiny size (~10km) and immense density (the equivalent of taking every Volkswagen ever made and crushing it into a teaspoonful), a neutron star is not quite spherical. This is because of the very stiff relation between pressure and density (called the equation of state - the equivalent of PV = nRT for an ideal gas if you remember from high school science). Although the scale of structures is quite small, the surface is quite irregular and "crusty." Occasionally the surface of a neutron star will readjust causing a "starquake." Starquakes are currently our best means for studying the structure of neutron stars. We don't see these directly, of course, but by changes in the spin of "pulsars" - which you probably know are rapidly rotating, highly magnetized neutron stars.
Although the surface of the neutron star may be quite hot (depending upon how long it has been since the neutron star was "born" in a supernova explosion), we do not generally see the radiation emitted directly from the surface. The radiation that we see comes from energetic electrons, emitted from the surface of neutron star, being accelerated through the intense magnetic field. Since this field is strongest at the poles, the radiation is also strongest near the poles, and the neutron star is detected as a pulsar by the "lighthouse effect" of the polar radiation beams sweeping past us as the neutron star rotates many times per second. Most pulsars are detected in x-rays or radio, but a number have now been detected by their pulsations in visual light (e.g. the pulsar in the Crab Nebula and the x-ray source Hercules X-1).
But perhaps your question is, "What would a neutron star look like if it weren't a pulsar?" Well, a young neutron star rapidly cools from about a trillion degrees down to about a million degrees, where it emits most of its thermal radiation in x-rays. (VERY early on most of the emission is in the form of neutrinos.) A few young, nearby neutron stars have been detected in steady x-ray emission which is believed to be this thermal radiation, but interpretation of this radiation is difficult because we don't understand how the radiation is processed by the highly magnetized atmosphere of the neutron star. At optical wavelengths, a neutron star even just 10 light years away would still be many magnitudes too faint to be seen with the unaided eye.
Another big question I have lately has to do with the Special Theory of Relativity and with how we measure the distance of stars by the red-shift of the light coming to us from the star being measured. According to Einstein, the speed of light is absolute and will travel at the same speed through space regardless of the velocity of the body emitting that light. Part of the proof for that theory involved experiments where the velocity of light was measured coming from both sides of the Sun. The Sun rotates and so one side is rotating towards us while the other rotates away from us. Such experiments reveal that light coming from both sides of the Sun arrive to Earth at the same velocity. If the speed of light is absolute at all times, why is the light from stars red-shifted? It seems to me that according to Special Relativity the light from stars moving away from us, whether closer or further should arrive to earth at the same velocity.
Here is the answer: it's the frequency of the light (the frequency which the light makes the local electromagnetic potential field oscillate) that determines it color, which is different and can vary independently from its velocity. I.e., redshifted light moves at the same speed as blue light.

(Actually, light does always travel at the same speed only in a vacuum - it travels slower in denser media.) But let's just concentrate on a vacuum and a constant speed.

Here is an analogy that works for me. Suppose I am a distance from you and I am shooting tennis balls at you 1 per sec each traveling 10 feet/second. You receive a ball every second. That's the ball frequency or color (or frequency of occurrence of peaks of the electrical magnetic disturbance). They are 10 feet apart - that's their period or wavelength. Now, I start backing away from you at 1 foot per second. My smart tennis ball gun adjusts its velocity to compensate and begins to shoot balls 11 feet per second from the gun, so the balls are traveling at you still (from your perspective) at 10 ft per second. They are also traveling with respect to the ground at 10 ft per sec. I keep firing 1 per second.

But now there is more distance between them, because I am stepping a foot back before I shoot each one. There used to be 10 feet between each one. Now there are 11 feet between each one. While they are still flying over the ground at you at 10 feet per second, they are arriving less frequently, one arriving each 1.1 second, since they have that extra foot to cover at 10 feet/sec, so they are arriving at 1/1.1 sec = 0.909 tennis balls per sec. So the ball wavelength has gone up, the ball frequency has gone down, and the ball velocity has remained the same. This is a redshift.

This actually is a classical situation, not just a relativistic situation, in that the same thing happens with a train whistle in air when the listener is fixed. Since sound waves travel through air at a velocity fixed by air density and pressure and not the motion of the emitter, the speed of sound is also fixed (otherwise there would be no sonic booms - where a plane actually catches up with its sound). The Doppler shift occurs with trains and planes too with constant sound speed, since the sound frequency is effective by relative motion, but not its speed.

The relativity part comes in above where my tennis ball gun is "smart." In the Universe where the tennis ball speed is fixed at 10 feet/sec, me and the gun experience time dilation when I start walking backwards. It looks to me like it's still firing with a velocity of 10 feet/sec when it's actually (in your frame) looking like it is firing faster relative to the gun, but at 10 feet per second relative to you.