|MadSci Network: Astronomy|
An M0 V star is a main sequence star with a surface temperature of about 3500 K or so. This means that the light from the star will be very red; the peak of the star's spectrum is actually in the infrared! The luminosity (brightness) of the star will only be about 0.06 of the Sun's (although that means the star will still be much brighter than the Full Moon at the distance from the Sun). The star itself will be smaller than the Sun, with a radius of about 0.6 of the Sun. The mass of an M0 V star is about half the Sun's.
So what does all this mean? Since the star is half the temperature of the Sun, the planet will have to be much closer to get the same warmth the Earth gets from the Sun. Many people assume the planet must be rotationally locked to the star (that is, it rotates once every time it goes around the star once, like the way the Moon rotates as it orbits the Earth, always sowing the same face to us). I have my doubts. Mercury, for example, rotates three times every time it goes around its orbit twice. If the planet has a moon, I think that would help keep it from getting the 1:1 tidal lock.
The light from the star is extremely red, with almost no light with wavelengths shorter than yellow or so. That means the planet's sky will not be blue! We get our blue sky by scattering blue light from the Sun. That means the sky will be very dark, even in full day. Since the star is about 1/16th the Sun's luminosity, you'd have to be four times closer for it to be as bright as the Sun. The temperature of the planet will increase roughly as it's distance from the star to the 1/4 power. At this point I'll let you play with the math! Note also that if you are 4 times closer than the Earth, the star will be about twice as big in the sky as the Sun, too.
If the planet has a moon, giving the moon a rotation will not affect the planet all that much. But the tidal system of a planet/moon so close to a star is pretty complicated. I suggest you read about tidal evolution, but I think it would be pretty hard to figure out what would happen in this case. I have a short description of tides on my web page. Take a look at it and it might help you with all this!
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