Why aren’t the stars yellow and why doesn’t the sun “twinkle” (shimmer)?

Star come in different colors depending on their temperature. These can be discerned with a large enough telescope. Since they are so far away, they appear as points and your eye integrates over the spectral content so that most stars look white. Mars, a planet, appears red to the naked eye but it can be somewhat brighter than the stars.

The stars appear to twinkle for the reasons you indcate and the fact that they look like points so that the path their light takes through the atmopshere is restricted to a very narrow cone. The sun, on the other hand, is rather extended - it fills a half a degree or more of the sky and is very bright. It is more than a billion time brighter than the brightest star. Twinkling due to the atmosphere is impreceptible because the Sun is so bright and takes up a fair amount of the sky.

The Sun appears white from Earth too, except when it is near the horizon, at sunset or sunrise. The amount of scattering is related to the path length the light takes through the atmosphere on the way to your eye, and when it is high in the sky that path length is pretty short, so not much light gets scattered.

The Sun (and Moon too) can be seen to shimmer sometimes, especially when setting or rising, but because they appear so big in the sky the shimmering doesn't look like twinkling. But look through a telescope at the Moon (or Sun with safe filtering) and you will see the shimmering.

Actually, the Sun appears _white_ when high in the sky. The answers you often see here saying it's yellow are wrong, posted by people who have never actually observed the Sun in a telescope. So it's not surprising that the stars appear white as well.

All the stars (other than the Sun) are very far away, so that the light rays coming from them to your eye pass through a very small cylinder no more than 7mm across, so are easily deflected by the atmosphere, causing them to twinkle. The planets and the Sun are close enough that the light rays from them form a cone, still 7mm across at your eye, but much wider in the upper atmosphere, so unlikely to be affected by atmospheric turbulence. What you _do_ see, looking at a planet or the Sun or Moon through a telescope, is atmospheric ripples moving across the disk, making it look like it is under water.

a) Because many stars are so far away you can't distinguish the color. We can with a good telescope or a spectrograph, but just by looking, most will look white. Just like far away cars - you can see them, but usually you can't tell what color they are until they get closer.

b) Because we're getting so much light from the sun that even with a few scattered photons, we don't notice the difference. Unlike the rest of the stars, which are only made up of a few photons to begin with, so a few being scattered makes a big difference in how bright they appear from moment to moment.

Some stars tend to emit yellow to red color and some seem blue depending on the velocity they have relative to the earth. As the Doppler effect says the stars moving away tend to red color because the wavelength of their light increases and this is reversed for blue stars that their approach toward us causes shorter wavelengths and a blue shift.