Explain why the planets do not twinkle.
Planets do not twinkle because they are much closer to the Earth compared to stars, and are thus seen as extended sources of light rather than point-sized sources.
When we consider a planet as a collection of a large number of point-sized sources of light, the total variation in the amount of light entering our eye from all these individual point-sized sources averages out to zero. This effectively nullifies the twinkling effect that would otherwise occur due to atmospheric refraction.
Unlike stars, which are very distant and approximate point-sized sources, planets appear as extended sources, so the twinkling effect is not observed.
Explanation
The textbook explains that planets, being much closer to Earth, are seen as extended sources. When a planet is considered as a collection of many point-sized sources, the total variation in light entering the eye averages out to zero, nullifying the twinkling effect. This is in contrast to stars which are distant point-sized sources where atmospheric refraction causes fluctuations in apparent position and brightness.