We know that each day the shapes/phases of the Moon differs from its previous day and it is periodic with a period of 29 days. So, why it isn't the case in Sun? Or why do we have these different shapes/phases of the Moon?
I guess you're addressing lunar phases and not the moon illusion
The size or the shape of the moon doesn't really change at all as it appears.What makes it look like that is our view of the lit side of the moon, which changes periodically over a course of approximately 28 days while the moon revolves around the earth.And to answer your second question of why sun doesn't appear so , the answer is simply because it itself is the source of light and emits in all directions , if we pretend that sun too is emitting only from one side we would then certainly see a cyclic change over an year, assuming the sun doesn't rotate on its axis.
Although there are psychological effects that may make it appear larger at the horizon vs the clear sky, the angular diameter of the moon and sun actually do change: the moon subtends between 29'20'' and 34'6'', the sun 31'33'' to 32'33''. This is due to the fact that their orbits are elliptical, not circular; the change in distance is enough to change their apparent size in the sky.
While the difference in the Sun's apparent size is rather small (~3% change in diameter) the moon's is somewhat more substantial (~15%) - enough that it's perceptible.
Incidentally, the angular diameters are very similar and is the reason we get a fantastic view of the suns coronal when there is a total solar eclipse.
Based on the edited question: although the apparent size of the moon (or sun) does change daily, I doubt this would be observable with the unaided eye.
Because the sun is never in the night sky, by definition! I kid, I kid.
The truth is that the apparent size of the sun does vary through the year, hitting a maximum when the Earth is at perihelion, and a minimum at aphelion. The variation in the apparent size of the sun is just smaller than the variation in the apparent size of the moon because the eccentricity of the Earth's orbit around the sun is smaller than the eccentricity of the Moon's orbit around the Earth.
protected by Qmechanic♦ Oct 9 '16 at 5:28
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