astronomyearthgeometrymoonsun
I know that the full Moon appears when Sun, Moon and Earth are in a straight line, but if we consider that they are in straight line, why is the Moon illuminated?
I mean to say that Earth should block all the rays of the Sun and shouldn't allow any light ray to reach the Moon. In this case the moon should not get illuminated as no light has reached it which it can reflect back. Then why do we see a fully illuminated hemisphere of the Moon?
This is what you expect, in terms of the moon pointing towards the sun:
That is, the line across the moon appears perpendicular to the line towards the sun.
Now the above is a flat drawing. The sky appears curved (i.e. the dome of the starry sky). So that curve may introduce some apparent distortion.
To make a drawing that avoids the curvature issue, consider a drawing that only includes the sun, the moon, and a small amount of sky around the line connecting the two. (By the way, even for the curved bowl of the sky, the shortest line connecting the two is well defined except in the case of a new or full moon.) That drawing is approximately flat and will show the above relation.
The moon was just over 1/2 lit even though it was obvious that the earth was not casting any kind of shadow on the moon and the position of the sun on the opposite end of the sky should have lit the moon at around 90%.
That the Earth's shadow is responsible for the phases of the Moon apparently is a widely held misconception, enough so that multiple sites spend some time addressing this concept. The Earth's shadow is responsible for lunar eclipses, but not the phases of the Moon. The Moon's orbit about the Earth is what is responsible for the phases of the Moon. This is depicted below.
Image source: http://starchild.gsfc.nasa.gov/docs/StarChild/teachers/moonglow2.html
Except for lunar eclipses, the Sun always illuminates about half of the Moon, but that illuminated half typically is not the same half we see from the Earth. Today is one day before the Moon will be half full (waning), which is position 7 in the above diagram. We only see half of the Moon being lit in that position because the other half of the Moon we see is shadowed by the Moon itself.
Lunar eclipses occur when the Moon's orbit takes the Moon into the Earth's shadow. From the diagram, it should be obvious that this can only happen when the Moon would otherwise be full. We do not see an eclipse every month as the above diagram would suggest. This is because the Moon's orbit about the Earth is tilted with respect to the Earth's orbit about the Sun. Instead, total lunar eclipses occur only about once per year.
Best Answer
The orbital plane of the Moon around the Earth is at an angle to the orbital plane of the Earth about the Sun.
This diagram was drawn to show why we do not have eclipses more often but is also shows how it is that a full Moon occurs.
Image downloaded from Taylor Science Geeks website