Do solar eclipse occur at a full moon?
No. A solar eclipse occurs at the new moon. A lunar eclipse occurs during the full moon.
A lunar eclipse can only occur at full moon and a solar eclipse can only occur at new moon. A solar eclipse occurs when the Moon passes between the Earth and the Sun and a lunar eclipse occurs when the Earth passes between the Sun and the Moon. Earth blocks out the light to the moon in a lunar eclipse. The moon blocks out the light to the earth in a solar eclipse
Why does a lunar eclipse occur when there is a full moon and a solar eclipse occur when there is a new moon?
What we commonly call a solar eclipse can occur ONLY at the time of the new moon. In order for the solar eclipse to occur, one of the nodes of the lunar orbit must be aligned with the sun at the time of new moon; hence, a solar eclipse doesn't occur at every new moon. Solar eclipse can only happen at new moon.
A solar eclipse can't happen during a full Moon. For a solar eclipse, the Moon would be between Earth and the Sun, and would partially or totally block the sun. However, a lunar eclipse can occur when there is a full Moon, as the Earth is between the Sun and the Moon and can cast a shadow on the Moon.