Question

While full solar eclipse the sun is fully covered by the Moon. Now determine the relation between sun and moons size and distance in this condition?sun's radius=R;moon's=r & distance of sun and moon from earth respectively D & d

Answer 1

The angular diameter of the Moon needs to be greater than the angular diameter of the Sun for a total solar eclipse to occur.

Explanation:

The angular diameter `theta` of the Moon is related to the radius `r` of the Moon and the distance `d` of the Moon from the Earth.

`2r=d theta`

Likewise the angular diameter `Theta` of the Sun is:

`2R=D Theta`

So, for a total eclipse the angular diameter of the Moon must be greater than that of the Sun.

`theta > Theta`

This means that the radii and distances must follow:

`r/d > R/D`

Actually this is just one of three conditions required for a total solar eclipse to occur. Effectively this condition means that the Moon can't be near its apogee when it is furthest from Earth and its angular diameter is smallest.

The second condition is that it must be a new Moon. This is when the Moon is in alignment between the Earth and the Sun.

The third condition is that the Moon must be close to one of its nodes. The Moon's orbit is inclined at `5^@` to the ecliptic, which is the plane of the Earth's orbit around the Sun. The points where the Moon's orbit intersects the ecliptic are called nodes.

So, a total eclipse can only occur when the Moon is close to a node at the time of a new Moon. These are the only times that the Earth, Moon and Sun are in true alignment. The Moon also needs to be close enough to the Earth to have an angular diameter greater than that of the Sun.