with that of the Earth. Then those approaching it at any
angle less than that which makes will be visible at sunset ; those at a greater angle, at sunrise. The angle
is given by the relation,
,
in which is the Earth's velocity, the meteor's, and
is reckoned from the Earth's quit.
The portion of the celestial dome covered at sunset is, therefore,
,
where is the azimuth,
that at sunrise, .
If the meteors have direct motion only, can never exceed 90°, and the limits become,
for sunset, ,
and for sunrise, .
The mean inclination at sunset is
,
in which must be expressed in terms of , etc.
From this it appears that the relative number of bodies, travelling in all directions and at parabolic speed, which the Earth would encounter at sunrise and sunset respectively would be:—