| ⌠ | 90° | ⌠ | 360° | |
| ⎮ | ⎮ | sin θ·dθ·dφ. | ||
| ⌡ | θ₁ | ⌡ | 0 |
The mean inclination at sunset is
| ⌠ | θ₁ | ⌠ | 360° | |
| ⎮ | ⎮ | θ₁ · sin θ·dθ·dφ, | ||
| ⌡ | 0 | ⌡ | 0 |
⸻⸻⸻⸻ ,
| ⌠ | θ₁ | ⌠ | 360° | |
| ⎮ | ⎮ | sin θ·dθ·dφ, | ||
| ⌡ | 0 | ⌡ | 0 |
in which θ₁ must be expressed in terms of θ, 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:—
| sunrise | 5.8 |
| sunset | 1.0 |
and with the speed of the short-period comets,
| sunrise | 8.0 |
| sunset | 1.0 |