If the satellite be moving in its orbit less fast than this, its space-speed will exceed that of the average particle; it will strike the particle at its own rear and be accelerated by the collision. If faster, the particle will strike it in front and retard it in its motion round its primary.
From the table it appears that all the large satellites of all the planets have an orbital speed round their primaries exceeding those in either column. In consequence, all of them must have been retarded during their formation by the impact of interplanetary particles and forced nearer their primaries than would otherwise have been the case; and this whether the particles were distributed more densely toward the Sun, as 1/a₁, or were equally strewn throughout.
For interplanetary particles whose orbits lie without the particular planet’s path the mean speed is the parabolic at the planet’s distance, given in the third column of the table. This is the case on either supposition of distribution. The orbital speed of the satellite which shall not be affected by collisions with them is, for the several planets:—
| Miles a second | |
|---|---|
| Jupiter | 3.4 |
| Saturn | 2.5 |
| Uranus | 1.7 |
| Neptune | 1.4 |
All the satellites but Iapetus have orbital speeds exceeding this, and consequently are retarded also by these particles.
For particles crossing the orbit (2) the mean velocity would be practically parabolic, 1.4, even if the distribution were as 1/r′, r′ being the distance from the Sun. The effect would depend upon the angle of approach and in the mean give a greater velocity for the particle than for the satellite within the orbit, a less one without; retarding the satellite in both cases. Thus the total effect of all the particles encountering the large satellites is to retard them and to tend to make them hug their primary.
For retrograde satellites the velocities of impact with inside and outside particles moving direct are respectively:
| Inside | Outside | |
|---|---|---|
| Jupiter | 2.0 + v | v + 3.4 |
| Saturn | 1.5 + v | v + 2.5 |
| Uranus | 1.0 + v | v + 1.7 |
| Neptune | 0.8 + v | v + 1.4 |
In both cases the impact tends to check the satellite.
Comparing with these the velocities of impact for direct satellites in a direct plenum:—