Page:The evolution of worlds - Lowell.djvu/289

Rh for the case of no action, the other terms being insensible for the satellites in the table, since in all $$\scriptstyle{r<\frac{R}{400}}$$.

Supposing, now, the particles within the orbit of the planet to be equally distributed according to their major axes, then as the velocity of any one of them, taking $$\scriptstyle{R-r=R}$$ approx. as unity, is

$\scriptstyle{v_1={\left(\frac{2}{1}-\frac{1}{a_1}\right)}^\frac{1}{2}}$,|undefined

the mean velocity of all of those which may encounter the satellite is, at the point of collision,

that is, just over three-quarters of the planet's speed in its orbit.

If we suppose the particles to be equally distributed in space, we shall have more with a given major axis in proportion to that axis, and our integral will become