mass of the planet has been cancelled out; the mass of the sun
remains, multiplied by the gravitation-constant, and is seen to be
proportional to the cube of the distance divided by the square of the
periodic time: a ratio, which is therefore the same for all planets
controlled by the sun. Hence, knowing _r_ and _T_ for any single planet,
the value of _VS_ is known.

No. 4. So by knowing the length of year and distance of any planet from
the sun, the sun's mass can be calculated, in terms of that of the
earth.

No. 5. For the satellites, the force acting depends on the mass of
_their_ central body, a planet. Hence the mass of any planet possessing
a satellite becomes known.

The same argument holds for any other system controlled by a central
body--for instance, for the satellites of Jupiter; only instead of _S_
it will be natural to write _J_, as meaning the mass of Jupiter. Hence,
knowing _r_ and _T_ for any one satellite of Jupiter, the value of _VJ_
is known.

Apply the argument also to the case of moon and earth. Knowing the
distance and time of revolution of our moon, the value of _VE_ is at
once determined; _E_ being the mass of the earth. Hence, _S_ and _J_,
and in fact the mass of any central body possessing a visible satellite,
are now known in terms of _E_, the mass of the earth (or, what is
practically the same thing, in terms of _V_, the gravitation-constant).
Observe that so far none of these quantities are known absolutely. Their
relative values are known, and are tabulated at the end of the Notes
above, but the finding of their absolute values is another matter, which
we must defer.

But, it may be asked, if Kepler's third law only gives us the mass of a
_central_ body, how is the mass of a _satellite_ to be known? Well, it
is not easy; the mass of no satellite is known with much accuracy. Their
mutual perturbations give us some data in the case of the satellites of
Jupiter; but to our own moon this method is of course inapplicable. Our
moon perturbs at first sight nothing, and accordingly its mass is not
even yet known with exactness. The mass of comets, again, is quite
unknown. All that we can be sure of is that they are smaller than a
certain limit, else they would perturb the planets they pass near.
Nothing of this sort has ever been detected. They are themselves
perturbed plentifully, but they perturb nothing; hence we learn that
their mass is small. The mass of a comet may, indeed, be a few