An introduction to astronomy: designed as a text-book for the use of students in college. By Denison Olmsted ...

184 THE PLANETS.
30S. The distance of an, inferior planet fromn the sun, may
be foutnd by observations at the time of its greatest elongation.
Thus if E (Fig. 62) be the place of the earth, and C that of
Venus at the time of her greatest elongation, the angle SCE
will be known, being a right angle. The angle SEC is the
greatest elongation; this is known by observation. Ience, if
ES is considered to be known, Rad: sin E:: SE SC, whichl
is the distance of the planet from the sun. But
if SE be not definitely known, then this proportion gives only the ratio of the distances of
the earth and the inferior planet from the sun.
In finding the earth's distance from the sun by
means of the transit of Venus (Art. 318), this
ratio will be employed. If the orbits were
both circles, this method would be very exact;
but being elliptical, we obtain the means value
of the radius SC by observing its greatest elongation in different parts of its orbit.*
309. The orbit of Xercztry is more eccentric,
and more inclined to the ecleptic, than that of
any oth/er planet;t while that of Venus is nearly circular, and
but little inclined to the ecliptic.
The eccentricity of the orbit of Mercury is nearly - of its
semi-major axis, while that of Venus is TIS; and that of the
earth only -a-; the inclination of Mercury's orbit is 7~, while
that of Venus is only 3~.:4 At the perihelion, Mercury is
only 29 millions of miles from the sun, while at the aphelion
his distance is 44 millions, a variation of 15 millions, and more
than five times as great as in the case of the earth. On account of his different distances from the earth, Mercury is also
subject to much variation in his apparent diameter, which is
12" in perigee, but only 5" in apogee.
310. After the mean distance has been found (Art. 307),
the periodic time is obtained, by applying Kepler's third law
to the orbit of the planet, and that of the earth. From this is
e4.culated the synodical period (Art. 304).
fl Herschel's Outlines, p. 275. t The asteroids are of course excepted.
t Baily's Tables.