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

y88'iT4ile SUN,
vanttcs fabout 6 1' inll 24- ]lours, and at aphtlion only about 57/.
Now +t..... t. 107, which is the square of Jf.034, the ratio of apparent diameCters at tlhe samce points. Indeed, a careful comparis-on of tthe sun's angular velocities, iil all parts of theC orbit,
filows tlhat they vary.iaveirscly as the sq.ua'cs qf the d-istaCC8es.
If ch1lanlges iln annulllar (i. e., apparent) velocity wrwee caused
wholly t) diffcrce of distalnce, theln it would vary2, inv1scely
1only as tie first power of the distlanlce, just as thle apparent
dialeter does. Buttt since tlte anglular velocity varies inversely
as tlhe sqrata're, instcad of thte first powcr of tile distanee, the
absolute velocity must also be greater as tle distance is less,
anld tlice vtr.'lhus wv perceive, that when thle sunl is nearcst to Ius, ic, tappears to ml\ove fatstest for two r6asons, —- irst, bc)
cause the same)e rate of motion -would appecar greater, if nearcr
to 11s, and secondly, becaluse t.e actual motion is then greater;
and efach of tltese is il the inverse ratio of th}e distance-.
1(56. It mulst be rememblerdcd, that this reasoning proceeds
on tlhe ground tthat the line of motion is everywherev at right
angles to the radiutt,s vector. That this is true witlhout sensible,
dcviatiolt, appe)t)ars fromt tlhe fact that tlhe solar orbit is very
nearly circular, witlh thbe earth at its center. ]if truly representetc oil p)at)er, it could not be distincgtishcd by tit ryhe from
a circle.
This relation between (distances and app'l trent velocities
thalvit) Ing ell (been ce establislled, advanltage lle ttl aken of tlhe'apid l:rate t)f camltge in te tlatt:elr, to (letrtmile tihe variatiomns
inll the radiuts vcct(r more accurate - lFig.,83.
ly than can1 be (1d1on by tlhe appat - rl -
ent diameter.
1 67.'1he angular velocity being \
inverscTly as tlhe square of tile (dis-
tance inl all' parts of thte solar orbit,
it follows thtat, the pr'odect of tfe\
angle de/scrib n-ed ian any gi. ven time,
bln l/to,lare oti. f tihe (bIistance, -is
(Il wa,/0 the samune eolstac.Nt quantity..
Fo r if two ftactors, A x13, A is in-.