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

DrISTA^NClES 1FRO'rl, SUN. t1.7
Uranus twicc that of Saturn. I[f this, however, cere a perfcctly correct rule, Neptune mwould be twice as far frolml the
sun as Uranus, and therefore 3,600 millions of mniles,.Iswhereas
its actual (listance is short of 3,000 millions. Between the
orbits of Mars and Juliter a great chasm appeared, lwhicll
)broke the continuity; but the discovery of the planetoids hlas
filled the vOid. A morte xact law of the series is that called.rHodse' law. it is as follows: if we represent the distanlce of:ncrcury by 4, and increase the following tcrm s by the p)roduct of 3 into thle rscendling powers of 2, wN shall obtain the
relative distances of the plancts friom the sun.'thus,.le rcurcllyy,....... ^4: 4
Venus,.4...-~13.20:. 7
Lavtthl... 4: 3.21':: 10:Mars....... t-3.2::::: 16
P'lanetoids,..... 3.2: 28
Jupiter,..4-1 3.2: 59.
Sattir,....... t4-.3.2a.: 100
lUranus,....... 4-1-3.2.:::190
lNeptulne....:.....388
cfore t.lhe discovery of Neptunc, vBe -ode's law rudely expressed the relative distances fiom the sunl; butt it signally
fails of including the new planlt, as it gives near 3,600 millions
inlstelad of thle true distance,, 2,800 millions.
]Iut tie relative distances fiom thle sun are acclurately obtained by Kepler's third law,-.- that the square s of the periodic
times are as the cubes of the distances (Art. 171). TI'hlus tho
Eartl's (istance being previously ascertaitled by meats of thle
sun'11s lhoriontal )aralll ax (Art. 87), and the periodl of any other
planet, as Jupiter, bling learned friom observation, we ml1nay say,
as tllhe square of thoe Earth's period (365.'256 days) is to the
square of Jupiter's period (4332.586 days), so is the cube of the
]art t's dis iStance to the cube of Jupiter's distance, the cube root
of whllich will be the distance itself. Or, to cxpress the same
truth ln:)roe cotlcisely, 365.2,56' 4332.586':: 1' 5.2023. )f
t:llrse, tllis method can as yet be u-sed only aplproximately fol.Neptule, whihel has desclribed but a short portionl of its orbit
silcee its liscovery.
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