Page:The Solar System - Six Lectures - Lowell.djvu/61

Mercury

43

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done in a given time by tide-raising forces, we have, then, $\textstyle ({\frac {2m\rho }{r}}+{\frac {3m\rho ^{2}}{r}})^{2}$ or for most cases sufficiently well, taking only the first term, $\textstyle {\frac {4m^{2}\rho ^{2}}{r^{6}}}$ That is, it is as the square of the attracting mass and the square of the radius of the affected body directly and inversely as the sixth power of the latter's distance.

Work done by Tide-raising force in Unity of time in Ratio to Sun's Action on the Earth taken as Unity.

By Sun on :-									$\scriptstyle {\frac {4m^{2}\rho ^{2}}{r^{6}}}$ (approx)
Mercury		.	.	.	.	.	.	.	.	43-26
Venus		.	.	.	.	.	.	.	.	6.60
Earth		.	.	.	.	.	.	.	.	1.00
Mars	.	.	.	.	.	.	.	.	.	0.023
Jupiter		.	.	.	.	.	.	.	.	0.006

On Earth by :-							$\scriptstyle \lbrack {\frac {2m\rho }{r^{3}}}+{\frac {3m\rho ^{2}}{r^{4}}}\rbrack ^{2}$
Sun	.	.	.	.	.	.	.	.	.	1.00
Moon		.	.	.	.	.	.	.	.	4.97

On Satellites by their Primaries :-						$\scriptstyle \lbrack {\frac {2m\rho }{r^{3}}}+{\frac {3m\rho ^{2}}{r^{4}}}\rbrack ^{2}$
Iapetus	.	.	.	.	.	.	.	27.6
Callisto	.	.	.	.	.	.	32,549.0
Ganymede	.	.	.	.	.	.	1,385,600.0
Moon	.	.	.	.	.	.	.	2,374.4