Treatise on natural philosophy : Vol 1. Part 2 / by Sir William Thomson and Peter Guthrie Tait.
- Date:
- 1883
Licence: Public Domain Mark
Credit: Treatise on natural philosophy : Vol 1. Part 2 / by Sir William Thomson and Peter Guthrie Tait. Source: Wellcome Collection.
Provider: This material has been provided by the Royal College of Physicians of Edinburgh. The original may be consulted at the Royal College of Physicians of Edinburgh.
537/594 page 507
![velocity, and by the law of periodic times we have t~3 y3 = /x (M + m) where fx is the attraction between unit masses at unit distance. Then by substitution for y fx2(.Mmf ) ■ This system of units will be found to make the three following functions each equal to unity, viz. /x-Mm (M + m)~fxMm, and C. The units are in fact derived from- the consideration that these functions are each to be unity. In the case of the earth and moon, if we take the moon’s mass as y-Vnd of the earth’s, and the earth’s moment of inertia as •jy Mar [see § 824], it may easily be shown that the unit of mass is -gJg- of the earth’s mass, the unit of length is 5'26 earth’s radii or 33,506 kilometres, and the unit of time is 2 hrs. 41 minutes. In these units the present angular velocity of the earth’s diurnal rotation is expressed by *7044, and the moon’s present radius vector by 1T454. The two bodies being supposed to revolve in circles about their common centre of inertia with an angular velocity O, the moment of momentum of orbital motion is Numerical values of the units for earth and moon. Moment of momentum and energy of system. M mr n ( Mr 12 + m (-Y7-— \M+ O Mm r2a \M + m) \M + mj M + m Then, by the law of periodic times, in a circular orbit, OV3 = fx {M + to) whence fir2 = ^(i¥+m)-r-. And the moment of momentum of orbital motion = /x2 Mm (.M + m)-2 r-, and in the special units this is equal to r-. The moment of momentum of the planet’s rotation is Cn, and 0 = 1, in the special units. Therefore h=n + r^ (1). Again, the kinetic energy of orbital motion is Q2 + °2 = ^ \M + mj “ \M + mj 1 M + m 2 fxMm](https://iiif.wellcomecollection.org/image/b21987312_0537.jp2/full/800%2C/0/default.jpg)
