1836.] 



On the Mass of the Planet Jupiter. 



131 



XII.— On the Mass of the Planet Jupiter.— By Goday Venkata 



JUGGAROW. 



I believe I shall not be quite mistaken, if I affirm that, till very 

 lately, the science of Mathematics was but little studied, if not un- 

 known altogether, among my countrymen. The air of mystery with 

 which it has been invested by those who, while they admire, shrink 

 from a nearer approach to it, has succeeded in keeping many of my 

 timid brethren at a respectful distance, in the outer court of the tem- 

 ple. With a view to encourage the beginner, and persuade those more 

 advanced of the possibility of comprehending; a great deal, with a 

 moderate quantity of knowledge only, I shall, from the observations 

 which have been made for the purpose, and without any great mathe- 

 matical display, proceed to weigh the planet Jupiter. This may appear 

 a bold and presumptuous step, but the computation which follows will 

 I hope, leave no doubt of its practicability. 



The weight of a body is found to vary, according to the circumstance 

 of its situation— thus, upon the top of a mountain, a body is found to 

 weigh less than on the plain below ; and, at the distance of the moon, 

 the weight of a body would be found reduced to 1-3600 of its weight at 

 the surface of the earth — a fact which is immediately arrived at from 

 the law, " that the force of gravity varies inversely as the square of the 

 distance." 



In the case of the planet Jupiter, and, indeed, of all the other 

 planets, they are each kept in their oibit, by the attraction of gravity, 

 being proportional to the centrifugal force in the orbit. Hence the 

 distance of any body from the sun, varies with the time of its revolu- 

 tion round the sun, and may be determined from the Keplerian law 7 , 

 " that the square of the periodical time varies as the cube of the mean 

 distance." 



With these two laws, which it only requires common sense to render 

 obvious, and the further consideration that the force of gravity varies 

 as the mass of the attracting body, we will now set to work. 



From the Cambridge observations for 1834, we find that when Jupi- 

 ter's fourth satellite was at its greatest distance from the planet, as seen 

 from the earth, it subtended an angle of 10' 45" 9. From the Nautical 

 Almanac we find the logarithm of the distance of Jupiter from the earth 

 m 0, 6488251 = D. Hence we find, the distance from Jupiter at 

 which his fourth satellite revolves, as follows — as rad : D : .* sin 10' 

 45" 9 : d = ,012055 (the earth's distance from the sun being 1). Now 

 the time occupied by this satellite to revolve round Jupiter, is I6d. 

 I6h. 32m. 8s. or 1441923 seconds, or, in one second of time, it per- 

 forms in its orbit 0", 89 88. 



Let the subjoined figure represent the orbit of Jupiter's fourth 

 satellite; a being its situation at one moment, and c its position at 



