by Jules Verne
CHAPTER IV
REPLY FROM THE OBSERVATORY OF CAMBRIDGE
Barbicane, however, lost not one moment amid all the enthusiasmof which he had become the object. His first care was toreassemble his colleagues in the board-room of the Gun Club.There, after some discussion, it was agreed to consult theastronomers regarding the astronomical part of the enterprise.Their reply once ascertained, they could then discuss themechanical means, and nothing should be wanting to ensure thesuccess of this great experiment.
A note couched in precise terms, containing specialinterrogatories, was then drawn up and addressed to theObservatory of Cambridge in Massachusetts. This city, where thefirst university of the United States was founded, is justlycelebrated for its astronomical staff. There are to be foundassembled all the most eminent men of science. Here is to beseen at work that powerful telescope which enabled Bond toresolve the nebula of Andromeda, and Clarke to discover thesatellite of Sirius. This celebrated institution fully justifiedon all points the confidence reposed in it by the Gun Club.So, after two days, the reply so impatiently awaited was placedin the hands of President Barbicane.
It was couched in the following terms:
_The Director of the Cambridge Observatory to the President of the Gun Club at Baltimore._
CAMBRIDGE, October 7.On the receipt of your favor of the 6th instant, addressed tothe Observatory of Cambridge in the name of the members of theBaltimore Gun Club, our staff was immediately called together,and it was judged expedient to reply as follows:
The questions which have been proposed to it are these--
"1. Is it possible to transmit a projectile up to the moon?
"2. What is the exact distance which separates the earth fromits satellite?
"3. What will be the period of transit of the projectile whenendowed with sufficient initial velocity? and, consequently, atwhat moment ought it to be discharged in order that it may touchthe moon at a particular point?
"4. At what precise moment will the moon present herself in themost favorable position to be reached by the projectile?
"5. What point in the heavens ought the cannon to be aimed atwhich is intended to discharge the projectile?
"6. What place will the moon occupy in the heavens at the momentof the projectile's departure?"
Regarding the _first_ question, "Is it possible to transmit aprojectile up to the moon?"
_Answer._-- Yes; provided it possess an initial velocity of1,200 yards per second; calculations prove that to be sufficient.In proportion as we recede from the earth the action of gravitationdiminishes in the inverse ratio of the square of the distance;that is to say, _at three times a given distance the action isnine times less._ Consequently, the weight of a shot will decrease,and will become reduced to _zero_ at the instant that the attractionof the moon exactly counterpoises that of the earth; that is to sayat 47/52 of its passage. At that instant the projectile willhave no weight whatever; and, if it passes that point, it willfall into the moon by the sole effect of the lunar attraction.The _theoretical possibility_ of the experiment is thereforeabsolutely demonstrated; its _success_ must depend upon the powerof the engine employed.
As to the _second_ question, "What is the exact distance whichseparates the earth from its satellite?"
_Answer._-- The moon does not describe a _circle_ round theearth, but rather an _ellipse_, of which our earth occupies oneof the _foci_; the consequence, therefore, is, that at certaintimes it approaches nearer to, and at others it recedes fartherfrom, the earth; in astronomical language, it is at one time in_apogee_, at another in _perigee_. Now the difference betweenits greatest and its least distance is too considerable to beleft out of consideration. In point of fact, in its apogee themoon is 247,552 miles, and in its perigee, 218,657 miles onlydistant; a fact which makes a difference of 28,895 miles, ormore than one-ninth of the entire distance. The perigeedistance, therefore, is that which ought to serve as the basisof all calculations.
To the _third_ question.
_Answer._-- If the shot should preserve continuously its initialvelocity of 12,000 yards per second, it would require littlemore than nine hours to reach its destination; but, inasmuch asthat initial velocity will be continually decreasing, it willoccupy 300,000 seconds, that is 83hrs. 20m. in reaching thepoint where the attraction of the earth and moon will be _inequilibrio_. From this point it will fall into the moon in50,000 seconds, or 13hrs. 53m. 20sec. It will be desirable,therefore, to discharge it 97hrs. 13m. 20sec. before the arrivalof the moon at the point aimed at.
Regarding question _four_, "At what precise moment will the moonpresent herself in the most favorable position, etc.?"
_Answer._-- After what has been said above, it will benecessary, first of all, to choose the period when the moon willbe in perigee, and _also_ the moment when she will be crossingthe zenith, which latter event will further diminish the entiredistance by a length equal to the radius of the earth, _i. e._3,919 miles; the result of which will be that the final passageremaining to be accomplished will be 214,976 miles. But althoughthe moon passes her perigee every month, she does not reach thezenith always _at exactly the same moment_. She does not appearunder these two conditions simultaneously, except at longintervals of time. It will be necessary, therefore, to wait forthe moment when her passage in perigee shall coincide with thatin the zenith. Now, by a fortunate circumstance, on the 4th ofDecember in the ensuing year the moon _will_ present thesetwo conditions. At midnight she will be in perigee, that is,at her shortest distance from the earth, and at the same momentshe will be crossing the zenith.
On the _fifth_ question, "At what point in the heavens ought thecannon to be aimed?"
_Answer._-- The preceding remarks being admitted, the cannonought to be pointed to the zenith of the place. Its fire,therefore, will be perpendicular to the plane of the horizon;and the projectile will soonest pass beyond the range of theterrestrial attraction. But, in order that the moon shouldreach the zenith of a given place, it is necessary that theplace should not exceed in latitude the declination of theluminary; in other words, it must be comprised within thedegrees 0@ and 28@ of lat. N. or S. In every other spot the firemust necessarily be oblique, which would seriously militateagainst the success of the experiment.
As to the _sixth_ question, "What place will the moon occupy inthe heavens at the moment of the projectile's departure?"
_Answer._-- At the moment when the projectile shall be dischargedinto space, the moon, which travels daily forward 13@ 10' 35'',will be distant from the zenith point by four times that quantity,_i. e._ by 52@ 41' 20'', a space which corresponds to the pathwhich she will describe during the entire journey of the projectile.But, inasmuch as it is equally necessary to take into account thedeviation which the rotary motion of the earth will impart to theshot, and as the shot cannot reach the moon until after a deviationequal to 16 radii of the earth, which, calculated upon the moon'sorbit, are equal to about eleven degrees, it becomes necessary toadd these eleven degrees to those which express the retardation ofthe moon just mentioned: that is to say, in round numbers, aboutsixty-four degrees. Consequently, at the moment of firing thevisual radius applied to the moon will describe, with the verticalline of the place, an angle of sixty-four degrees.
These are our answers to the questions proposed to theObservatory of Cambridge by the members of the Gun Club:
To sum up--
1st. The cannon ought to be planted in a country situatedbetween 0@ and 28@ of N. or S. lat.
2nd. It ought to be pointed directly toward the zenith of the place.
3rd. The projectile ought to be propelled with an initialvelocity of 12,000 yards per second.
4th. It ought to be discharged at 10hrs. 46m. 40sec. of the 1stof December of the ensuing year.
5th. It will meet the moon four days after its discharge,precisely at midnight on the 4th of December, at the moment ofits transit across the zenith.
The members
of the Gun Club ought, therefore, without delay, tocommence the works necessary for such an experiment, and to beprepared to set to work at the moment determined upon; for, ifthey should suffer this 4th of December to go by, they will notfind the moon again under the same conditions of perigee and ofzenith until eighteen years and eleven days afterward.
The staff of the Cambridge Observatory place themselves entirelyat their disposal in respect of all questions of theoreticalastronomy; and herewith add their congratulations to those ofall the rest of America. For the Astronomical Staff, J. M. BELFAST,_Director of the Observatory of Cambridge._
