Reply From The Observatory Of Cambridge

: From The Earth To The Moon

Barbicane, however, lost not one moment amid all the enthusiasm

of which he had become the object. His first care was to

reassemble his colleagues in the board-room of the Gun Club.

There, after some discussion, it was agreed to consult the

astronomers regarding the astronomical part of the enterprise.

Their reply once ascertained, they could then discuss the

mechanical means, and nothing should be wanting to ensure t e

success of this great experiment.



A note couched in precise terms, containing special

interrogatories, was then drawn up and addressed to the

Observatory of Cambridge in Massachusetts. This city, where the

first university of the United States was founded, is justly

celebrated for its astronomical staff. There are to be found

assembled all the most eminent men of science. Here is to be

seen at work that powerful telescope which enabled Bond to

resolve the nebula of Andromeda, and Clarke to discover the

satellite of Sirius. This celebrated institution fully justified

on all points the confidence reposed in it by the Gun Club.

So, after two days, the reply so impatiently awaited was placed

in 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 to

the Observatory of Cambridge in the name of the members of the

Baltimore 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 from

its satellite?



"3. What will be the period of transit of the projectile when

endowed with sufficient initial velocity? and, consequently, at

what moment ought it to be discharged in order that it may touch

the moon at a particular point?



"4. At what precise moment will the moon present herself in the

most favorable position to be reached by the projectile?



"5. What point in the heavens ought the cannon to be aimed at

which is intended to discharge the projectile?



"6. What place will the moon occupy in the heavens at the moment

of the projectile's departure?"



Regarding the first question, "Is it possible to transmit a

projectile up to the moon?"



Answer.-- Yes; provided it possess an initial velocity of

1,200 yards per second; calculations prove that to be sufficient.

In proportion as we recede from the earth the action of gravitation

diminishes in the inverse ratio of the square of the distance;

that is to say, at three times a given distance the action is

nine times less. Consequently, the weight of a shot will decrease,

and will become reduced to zero at the instant that the attraction

of the moon exactly counterpoises that of the earth; that is to say

at 47/52 of its passage. At that instant the projectile will

have no weight whatever; and, if it passes that point, it will

fall into the moon by the sole effect of the lunar attraction.

The theoretical possibility of the experiment is therefore

absolutely demonstrated; its success must depend upon the power

of the engine employed.



As to the second question, "What is the exact distance which

separates the earth from its satellite?"



Answer.-- The moon does not describe a circle round the

earth, but rather an ellipse, of which our earth occupies one

of the foci; the consequence, therefore, is, that at certain

times it approaches nearer to, and at others it recedes farther

from, the earth; in astronomical language, it is at one time in

apogee, at another in perigee. Now the difference between

its greatest and its least distance is too considerable to be

left out of consideration. In point of fact, in its apogee the

moon is 247,552 miles, and in its perigee, 218,657 miles only

distant; a fact which makes a difference of 28,895 miles, or

more than one-ninth of the entire distance. The perigee

distance, therefore, is that which ought to serve as the basis

of all calculations.



To the third question.



Answer.-- If the shot should preserve continuously its initial

velocity of 12,000 yards per second, it would require little

more than nine hours to reach its destination; but, inasmuch as

that initial velocity will be continually decreasing, it will

occupy 300,000 seconds, that is 83hrs. 20m. in reaching the

point where the attraction of the earth and moon will be in

equilibrio. From this point it will fall into the moon in

50,000 seconds, or 13hrs. 53m. 20sec. It will be desirable,

therefore, to discharge it 97hrs. 13m. 20sec. before the arrival

of the moon at the point aimed at.



Regarding question four, "At what precise moment will the moon

present herself in the most favorable position, etc.?"



Answer.-- After what has been said above, it will be

necessary, first of all, to choose the period when the moon will

be in perigee, and also the moment when she will be crossing

the zenith, which latter event will further diminish the entire

distance by a length equal to the radius of the earth, i. e.

3,919 miles; the result of which will be that the final passage

remaining to be accomplished will be 214,976 miles. But although

the moon passes her perigee every month, she does not reach the

zenith always at exactly the same moment. She does not appear

under these two conditions simultaneously, except at long

intervals of time. It will be necessary, therefore, to wait for

the moment when her passage in perigee shall coincide with that

in the zenith. Now, by a fortunate circumstance, on the 4th of

December in the ensuing year the moon will present these

two conditions. At midnight she will be in perigee, that is,

at her shortest distance from the earth, and at the same moment

she will be crossing the zenith.



On the fifth question, "At what point in the heavens ought the

cannon to be aimed?"



Answer.-- The preceding remarks being admitted, the cannon

ought 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 the

terrestrial attraction. But, in order that the moon should

reach the zenith of a given place, it is necessary that the

place should not exceed in latitude the declination of the

luminary; in other words, it must be comprised within the

degrees 0@ and 28@ of lat. N. or S. In every other spot the fire

must necessarily be oblique, which would seriously militate

against the success of the experiment.



As to the sixth question, "What place will the moon occupy in

the heavens at the moment of the projectile's departure?"



Answer.-- At the moment when the projectile shall be discharged

into 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 path

which she will describe during the entire journey of the projectile.

But, inasmuch as it is equally necessary to take into account the

deviation which the rotary motion of the earth will impart to the

shot, and as the shot cannot reach the moon until after a deviation

equal to 16 radii of the earth, which, calculated upon the moon's

orbit, are equal to about eleven degrees, it becomes necessary to

add these eleven degrees to those which express the retardation of

the moon just mentioned: that is to say, in round numbers, about

sixty-four degrees. Consequently, at the moment of firing the

visual radius applied to the moon will describe, with the vertical

line of the place, an angle of sixty-four degrees.



These are our answers to the questions proposed to the

Observatory of Cambridge by the members of the Gun Club:



To sum up--



1st. The cannon ought to be planted in a country situated

between 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 initial

velocity of 12,000 yards per second.



4th. It ought to be discharged at 10hrs. 46m. 40sec. of the 1st

of 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 of

its transit across the zenith.



The members of the Gun Club ought, therefore, without delay, to

commence the works necessary for such an experiment, and to be

prepared to set to work at the moment determined upon; for, if

they should suffer this 4th of December to go by, they will not

find the moon again under the same conditions of perigee and of

zenith until eighteen years and eleven days afterward.



The staff of the Cambridge Observatory place themselves entirely

at their disposal in respect of all questions of theoretical

astronomy; and herewith add their congratulations to those of

all the rest of America.

For the Astronomical Staff,



J. M. BELFAST,

Director of the Observatory of Cambridge.