The Moon-Voyage

CHAPTER IV.

AN­SWER FROM THE CAM­BRIDGE OB­SER­VA­TO­RY.

In the mean­time Bar­bi­cane did not lose an in­stant amidst the en­thu­si­asm of which he was the ob­ject. His first care was to call to­geth­er his col­leagues in the board-​room of the Gun Club. There, af­ter a de­bate, they agreed to con­sult as­tronomers about the as­tro­nom­ical part of their en­ter­prise. Their an­swer once known, they would then dis­cuss the me­chan­ical means, and noth­ing would be ne­glect­ed to as­sure the suc­cess of their great ex­per­iment.

A note in pre­cise terms, con­tain­ing spe­cial ques­tions, was drawn up and ad­dressed to the ob­ser­va­to­ry of Cam­bridge in Mas­sachusetts. This town, where the first Uni­ver­si­ty of the Unit­ed States was found­ed, is just­ly cel­ebrat­ed for its as­tro­nom­ical staff. There are as­sem­bled the great­est men of sci­ence; there is the pow­er­ful tele­scope which en­abled Bond to re­solve the neb­ula of An­drome­da and Clarke to dis­cov­er the satel­lite of Sir­ius. This cel­ebrat­ed in­sti­tu­tion was, there­fore, wor­thy in ev­ery way of the con­fi­dence of the Gun Club.

Af­ter two days the an­swer, im­pa­tient­ly await­ed, reached the hands of Pres­ident Bar­bi­cane.

It ran as fol­lows:--

"_The Di­rec­tor of the Cam­bridge Ob­ser­va­to­ry to the Pres­ident of the Gun Club at Bal­ti­more_.

"On the re­ceipt of your favour of the 6th in­st., ad­dressed to the Ob­ser­va­to­ry of Cam­bridge in the name of the mem­bers of the Bal­ti­more Gun Club, we im­me­di­ate­ly called a meet­ing of our staff, who have deemed it ex­pe­di­ent to an­swer as fol­lows:--

"The ques­tions pro­posed to it were these:--

"'1. Is it pos­si­ble to send a pro­jec­tile to the moon?

"'2. What is the ex­act dis­tance that sep­arates the earth and her satel­lite?

"'3. What would be the du­ra­tion of the pro­jec­tile's tran­sit to which a suf­fi­cient ini­tial speed had been giv­en, and con­se­quent­ly at what mo­ment should it be hurled so as to reach the moon at a par­tic­ular point?

"'4. At what mo­ment would the moon present the most favourable po­si­tion for be­ing reached by the pro­jec­tile?

"'5. What point in the heav­ens ought the can­non, des­tined to hurl the pro­jec­tile, be aimed at?

"'6. What place in the heav­ens will the moon oc­cu­py at the mo­ment when the pro­jec­tile will start?'

"Re­gard­ing ques­tion No. 1, 'Is it pos­si­ble to send a pro­jec­tile to the moon?'

"Yes, it is pos­si­ble to send a pro­jec­tile to the moon if it is giv­en an ini­tial ve­loc­ity of 1,200 yards a sec­ond. Cal­cu­la­tions prove that this speed is suf­fi­cient. In pro­por­tion to the dis­tance from the earth the force of grav­ita­tion di­min­ish­es in an in­verse ra­tio to the square of the dis­tance--that is to say, that for a dis­tance three times greater that force is nine times less. In con­se­quence, the weight of the pro­jec­tile will de­crease rapid­ly, and will end by be­ing com­plete­ly an­nulled at the mo­ment when the at­trac­tion of the moon will be equal to that of the earth--that is to say, at the 47/52 of the dis­tance. At that mo­ment the pro­jec­tile will have no weight at all, and if it clears that point it will fall on to the moon on­ly by the ef­fect of lu­nar grav­ita­tion. The the­oret­ic pos­si­bil­ity of the ex­per­iment is, there­fore, quite demon­strat­ed; as to its suc­cess, that de­pends sole­ly in the pow­er of the en­gine em­ployed.

"Re­gard­ing ques­tion No. 2, 'What is the ex­act dis­tance that sep­arates the earth from her satel­lite?'

"The moon does not de­scribe a cir­cle round the earth, but an el­lipse, of which our earth oc­cu­pies one of the fo­ci; the con­se­quence is, there­fore, that at cer­tain times it ap­proach­es near­er to, and at oth­ers re­cedes far­ther from, the earth, or, in as­tro­nom­ical lan­guage, it has its apogee and its perigee. At its apogee the moon is at 247,552 miles from the earth, and at its perigee at 218,657 miles on­ly, which makes a dif­fer­ence of 28,895, or more than a ninth of the dis­tance. The perigee dis­tance is, there­fore, the one that should give us the ba­sis of all cal­cu­la­tions.

"Re­gard­ing ques­tion No. 3, 'What would be the du­ra­tion of the pro­jec­tile's tran­sit to which a suf­fi­cient ini­tial speed has been giv­en, and con­se­quent­ly at what mo­ment should it be hurled so as to reach the moon at a par­tic­ular point?'

"If the pro­jec­tile kept in­def­inite­ly the ini­tial speed of 12,000 yards a sec­ond, it would on­ly take about nine hours to reach its des­ti­na­tion; but as that ini­tial ve­loc­ity will go on de­creas­ing, it will hap­pen, ev­ery­thing cal­cu­lat­ed up­on, that the pro­jec­tile will take 300,000 sec­onds, or 83 hours and 20 min­utes, to reach the point where the ter­res­tri­al and lu­nar grav­ita­tions are equal, and from that point it will fall up­on the moon in 50,000 sec­onds, or 13 hours, 53 min­utes, and 20 sec­onds. It must, there­fore, be hurled 97 hours, 13 min­utes, and 20 sec­onds be­fore the ar­rival of the moon at the point aimed at.

"Re­gard­ing ques­tion No. 4, 'At what mo­ment would the moon present the most favourable po­si­tion for be­ing reached by the pro­jec­tile?'

"Ac­cord­ing to what has been said above the epoch of the moon's perigee must first be cho­sen, and at the mo­ment when she will be cross­ing her zenith, which will still fur­ther di­min­ish the en­tire dis­tance by a length equal to the ter­res­tri­al ra­dius--i.e., 3,919 miles; con­se­quent­ly, the pas­sage to be ac­com­plished will be 214,976 miles. But the moon is not al­ways at her zenith when she reach­es her perigee, which is once a month. She is on­ly un­der the two con­di­tions si­mul­ta­ne­ous­ly at long in­ter­vals of time. This co­in­ci­dence of perigee and zenith must be wait­ed for. It hap­pens for­tu­nate­ly that on De­cem­ber 4th of next year the moon will of­fer these two con­di­tions; at mid­night she will be at her perigee and her zenith--that is to say, at her short­est dis­tance from the earth and at her zenith at the same time.

"Re­gard­ing ques­tion No. 5, 'At what point in the heav­ens ought the can­non des­tined to hurl the pro­jec­tile be aimed?'

"The pre­ced­ing ob­ser­va­tions be­ing ad­mit­ted, the can­non ought to be aimed at the zenith of the place (the zenith is the spot sit­uat­ed ver­ti­cal­ly above the head of a spec­ta­tor), so that its range will be per­pen­dic­ular to the plane of the hori­zon, and the pro­jec­tile will pass the soon­est be­yond the range of ter­res­tri­al grav­ita­tion. But for the moon to reach the zenith of a place that place must not ex­ceed in lat­itude the dec­li­na­tion of the lu­mi­nary--in oth­er words, it must be com­prised be­tween 0° and 28° of north or south lat­itude. In any oth­er place the range must nec­es­sar­ily be oblique, which would se­ri­ous­ly af­fect the suc­cess of the ex­per­iment.

"Re­gard­ing ques­tion No. 6, 'What place will the moon oc­cu­py In the heav­ens at the mo­ment of the pro­jec­tile's de­par­ture?'

“At the mo­ment when the pro­jec­tile is hurled in­to space, the moon, which trav­els for­ward 13° 10' 35” each day, will be four times as dis­tant from her zenith point--i.e., by 52° 42' 20", a space which cor­re­sponds to the dis­tance she will trav­el dur­ing the tran­sit of the pro­jec­tile. But as the de­vi­ation which the ro­ta­to­ry move­ment of the earth will im­part to the shock must al­so be tak­en in­to ac­count, and as the pro­jec­tile can­not reach the moon un­til af­ter a de­vi­ation equal to six­teen radii of the earth, which, cal­cu­lat­ed up­on the moon's or­bit, is equal to about 11°, it is nec­es­sary to add these 11° to those caused by the al­ready-​men­tioned de­lay of the moon, or, in round num­bers, 64°. Thus, at the mo­ment of fir­ing, the vi­su­al ra­dius ap­plied to the moon will de­scribe with the ver­ti­cal line of the place an an­gle of 64°.

"Such are the an­swers to the ques­tions pro­posed to the Ob­ser­va­to­ry of Cam­bridge by the mem­bers of the Gun Club.

"To sum up--

"1st. The can­non must be placed in a coun­try sit­uat­ed be­tween 0° and 28° of north or south lat­itude.

"2nd. It must be aimed at the zenith of the place.

"3rd. The pro­jec­tile must have an ini­tial speed of 12,000 yards a sec­ond.

"4th. It must be hurled on De­cem­ber 1st of next year, at 10hrs. 46mins. 40secs. p.m.

"5th. It will meet the moon four days af­ter its de­par­ture on De­cem­ber 4th, at mid­night pre­cise­ly, at the mo­ment she ar­rives at her zenith.

"The mem­bers of the Gun Club ought, there­fore, at once to com­mence the labour ne­ces­si­tat­ed by such an en­ter­prise, and be ready to put them in­to ex­ecu­tion at the mo­ment fixed up­on, for they will not find the moon in the same con­di­tions of perigee and zenith till eigh­teen years and eleven days lat­er.

"The staff of the Ob­ser­va­to­ry of Cam­bridge puts it­self en­tire­ly at their dis­po­si­tion for ques­tions of the­oret­ic as­tron­omy, and begs to join its con­grat­ula­tions to those of the whole of Amer­ica.

"On be­half of the staff,

"J.M. BELFAST,

“_Di­rec­tor of the Ob­ser­va­to­ry of Cam­bridge_.”