Hence Mars, at the moment of departure, must be 180° minus 136° equals 44° ahead of the Earth in his orbit.
"Therefore, a departure for Mars on that type of elliptical path becomes a possibility only when Mars — as seen from the Sun — is 44° ahead of the Earth.
"During the outward voyage, the Earth will travel through 0.987 times 260° — 256° of arc. Once the ships have completed their full semi-ellipse of 180° and have arrived at Mars, the Earth — as seen from the Sun — will have advanced to 76° ahead of Mars.
"This gives us the key to the timing of the return voyage. Since the travel time is the same, it is apparent that at the moment of departure from Mars, Earth must be momentarily located 256° behind the intersection of the ellipse of return with her own orbit. That is to say, she must be at 256° minus 180° behind Mars, or 76°.
"Thus we have the following question with respect to how long the necessary waiting time on Mars will be: when the ships arrive at Mars, the Earth will be — as seen from the Sun — 76 degrees ahead of Mars, and the return cannot be undertaken until she is 76 degrees behind him. How long will it take for this condition to establish itself?
"The computation is relatively simple. On her shorter, inner orbit, Earth moves more rapidly in arc, and must cover 360 degrees minus twice 76, or 208 degrees with respect to Mars. The difference of movement in arc of the two planets is 0.987 minus 0.524 or 0.463 degrees per day. That is, Earth gains on Mars 0.463° each 24 hours. Thus 208° divided by 0.463 equals 449, the length of our waiting time in days."
"Before I finish, I want to give you some idea of the extent of the financial and other efforts, which the expedition will require. There will be manifold special research and development operations, but the main effort will consist in freighting the ships, supplies and propellants, into the satellite orbit of departure. At this time, we have only a relatively modest number of Sirius-class vessels adapted to this purpose. Each requires 5,583, almost 5,600, tons of propellants, and can transport 25 tons of payload into the orbit of Lunetta.
You've been shown that the 10 vessels destined for Mars will weigh 3,720 tons, a total of 37,200 tons of payload up to the satellite orbit of departure. That means 1,490 trips.
"The situation begins to appear somewhat less startling, however, if we consider the following factors. It is usual for a Sirius-class vessel to leave behind in Lunetta about eight tons of the reserve propellants she carries besides the regulation cargo. Furthermore, since our ellipse of departure lies in the ecliptic, ascent to it will be somewhat more economical of propellants than the trip to Lunetta, because we can utilize for the climb a greater component of the circumferential velocity of the Earth. This, we believe, will permit each shipload on the ferry trips to deposit some six additional tons of propellants in the orbit of departure. Thus we anticipate that each Si>ms-class ferry will leave there either 39 tons of propellants, or solid cargo amounting to 25 tons, plus 14 tons of residual propellants. This would reduce the number of ferry trips to about 950.
"Each ferry flight will, however, consume 5,600 tons of propellants or thereabouts — a total of 5,320,000 tons — which is the product of 950 and 5,600. It would take 443 tank steamers, each of 12,000 tons capacity, to hold this amount. This is about the equivalent of the fuel for six months in one of the theaters of World War III.
"Both the Mars vessels and the Sirius-class ferries will use highly concentrated hydrazine and nitric acid as propellants. These chemicals are produced by the suppliers of the Space Forces at an average price of about $100.00 per ton. The quantity envisaged will presumably necessitate some plant expansion. Thus the cost of the propellants for the ferry trips to the orbit of departure will be around $500 million. The same item with respect to the Mars vessels and their landing boats is almost negligible in comparison; the cost will be but three and a half million dollars, roughly.
"Just about one fourth of the entire two billion dollars will be expended in propellants for the ferry flights! We believe that the remaining three quarters will suffice for the solution of the other problems."
Spencer closed his speech abruptly. Sitting down on a chair in front of the witness box, he produced his cigar case and lit one of his villainous stogies after his usual elaborate preparations. Not a sound came from his listeners. Even the Mars Committee held its peace.
After some time, Perucci's white head rose into prominence as its owner addressed Spencer with a strong Italian accent.
"Mr. Spencer," he remarked, "please accept the gratitude of the committee from my lips. You have certainly cleared many matters in our minds. Many of us, I know, felt the same way about it as I, but you have removed many doubts and explained many hitherto moot points. Let us now proceed to a question session, for I know that not only I, but many other members of the committee have much to ask, judging from the busy pencils I saw during your address. I shall begin with one or two questions of my own.
"If I'm right, you stated that the aphelion of the elliptical path of a ship approaching Mars would be located just short of the orbit of Mars instead of right on it. This, I understand, is to prevent the ship from crashing vertically to the surface of the planet, overhauling it from astern. Rather the ship should be drawn into a curved hyperbolic path by the gravitation of Mars. Then when it approaches closest to the planet at the vertex of this hyperbola, the ship's velocity is to be slowed until it corresponds to the orbital velocity appropriate to its location. Have I understood you aright so far?"
"That's correct, Senator."
'There's something about it which I do not quite grasp. Apparently you have assumed the ellipse of interplanetary travel to result exclusively from the combined effect of the motion imparted to the ship in the form of kinetic energy and the gravitation of the Sun until such time as the ship approaches the field of gravity of Mars. But it would seem that the ensuing hyperbolic flight path is produced by Mars' gravitation alone. The orbit of Mars itself is certainly determined by the gravitation of the Sun, and so the hyperbolic flight path under discussion must, in some way, also be affected by solar gravity, even within the sphere of Martian gravity?"
"You're quite correct, sir," answered Spencer. "Perhaps I oversimplified my method of presentation on this detail to some extent, as also on other matters. In actuality, the business of entering a satellite orbit around Mars is quite a bit more involved than I have pictured it, and gravitation, both solar and Martian, must be used in the computations.
Poinoare, a French mathematician, evolved the mathematical methods he used when he solved the so-called "probleme restraint du probleme des trois corps." The same applies, furthermore, not only to the entry into a satellite orbit around Mars, but also to all four maneuvers and to unpowered interplanetary coasting, insofar as these take place not too remote from Mars or the Earth. The gravitation of our Moon adds a few complications to the mathematical aspect close to the Earth. None of these effects are quantitatively very large, nor do they affect the figures I quoted to any material extent; nonetheless, they must be taken into account in working out the navigation, both prior to and during the voyage."
"That brings up another question," said Perucci. "According to your drawing, the intersection of the ellipse of the voyage and the Martian orbit is at about 377 million kilometers from the point of departure from the Earth's orbit. Then you propose to effect the manpower of adaptation at Mars in such manner that the resulting satellite orbit shall be 1,000 kilometers distant from the surface. Should your departure data at the termination of the first thrust maneuver be even minutely in error as to velocity or direction, you might easily be many thousands or even millions of kilometers off when you approach the orbit of Mars. I can imagine that navigation will have to be kept current with extreme accuracy and that any errors will be subject to running corrections."