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Post by Lensman on Jul 25, 2006 22:28:51 GMT
Was it in Heinlein's Rocketship Galileo where it's pointed out that "speed" in interplanetary flight is a confusing term? Speed is always relative. When we talk about a car traveling at so many miles-per-hour or kilometers-per-hour, this speed is relative to the ground, which is considered to be unmoving, altho the Earth itself is rotating and traveling around the sun at a fair clip, not to mention the fact that the sun is orbiting the center of the galaxy at a fair clip itself... and also bobbing up and down relative to the plane of our galaxy. If you take the distance traveled, and therefore the speed, as being relative to the starting point (on Mars), then the numbers-- both distance and speed-- do work. When you consider the speed and distance as relative to, for example, the Earth or the Sun, it does-- as you say-- appear the spacecraft is travelling much farther. If I may correct one error, however, the Martian cylinders (or any vehicle on a ballistic trajectory between Mars and Earth) would travel much, much farther than 40 million miles if that is the distance between the planets at the time of launch. Again, it's the distance and position between the planets at the time of landing which is important when calculating interplanetary ballistics, not the distance at time of launch. Since the landing should coincide with opposition-- allowing the spacecraft to travel the minimum distance to get there-- it's appropriate to quote the opposition distance. From the point of view of the *spacecraft* that's how far it traveled. How fast the Earth is moving in its orbit is irrelevant to the spacecraft-- so long as the Earth arrives at the rendezvous at the appointed time.
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Post by Topaz on Jul 26, 2006 5:29:05 GMT
... Again, it's the distance and position between the planets at the time of landing which is important when calculating interplanetary ballistics, not the distance at time of launch. Since the landing should coincide with opposition-- allowing the spacecraft to travel the minimum distance to get there-- it's appropriate to quote the opposition distance. From the point of view of the *spacecraft* that's how far it traveled. How fast the Earth is moving in its orbit is irrelevant to the spacecraft-- so long as the Earth arrives at the rendezvous at the appointed time. Hmmm. Either we're talking about the same thing in different ways, or I'm not properly getting my point across. Since a picture is worth a thousand words... That's the trajectory for the NASA's Mars Reconaissance Orbiter, recently arrived at the red planet. I pulled this from the NASA JPL website. You'll note the relative positions of the two planets at launch and arrival, and the black line of the vehicle flight path. It's that flight path that is the total distance traversed over the flight time, and that distance, divided by the flight velocity, that determines the flight time from launch to landing. (Actually it's a calculus thing since the velocity isn't constant, but I'm sure you get the point.) The straight-line distance between the planets underestimates that flight time by a factor of at least four in this case, possibly more. The reference frame is, as I believe is common in celestial navigation, the sun, and the positions of both launch and target planets change during the flight time. This is a flight path from Earth to Mars, of course, but the reverse flight would essentially be the mirror image of the diagram above, and the same principals apply. Am I making this more clear? If you use either the launch or landing planet as the reference frame, and plot the flight distance as a direct line between the two (as I believe you're saying), then that is, indeed, a much 'shorter distance', but the 'apparent' flight velocity in that case is much lower, since the launch and landing planets are themselves moving at a pretty good clip and their velocities would need to be accounted for in the system. The total flight time would be the same regardless of the reference frame, but the apparent velocity would be very, very different.
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Post by Lensman on Jul 26, 2006 9:07:21 GMT
I'm not sure what point you're trying to make. From the looks of the diagram, that transfer orbit does *not* take advantage of the minimum distance for a transit from Earth to Mars. At any rate, I'll point out that the NASA transfer orbit in your diagram requires months of travel. The evidence in WotW indicates the Martians traveled to Earth *much* more quickly. In fact, the Narrator notes the distance at the time the second cylinder was launched was "Forty millions of miles from us--more than forty millions of miles of void." So it's clear Mars was quite close to the minimum distance at that time. If anything, this indicates an even faster transit than Charles and I are advocating. And yes, if you pick the sun as your supposed "stationary" viewpoint instead of Mars or the spacecraft, then you will measure the spacecraft's velocity as much higher. But that doesn't alter the fact that all the evidence in the novel indicates a *much* shorter transit than NASA uses for its probes. "A flight to Mars in two weeks would almost follow a straight line, and would definitely not resemble a Hohmann ellipse..." --http://www.phy6.org/stargaze/StarFAQ10.htm#q168 This is a flight path from Earth to Mars, of course, but the reverse flight would essentially be the mirror image of the diagram above, and the same principals apply. Well yes and no. Assuming they are both Hohmann ellipses-- that is, minimum-energy transfer orbits-- they would both be elongated, curved paths; sections of ellipses. But since the orbital speed of Earth and Mars are different, the shape of the transfer orbit and the transit time should be noticably different.
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Post by Topaz on Jul 27, 2006 6:27:39 GMT
I'm not sure what point you're trying to make. ... Eh, we're falling into the same old argument again. ;D "A flight to Mars in two weeks would almost follow a straight line, and would definitely not resemble a Hohmann ellipse..." --http://www.phy6.org/stargaze/StarFAQ10.htm#q168 Ah, I see where you're going with that. We're approaching this from different directions. You're taking an inferred flight duration from the narrative and finding the required orbit to suit that, regardless of the requirements that imposes on the design and construction of the launch system. I'm coming at it from the same direction that one of the NASA guys would do in designing a mission: I need to get 'there' in a reasonably short amount of time, but I don't have infinite resources to pour into a launch system. What 'costs' more: a life-support and radiation-shielding schema that is sufficient for a somewhat longer trip, or a vastly larger launch system that could accomplish the flight in a couple of weeks? It drives 'my' design closer to the classic Hohmann case, and even the website you cite indicates it's desirable to find a flight path "...with the smallest initial velocity and initial thrust." Either approach is equally valid, in a sense, and the final choice depends on the resources available to the Martians and the ability of their economic and political system to assign those resources to the project at the expense of other needs. Off the top of my head, it's not explicitly stated in the book what the actual flight time was. As you've mentioned, he does mention a rough velocity (which I suspect he pulled out of the air completely), but I'd be curious to see what kind of actual orbit such a velocity would produce, and what flight time would result. I think it's probably a conceptual error to assume a particular flight path and then derive the flight time by dividing the resulting distance by an arbitrary velocity. I would say that the velocity determines the flight path, and the resulting distance determines the flight duration. In any event, I'm skeptical that the speed required to do the flight in a couple of weeks could be developed with any gun that falls within the realm of engineering possibility. The material strengths and/or thicknesses involved in the barrel would be... well, "staggering" comes to mind!
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Post by Lensman on Aug 6, 2006 5:40:17 GMT
Obviously it depends on what you consider of primary importance when trying to analyze how the Martians did it. I assume that if the author wrote something happened, then it happened. Admittedly sometimes this can't be justified in scientific terms-- such as Verne's space cannon, for which it's said it would have both smashed the passengers to chunky salsa* and failed to send the capsule higher than the surrounding trees.
*I don't care if that imagery is anachronistic for Victorian England or the USA. I like the imagery!
Nonetheless, that's what Verne wrote. And I'm sure you've read my article on fixing the date of the Martian Invasion, which includes an analysis of the amount of time between launch and landing. If you choose to disgregard the evidence presented, you're of course free to do so, but I think it's quite clear Wells intended to suggest a rapid passage.
Yes I'm aware it would be a tremendously greater challenge for the Martains to have traveled here in a short period of 2-6 weeks, instead of the 6-months-to-a-year NASA plans. But remember, the Martians are *not* us, and do *not* use the same approach to problems we do. The fact they don't use the wheel is an indication they think very differently. So while we would emphasize the lowest energy method of travel, it appears for the Martians the most important factor was travel time.
Why? Well an obvious answer is that they did not know how to recycle air, and had to complete the journey with just the air in their cylinders. Sure they could carry extra oxygen, but without CO2 scrubbers, they still would have had a very limited amount of time.
Of course that's pure speculation. We don't know *why* the Martians were willing to expend the energy to get here very quickly, or why they would trouble to build the space gun and capsules strongly enuff to do so. But unless you're interpreting the text very differently than I am, you can't deny that the Martians *did* do those things.
And actually, if you want to use modern science, we've discovered astronauts shouldn't be exposed to the radiation from that long a journey. Plus we know from experience that months spent in space leads to bone loss, loss of muscle tone, and other physical problems. If you're a Martian, do you *really* want to wind up on a planet with 250% of the gravity you're used to in an even weaker and more fragile condition than normal?
Come to think of it-- if you want to use modern science and assume the Martians were that smart, there are *excellent* reasons the Martians would have seen a very short passage as an absolute requirement!
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