Pedantry Alert
Jul. 20th, 2015 09:35 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowI'm reading Verne's classic From the Earth to the Moon / Around the Moon. Verne is the prototypical hard-science SF writer (and oh, my, is this text larded with technical details), but I just hit a major mathematical blunder.
The astronauts have passed into the shadow of the moon, and the excitable Ardan is asking what their fate is to be. His (more technically educated) companions respond by discussing orbits (which, of course, Ardan does not understand).
But what about Galileo, you may ask? Sadly, the acceleration due to gravity, even close to the surface of the Earth, is not quite constant, and the parabolas his equations predict turn out, in reality, to be arcs of extremely narrow ellipses.
And, of course, all this ignores the fact that the crew is involved in a three-body problem, so Keplerian conics are not in the picture. (Actually, it's at least a four-body problem, since the vessel was diverted slightly by a close encounter with a hypothetical second satellite of Earth.)
Oh, well. Only Hal Clement ever actually got things right.
The astronauts have passed into the shadow of the moon, and the excitable Ardan is asking what their fate is to be. His (more technically educated) companions respond by discussing orbits (which, of course, Ardan does not understand).
"Just so", replied Barbicane. "With a certain speed it will assume the parabola, and with a greater the hyperbola."Um, no. There are three options, not two; Barbicane has omitted the ellipse. But, beyond that, there are only two genuine possibilities. Parabolas do not happen. A parabola is a conic whose eccentricity is exactly 1; an ellipse has eccentricity less than 1, a hyperbola, greater. Pick a positive real number at random, using any continuous distribution you like: the probability of getting exactly 1 is literally 0.
But what about Galileo, you may ask? Sadly, the acceleration due to gravity, even close to the surface of the Earth, is not quite constant, and the parabolas his equations predict turn out, in reality, to be arcs of extremely narrow ellipses.
And, of course, all this ignores the fact that the crew is involved in a three-body problem, so Keplerian conics are not in the picture. (Actually, it's at least a four-body problem, since the vessel was diverted slightly by a close encounter with a hypothetical second satellite of Earth.)
Oh, well. Only Hal Clement ever actually got things right.
no subject
Date: 2015-07-21 08:08 pm (UTC)Comments like this always make me glad I don't try to write hard SF [wry g].