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Jenab
#36
Jul3-04, 08:27 PM
Sci Advisor
P: 115
I regard Robert A. Heinlein as one of the greatest science-fiction writers ever. His science was as meticulous as his stories were fun to read. Someone who didn't have a scientific background might think he was only "hand-waving" at number-crunching that he had not actually done. On the contrary; he did it. He just didn't flaunt it.

A good example of his low-profile diligence is the celestial mechanics that forms part of the story of his novel The Rolling Stones. In order to get the full picture of the world behind this story, one would also need to read two other books, namely The Moon is a Harsh Mistress and The Cat Who Walked Through Walls.

Here's some historical background. Hazel Meade Stone was born on 25 Dec 2063, and, as is chronicled in The Moon is a Harsh Mistress she fought the evil Terran military goons with great distinction during the Earth-Moon War of 2076. She later married Slim Lemke. Their children were Roger (b. 22 Sep 2078, an early first child) and Ingrid (born later).

Roger Stone (family name taken from his mother?) married Edith (maiden name unknown) while he was mayor of Luna City (2122-2130). Their children were Meade (b. 2130), the twins Castor and Pullox (b. 2133), and Lowell (b. 2144).

As The Rolling Stones opens, it is early to mid-2148. Castor and Pullox are both 15, however very well-educated by our standards today, especially in mathematics. The twins plan to buy a spaceship and fly off to the asteroid belt, there to make a fortune mining high-grade metal ore. But their father gets wind of the plan and scotches it. The idea of an extended family outing in a larger, more expensive space yacht takes root, however, and before long Roger, assisted by Hazel (who knows how to arm-twist spaceship merchants), has bought a spaceship and is calling himself 'Captain.'

After some harranguing, the ship is named "The Rolling Stone," and Mars is selected as the first destination because the launch window for the minimum energy trajectory from Earth to Mars will soon be open.

In fact, that's quite correct. It opened (in the real world "will open") for departure from Earth around September 2148.

There is a valid transfer orbit, an ellipse with perihelion at departure (6 September 2148), from Earth to Mars, with a transit time of 259 days, with arrival occuring on 23 May 2149. The heliocentric longitude of Earth at departure will be 341.69 degrees; that of Mars at departure will be 23.76 degrees; and that of Mars at arrival will be 152.08 degrees.

Orbital elements of Earth.
a 1.00000011
e 0.01671022
i 0 (zero)
L 0 (zero)
w 102.94719 deg
T JD 2453009.3

Orbital elements of Mars.
a 1.523688
e 0.093405
i 1.8497 deg
L 47.5574 deg
w 286.5016 deg
T JD 2452873.0

Orbital elements of the transfer orbit.
a 1.3411728 AU
e 0.248072
i 10.608 deg
L 341.687 deg
w 0 (zero) deg

The magnitude of the departure delta-vee is 6.8277 km/sec.*
The magnitude of the arrival delta-vee is 4.2570 km/sec.

*Does not take into account the difference between preburn orbital speed and the local escape speed relative to Earth. The "departure" is really the thrust applied near Earth after having dropped toward perigee from the moon, so probably another half kilometer per second (or thereabout) may be needed.

Jerry Abbott