Heinlein's Calculations for Trip to Pluto in Expanded Universe Volume 2

[feralreason]

I'm re-reading Heinlein's Expanded Universe (imho one of the best books to learn something about Heinlein's thinking and method).

Anyway - on p.25 of Volume 2 he starts some calculations to demonstrate the value of "constant boost" spaceship engines. The first calculation is Earth to Mars and back again. He finishes this on page 27 and starts a calculation to Pluto. But, before finishing, indicates: "Please turn to page 94 (Volume II) and see why I wanted our trip to Pluto to be a distance of 31.6 A.U." I turned to page 94 - couldn't find it. (I'm using an E-book checked out from a library - pages could be numbered differently.) At any rate - if anyone knows where I might find the conclusion to this (by page number or just indicating what article, etc. it shows up in... or after) , I would really appreciate it! (As soon as there is a constant-boost service to Pluto, I'll send you a postcard )



Thanks much!

 

[Orcadian]

I'm re-reading Heinlein's Expanded Universe (imho one of the best books to learn something about Heinlein's thinking and method).
... "Please turn to page 94 (Volume II) and see why I wanted our trip to Pluto to be a distance of 31.6 A.U." I turned to page 94 - couldn't find it .... At any rate - if anyone knows where I might find the conclusion to this (by page number or just indicating what article, etc. it shows up in... or after) , I would really appreciate it!

A search for "Heinlein's Explanded Universe" at the Internet Archive returns these options: https://archive dot org/search?query=Heinlein's+Expanded+Universe&sin=TXT Not sure if any of those is what you're hunting for? (N.B. You'll need to replace the " dot " with a period. I had to change that to stop the editor replacing my URL with an infoblurb.)

 

[tinkerdan]

There is supposed to be a chapter called Answers on that page.
It has all the answers to the problems presented in the chapter called Where to or 1950 Where to
In a nutshell:
He is using historical ocean route times to compare to those times; in the case of the Pluto round trip problem the time it takes to travel 31.6 AU would be 2 years and 9 months which is the time it took for a commercial voyage for China Clipper sailing out of Boston(19th century?)

I have the HB single volume copy of this and there is difference in page numbers.
However I did check the 2 volume e-book amazon offers and the TOC does list a chapter called Answers.

 

[feralreason]

A search for "Heinlein's Explanded Universe" at the Internet Archive returns these options: https://archive dot org/search?query=Heinlein's+Expanded+Universe&sin=TXT Not sure if any of those is what you're hunting for? (N.B. You'll need to replace the " dot " with a period. I had to change that to stop the editor replacing my URL with an infoblurb.)

Thanx Orcadian, I finally found it. The E-book's numbering sys

There is supposed to be a chapter called Answers on that page.
It has all the answers to the problems presented in the chapter called Where to or 1950 Where to
In a nutshell:
He is using historical ocean route times to compare to those times; in the case of the Pluto round trip problem the time it takes to travel 31.6 AU would be 2 years and 9 months which is the time it took for a commercial voyage for China Clipper sailing out of Boston(19th century?)

I have the HB single volume copy of this and there is difference in page numbers.
However I did check the 2 volume e-book amazon offers and the TOC does list a chapter called Answers.

tem is different than the original. Just had to leaf through all the pages. But I appreciate your help!

 

[feralreason]

Dan, you got it. Seems like I remember Heinlein documenting something like this in "Have Spacesuit will Travel" also. I'll have to see if I can dig up a copy of that. Thx for the response!

 

[Ravensquawk]

Got me interested!

I don't know how much this will help with all the "Borrow Unavailable" going on on Archive, but maybe they'll come out of all their legal hassles victorious.

Nearly all Archive books I've read are either right on with the page number sync, or about two pages off. (Almost always then page 94 in the online will get you page 92 in the original.)

How I search: Archive expanded universe heinlein

It shows up in an Overdrive search, but that may well be what you're reading already.

Can you do a text search in it? Of course, if you don't know what the answer on page 94 says, you might just have to do a search for "31.6 A.U.".

Worldcat shows where you can borrow library paper copies.

Back when books were affordable, I used to keep a list of the Heinlein books I'd read (22, lots of juveniles because I was one! until I Will Fear No Evil and Time Enough For Love, also a few decades back),
so that when I went to the local Sav-On (all the way to the back, on the left) I wouldn't buy a book I'd already read.
It might help you more if I'd actually read this one, but these are the steps I do to search for something that (1) is affordable (2) offers a way to read something that is no longer published and the few around get more expensive for collectors; (3) provides reading online for those who already have 5 heavy boxes of books in a small apartment. (Waves to all the lucky people with houses and book shelves.); (4) has variable text sizes and alternates; (5) makes books available to people who have to wait for a payday even to make a small donation (waves) or live in places and entire countries where bookstores, libraries or money are less available.

I know you've got an e-book already, but it might be worth trying another and searching for the text.
You might try Ocean of PDF. (Plus i can too and finally read it, ha.)

And you could even write home with the answer!

Although I'm guessing it has to be as close as it gets, orbiting on the same "side" of the sun as us.
From NASA's site:
"Pluto's orbit around the Sun is unusual compared to the planets: it's both elliptical and tilted. Pluto's 248-year-long, oval-shaped orbit can take it as far as 49.3 astronomical units (AU) from the Sun, and as close as 30 AU."

Before anyone else gets all P.O.'d or sad at Pluto being "demoted" from a planet (I did), you'd enjoy reading "How I Killed Pluto and Why It Had It Coming" by Mike Brown. (Links are leading to the wrong things, so no link. But it's on Wikipedia.)
It's conversational and clearly defines the actions and characteristics of a planet.

But get back to us on Heinlein's reason. (I bet even Heinlein couldn't work his weird personality quirks into an orbital calculation.)

 

[feralreason]

Got me interested!

I don't know how much this will help with all the "Borrow Unavailable" going on on Archive, but maybe they'll come out of all their legal hassles victorious.

Nearly all Archive books I've read are either right on with the page number sync, or about two pages off. (Almost always then page 94 in the online will get you page 92 in the original.)

How I search: Archive expanded universe heinlein

It shows up in an Overdrive search, but that may well be what you're reading already.

Can you do a text search in it? Of course, if you don't know what the answer on page 94 says, you might just have to do a search for "31.6 A.U.".

Worldcat shows where you can borrow library paper copies.

Back when books were affordable, I used to keep a list of the Heinlein books I'd read (22, lots of juveniles because I was one! until I Will Fear No Evil and Time Enough For Love, also a few decades back),
so that when I went to the local Sav-On (all the way to the back, on the left) I wouldn't buy a book I'd already read.
It might help you more if I'd actually read this one, but these are the steps I do to search for something that (1) is affordable (2) offers a way to read something that is no longer published and the few around get more expensive for collectors; (3) provides reading online for those who already have 5 heavy boxes of books in a small apartment. (Waves to all the lucky people with houses and book shelves.); (4) has variable text sizes and alternates; (5) makes books available to people who have to wait for a payday even to make a small donation (waves) or live in places and entire countries where bookstores, libraries or money are less available.

I know you've got an e-book already, but it might be worth trying another and searching for the text.
You might try Ocean of PDF. (Plus i can too and finally read it, ha.)

And you could even write home with the answer!

Although I'm guessing it has to be as close as it gets, orbiting on the same "side" of the sun as us.
From NASA's site:
"Pluto's orbit around the Sun is unusual compared to the planets: it's both elliptical and tilted. Pluto's 248-year-long, oval-shaped orbit can take it as far as 49.3 astronomical units (AU) from the Sun, and as close as 30 AU."

Before anyone else gets all P.O.'d or sad at Pluto being "demoted" from a planet (I did), you'd enjoy reading "How I Killed Pluto and Why It Had It Coming" by Mike Brown. (Links are leading to the wrong things, so no link. But it's on Wikipedia.)
It's conversational and clearly defines the actions and characteristics of a planet.

But get back to us on Heinlein's reason. (I bet even Heinlein couldn't work his weird personality quirks into an orbital calculation.)

You suggest some interesting sources. But I already solved this one - brute force, going page by page, probably what I should have done in the first place As to Heinlein's calculations -- he had a secret weapon, Virginia.

 

[Ravensquawk]

I found a Heinlein Wall-O'Text. Page numbers may have been edited for different versions.
But you're right: brute force, technology limitations, mass, energy, and probably low enough G to keep from being pulped, lifespan, relative orbital positions.....

THE ANSWERS

(to Problems on Pages 334-338)

N.B.: All trips are Earth parking orbit to Earth parking orbit without

stopping at the target planet (Mars or Pluto). I assume that Hot Pilot Tom Corbett

will handle his gravity-well maneuvers at Mars and at Pluto so as not to waste

mass-energy-but that's his problem. Now about that assumption of "flat space" only

slightly uphill: The Sun has a fantastically deep gravity well; its "surface"

gravity is 28 times as great as ours and its escape speed is 55 + times as great-but

at the distance of Earth's orbit that grasp has attenuated to about one thousandth

of a gee, and at Pluto at 31.6 A.U. it has dropped off to a gnat's whisker, one

millionth of gee.

(No wonder it takes 21/2 centuries to swing around the Sun. By the way, some

astronomers seem positively gleeful that today Pluto is not the planet farthest from

the Sun. The facts: Pluto spends nine-tenths of its time outside Neptune's orbit,

and it averages being 875,000,000 miles farther out than Neptune-and at maximum is

nearly 2 billion miles beyond Neptune's orbit (1.79 x lO~ miles)-friends, that's

more than the

ROUND TRIP BOOST

COMPARISON OF ELAPSED TIME

Earth-Mars-Earth - Earth- Pluto-Earth

@1 gee

4.59 days vs. 4.59 weeks

~w'Iio gee

14.5 days vs. 14.5 weeks

~~/too gee

45.9 days vs. 45.9 weeks

~1/tO0O gee

145 days vs. 145 weeks

distance from here to Uranus, nearly four times as far as from here to Jupiter. When

Page 155

Heinlein, Robert A - Expanded Universe.txt

Pluto is out there-l 865 or 2114 A.D.-it takes light 6 hours and 50 minutes to reach

it. Pluto-the Winnuh and still Champeen! Sour grapes is just as common among

astronomers as it is in school yards.)

-and the rabbit is out of the hat. You will have noticed that the elapsed-time

figures are exactly the same in both columns, but in days for Mars, weeks for

Pluto-i.e., with constant-boost ships of any sort Pluto is only 7 times as far away

for these conditions as is Mars even though in miles Pluto is about 50 times as far

away.

If you placed Pluto at its aphelion (stay alive another century and a

quarter-quite possible), at one gee the Pluto round trip would take 5.72 weeks, at

1/to gee 18.1 weeks, at 1/too gee 57.2 weeks-and at 'Iiooo gee 181 weeks, or 3 yrs &

25 wks.

I have added on the two illustrations at 'Iwoo of one gravity boost because

today (late 1979 as I write) we do not as yet know how to build constant-boost ships

for long trips at 1 gee, 1/10 gee, or even 1/too gee; Newton's Third Law of Motion

(from which may be derived all the laws of rocketry) has us (temporarily) stumped.

But only temporarily. There is E = mc2, too, and there are several possible ways of

"living off the country" like a foraging army for necessary reaction mass. Be

patient; this is all very new. Most of you who read this

will live to see constant-boost ships of 1/10 gee or better-and will be able to

afford vacations in space- soon, soon! I probably won't live to see it, but you

will. (No complaints, Sergeant-I was born in the horse & buggy age; I have lived to

see men walk on the Moon and to see live pictures from the soil of Mars. I've had my

share!)

But if you are willing to settle today for a constant boost on the close

order of magnitude of 1/1000 gee, we can start the project later this afternoon, as

there are several known ways of building constant-boost jobs with that tiny

acceleration-even light-sail ships.

I prefer to talk about light-sail ships (or, rather, ships that sail in the

"Solar wind") because those last illustrations I added (l/t000 gee) show that we

have the entire Solar System available to us right now; it is not necessary to wait

for the year 2000 and new breakthroughs.

Ten weeks to Mars . . . a round trip to Pluto at 31.6 A.U. in 2 years and 9

months. . . or a round trip to Pluto's aphelion, the most remote spot we know of in

the Solar System (other than the winter home of the comets).

Ten weeks-it took the Pilgrims in the Mayflower nine weeks and three days to

cross the Atlantic.

Two years and nine months-that was a normal commercial voyage for a China

clipper sailing out of Boston in the last century . . . and the canny Yankee

merchants got rich on it.

Three years and twenty-five weeks is excessive for the China trade in the

19th century.. . but no one will ever take that long trip to Pluto because Pluto

does not reach aphelion until 2113 and by then we'll have ships that can get out

there (constant boost with turnover near midpoint) in three weeks.

Please note that England, Holland, Spain, and Portugal all created worldwide

empires with ships that took as long to get anywhere and back as would a Vtooo-gee

spaceship. On the high seas or in space it is

not distance that counts but time. The magnificent accomplishments of our astronauts

up to now were made in free fall and are therefore analogous to floating down the

Mississippi on a raft. But even the tiniest constant boost turns sailing the Solar

System into a money-making commercial venture.

Now return to page 338.

"Tomorrow we again embark

upon the boundless sea."

-Horace, Odes, I, i.

 

[feralreason]

But get back to us on Heinlein's reason. (I bet even Heinlein couldn't work his weird personality quirks into an orbital calculation.)

Ah - missed the request for the "reason". Heinlein was trying to demonstrate the importance of continuous boost engines (Solar, fusion, fission, whatever.) So, whereas a classic chemical-based engine has to calculate a route based on orbits with scheduled "burns", continuous boost is... well... continuous. He looks at 1/100th of a 'g', 1/10th gee, and 1 gee and compares how much time it takes you to reach your destination. At 1/100th of a g acceleration, the round trip to Mars (parking orbit to parking orbit) could be made in about 145 days -- which sounds pretty reasonable -- given that fusion drives are still a long way off. But regarding calculations -- elsewhere in the book, RAH talks about Virginia and him working through more complex calculations -- seperately on rolls of butcher paper, so that she could check his math. Those were probably calculations for spacecraft that had to execute multiple burns -- much more complicated. I'm not there yet - no celestial mechanics in my background My guess is that Heinlein, with his Aeronautical Engineering background, had pretty sound physics and math capabilities. And I imagine his engineering was pretty well shielded from the 'quirkiness' of his politics & his early 20th-century gender-role biases.

 

[JimC]

Wasn't Robert's background in Mechanical Engineering rather than Aeronautical?

 

[feralreason]

In a way, aeronautical engineering evolved from mechanical engineering, so it's a natural question. Kitty Hawk happened in 1903 and Heinlein's BS degree, in Naval Engineering, was presented in 1929, 26 years later. I think of this as being similar to the transition between math and computer science. The Eniac was completed in 1945 but 25 years later there were still very few Computer Science degrees (although there were many courses.) Heinlein is listed as an Aeronautical Engineer (see Robert A. Heinlein - Wikipedia). Also see Volume I of The Authorized Biography. Heinlein wanted to be a pilot -- but failed exams on depth perception and visual acuity. A nice quote from p. 85: "The Navy gained an aeronautical engineer at a time when aviation was in its infancy -- and science fiction eventually gained a number of highly evocative stories based on that unfulfilled longing." There is also some good background in the two-volume "Heinlein's Expanded Universe" (although I don't recall which volume it was in).