Celestial salad debunked (warning, math may be involved)

Factual Questions
1

For some years I’ve had a column by Marilyn vos Savant on the refrigerator about what she calls a “Stellar Salad.” It goes like this: If the sun were a pumpkin 1 ft in diameter, Mercury would be a tomato seed about 50 feet away

Venus, pea, 75 feet away

Earth, pea, 100 feet away

Mars, raisin, 175 feet away

Jupiter, apple, 550 feet away

Saturn, peach, 1025 feet away

Uranus, plum, 2050 feet away

Neptune, plum, 3225 feet away

Pluto, smaller than a strawberry seed, nearly a mile away

Recently my 8-year-old has gotten very interested in astronomy. We wrote this on the whiteboard and he started drawing it, attempting to draw it to scale. His older brother–who very nearly did not graduate from high school because of awful grades–came over to watch football, looked at the distances, and said, “that’s messed up.” (Note: I am not saying he’s not smart. Just that he never paid attention in class.)
He then proceeded to fill the whiteboard with all sorts of calculations proving the smartest woman in the world wrong.

Or so he said. I frankly do not know enough math to even follow his theories, although he seemed to know what he was talking about. His conclusion was that the celestial bodies involved would be much smaller.

All those years I’d assumed Ms. vos Savant was correct. My only quibble with it had been that she called it “Stellar Salad” when the only star involved was the sun. I would have called it “Celestial salad,” had I been the editor.

Much knowledge exists on this board. Who is right, the smartest woman in the world, or my middle son?

2

*** “I frankly do not know enough math to even follow his theories, although he seemed to know what he was talking about.”***

What? If he needed to use anything beyond fifth grade arithmetic, he was probably off base. I know this because I did this exact problem in fifth grade. First we need the hard data:
NASA Planetary Fact Sheet

The scale is specified by the sun’s radius (865,000 mi = 1 ft.) i.e divide the number of miles by 865,000 to get the distance in feet.

Earth’s orbital radius would be 93 million/865,000 = 107.5 ft, while its diameter would be 7926/865,000 = .009 ft = .11 inch

The exact figure you use for the solar radius would be a judgement call. Since it is a ball of hot gas without a clear boundary, you have to define some criterion for its edge, but I’d say the 7.5% error above is “close enough” for the purposes of demonstration. On the other hand, “pea sized” makes me think of something closer to a quarter of an inch, not a ninth of an inch, so one could argue that “pea” overstates the size of the earth by a factor of two. I’ve certainly never seen a pea that tiny!

Overall, a quick glance at the numbers you gave gives me the impression Vos Savant got the sizes of the planets wrong (jupiter, for example, comes out to be 1.23 inches in diameter, which is hardly “peach sized”), but she got the size of their orbits right.

This is hardly the first time I’ve seen her be wrong, on a simple fact. In fact, I’ve long felt that she failed to learn a lesson that I learned well before fifth grade: “no matter how brilliant you are, you can be wrong - so double check everything” (I’ve often wondered if she simply has bad editors or is just a raging shrew if corrected)

I can imagine several reasons for this error in planetary sizes:

  1. she had figures for planetary diameters, but thought they were planetary data (factor of 2 error)
  2. she was using figures in feet, but thought they were in meters (factor of 3.3 error
  3. I am tired, and shouldn’t be doing math in my head at 3am

Explanations #1 and #2 nicely bracket the crude analogies she gave. #3 means I need to relearn my grade school lesson

3

Ok, if we change from millions of kilometers directly to feet, and inches, the solar system is about like this:

Mercury: @ 58 feet is .0588 inches A pretty small seed
Venus: @ 110 feet is .1452 inches A puny dried pea
Earth @ 150 feet is .1524 inches Still a puny pea
Mars @ 230 feet is .0816 inches A very small raisin
Jupiter @ 780 feet is 1.68 inches A crabapple, perhaps
Saturn @ 1400 feet is 1.44 inches Maybe an apricot, not a peach
Uranus @ 2900 feet is .612 inches A prune at best
Neptune @ 4500 feet is .588 inches A grape
Pluto @ 5900 feet is .027 inches Barely visible

If she has been quoted accurately, Miss Vos Savant seems to be in error.

Tris

4

There is a website called “Marilyn is wrong” with a list of all the known mistakes in Marilyn vos Savant’s columns. Here’s the webpage on the column that you’re talking about:

http://www.wiskit.com/marilyn/planets.html

To be honest, I think that it would be more useful for your 8-year-old son (and for you too) to learn to do the math yourselves rather than rely on Marilyn vos Savant’s calculations (or on our calculations). I think you should be slightly suspicious of anyone who calls themself “the smartest woman [or man] in the world.” If Cecil ever starts making errors in simple arithmetic like this, believe me, we will be complaining about it on the SDMB.

5

The rule of thumb often quoted in books, IIRC, is about 100 Earths could fit across the diameter of Jupiter, and 100 Jupiters could fit across the diameter of the Sun. I’ll see if I can trace this down with a reference citing to please the crowd.

“You think this crowd is ugly, you should see the dancing girls!” (Rolph, the Dog) - Jinx

6

Jinx writes:

> The rule of thumb often quoted in books, IIRC, is about 100
> Earths could fit across the diameter of Jupiter, and 100 Jupiters
> could fit across the diameter of the Sun.

Sorry, but no. The sun is 865,400 miles across, the earth is 7926 miles across, and Jupiter is 88,846 miles across. 865,400/88,846 = ~10, while 88,846/7926 = ~11. So approximately 11 Earths would fit across Jupiter and approximately 10 Jupiters would fit across the sun.

7

Which means that Jupiter is (roughly) 100 times as big in cross section as Earth, and similarly it would take roughly 100 Jupiter cross sections to cover one sun cross section.

So, the rule of thumb has been corrupted, but there’s a reasonable original base.

8

Thanks for the link, and you are right, of course, that we should teach the kid not to blindly accept the views of so-called experts.