Scaling Earth to a Marble

One of my toys is a blue marble with green continents painted on it. It not perfectly round, but a few random measurements with a 10-micrometer-repeatable dial caliper average to 21.85 millimeters diameter. What if we scaled the solar system, planets and distances, so that the Earth was the size of that marble?

We can use that mental image to imagine how much sunlight hits the planets. Looking from the position of the Sun, how much of the sky is blocked by planets? Scaled to a 2.2cm Earth-sized marble, the distance from the igloo-sized Sun to the marble-sized Earth would be more than a kilometer, not visible to the naked eye. Jupiter, a bit smaller than a volleyball, would also be "invisible" at 5.3 kilometer distance. To a first approximation, the solar system is empty.

Here's a text snapshot of a crude spreadsheet that I created:

Earth-Marble Scaled Solar System

Marble Scaled

Radius

Distance

sun fraction

Diameter

Distance

km

km

AU

Scaled m

Scaled m

Sun

695700

2.386

0

Mercury

2440

5.790E+07

0.39

4.440E-10

10.7%

0.008

397

Venus

6052

1.062E+08

0.71

8.119E-10

19.5%

0.021

728

Earth

6371

1.496E+08

1.00

4.534E-10

10.9%

0.02185

1026

Mars

3386

2.279E+08

1.52

5.519E-11

1.3%

0.012

1563

Jupiter

69173

7.786E+08

5.20

1.973E-09

47.4%

0.237

5341

Saturn

57316

1.434E+09

9.58

3.997E-10

9.6%

0.197

9833

Uranus

25266

2.873E+09

19.20

1.934E-11

0.5%

0.087

19703

Neptune

24552

4.495E+09

30.05

7.458E-12

0.2%

0.084

30833

total

4.164E-09

100.0%

Data from https://www.jpl.nasa.gov/edu/pdfs/scaless_reference.pdf (equatorial, not polar radius) and other sources

How does the above compare to the images on the pages of a book?

Lets measure two books - the Cokesbury Bible I was given at age 11, and Christopher Mason's fascinating "The Next 500 Years". In both, a printed period is about 0.35 millimeters across, about 0.1 square millimeters, crudely estimated with the dial micrometer and a magnifier. The Bible has 1164 pages (both sides and endpapers) measuring 126 millimeters by 177 millimeters, or 26 million square millimeters of page surface. Mason's book has 300 pages, 150 millimeters by 227 millimeters, a mere 10 million square millimeters of page surface (though with more verifiable references).

A single period is 1e-8 of all the page surface of Mason, and 3.8e-9 of the page surface of the Cokesbury Bible.

Here's the box score:

Period fraction of the Cokesbury Bible

3.8e-9

Solar system planetary sunlight intercept

4.2e-9

Earth sunlight intercept

4.6e-10

Period fraction of "The Next 500 Years"

10e-9

Mason's "period fraction" would diminish markedly if we included his thesis and his MANY papers. Perhaps he can assign a grad student to count, and measure, and average the periods in each document to fractional-percent accuracy.

So what's the point?

The solar system is an empty book, a star radiating effectively all its light into an empty universe. We can talk about sending fragile humans across the galaxy to find more places to park their fragile meat, or we can invent ways to embed intelligence into a static shell around the Sun, increasing intelligence productivity by factors approaching billions.

If we make that shell distant and cold, say at 50 AU with a corresponding black body emission temperature around 60 Kelvin, we can store and manipulate information bits with 20% of the energy of a bit stored in a 300 Kelvin brain. A brain cell consumes a lot of energy for self-repair, as will a memory element in a bath of cosmic rays, but the rate of chemical decay at 60 Kelvin is practically zero.

I have no idea how that will be done, but I expect intelligent beings will figure it out in less than a millenium; far more quickly than we can travel to AND STOP AT a different solar system.

The infrared emitted by that hypothetical 60K shell would be visible as a multipixel disk 400 parsecs away from the Webb Space Telescope. If we detect candidates for such disks with Webb, that will be a strong incentive to build a much larger telescope, collect more data, and build more accurate models. With that data, we might reverse-engineer those hypothetical shells, and evolve into our own shell in less than 500 years.

EarthMarble (last edited 2022-09-24 04:23:25 by KeithLofstrom)