A 1:10 trillion scale model of the Solar System (and beyond)

It is for me - maybe it's Facebook's clever methods for deciding who can see what.

Here's the link taken directly from a window showing the post:

https://www.facebook.com/therealjoshjordan/posts/88800689565...

If you can't link from that, then something is weird.

Here is the text:

Here I describe a 1:10 billion scale model of the solar system, with the Sun centered the middle of the house I grew up in. The solar system is exactly 10 billion times larger than this model. And since mass scales as the cube of length, and every object in the solar system has a mass of exactly 10^30 times the mass of its counterpart in the model. Let's walk through our solar system, imagining that the planets are aligned with my driveway. We'll start in the living room.

1. THE INNER SOLAR SYSTEM

In the very center of the octagon-shaped house -- built by my parents with hand tools -- is the Sun. The size of a large melon (14 cm), it hovers in the middle of the room, emitting light and heat. Our model Sun weighs about 2 kg.

Mercury, the size of the ball of a very fine (550 µm) ballpoint pen, is circling the inside of the living room slowly at a distance of 6 m from the Sun, making a complete circuit once every 88 days. It weighs just 330 µg.

Just as we step outside the house, 11 m from the Sun, we find Venus, a tiny ball about the size of a lower-case 'o' (1.2 mm) weighing 5 mg.

A few steps further, 15 meters from the Sun, we cross the orbit of Earth, a 1.3 mm ball weighing 6 mg, which circles the octagon once a year. It takes 500 seconds for the light from the Sun to reach the Earth, so the speed of light in our model is 30 mm/s. The Moon is a 70 µg ball about the size of a period (300 µm), just 40 mm away from Earth.

As we reach the inner edge of Frisbee Field, 23 meters from the house, we cross the orbit of Mars. Measuring 640 µg at 700 µm in diameter, Mars is the ball of a ballpoint pen just slightly less fine than that of Mercury.

We pass through Frisbee Field, which itself corresponds to the the main asteroid belt which lies between Mars and Jupiter.

2. THE OUTER SOLAR SYSTEM

As we come to the outer edge of Frisbee field, 80 meters from the house, we cross the orbit of Jupiter, a marble-sized object (14 mm) which weighs about 2 g.

A little further down the road, 140 m from the house, we look down and see the tree fort code named Top Secret which crosses the orbit of Saturn. Weighing 600 mg and measuring 12 mm in diameter, Saturn is about the size and weight of a sugar cube, and it passes by this spy headquarters once every 29 years.

After we cross the bridge, approximately 300 m from the house, we pass the abandoned 1950s-era Ford truck we nicknamed Sadie and with it, the orbit of Uranus. Weighing about 90 mg, Uranus is a 5 mm ball -- about the size of Facebook's "World" button in the upper-right corner of the screen.

As we begin the final stretch of the driveway, 450 meters from the house, we pass under the Rimpells trailer and the orbit of Neptune. Neptune is about the same size as Uranus, but weighs a bit more (100 mg) and its orbit takes it all the way out here.

Finally, about 600 m from the house, we reach the Kuiper belt, and Pluto, a tiny 250 µm ball that weighs just 13 µg. It passes by this point just once every 250 years. With that, the driveway ends.

3. AND BEYOND ...

A light year in the real world is about 10^16 m; this is almost 1,000 km in the scale model. That's about the distance from the house (near Laytonville, CA, USA) to the border of Mexico. Alpha Centauri, the closest star system to us, is 4.3 light years away, which is the distance to New York City in the model.

So how far is it to the edge of the observable universe? Much further. Much, much further. The radius of the observable universe is about 45 billion light years or 450 Ym (that's the largest SI unit prefix - "yotta", meaning 10^24), a distance is so vast that words like "vast" don't do it justice. In order to represent the observable universe, our scale model would have to extend out about as far as the real Alpha Centauri. In all directions.

(*) I have rounded all numbers for simplicity. If my calculations are correct, the rounded numbers are within 6% of the true value, as it is currently known.

Diagrams made with Keith Enevoldse's ThinkZone's Solar System Scale Model Calculator (http://thinkzone.wlonk.com/SS/SolarSystemModel.php) and Google Earth.