The Toilet Paper Solar System
The Toilet Paper Solar System
(A 'distance/planet-size' scale model of the Solar system)

Inter-planetary travel in our time is pretty much just a fantasy relegated to sci-fi books and Hollywood movies due to the reality of the almost unimaginable distances between the planets in our Solar system and our current insufficient level of technology to traverse them. Even the unmanned NASA explorer vehicle/instrument named Voyager II, traveling at nearly 80,500 km/h across our Solar system, took over 12 years just to reach the planet Neptune .

Those distances are beyond our common cognition/experience and consequently we struggle to envision them coherently.

So is there any way to make these vast distances relatable? Well… perhaps we can find something in our day-to-day life that could be used to create a scale model to represent those distances and sizes. This then may give us some perspective as to what those size/distance dynamics are really about out there.

What is challenging in making a scale model of the Solar system is that the model be correct in portraying huge planetary distances but also show the correct relative size/diameter of the planets within it at the same time. Once you solve the problem of displaying the distances properly and 'to-scale' in a model, you are then challenged to correctly scale the size of the planets and Sun in the model to accurately reflect their sizes in proportion to these distances as well.

So how do we start?

Well, firstly you need a medium for the model to represent distance. It must be consistent in length and replicable. You need to be able to lay it out in a continuous, regular manner and it must display the reality of the scale.

Thinking it through, I came up with a common-to-find, easy-to-get item that I think would be very adequate for this: simple rolls of toilet paper.

A roll a toilet paper has many equal squares of tissue attached together in a long roll that you can use as a visual representation of distance if you roll it out in a long line across open ground (each individual sheet is about 10 cm (4 in) wide and you can declare each one to represent a specific number of actual kilometers out there). So walking along the laid out tissue paper, you’d be able to see each square by the next and realize that the distance being represented is surprisingly vast.

Next, you’d need to find globes or circles of various diameters (i.e. basketballs, baseballs, marbles, peas, seeds, tennis balls, etc., or hoola-hoops, or custom made circles of some sort) to represent the Sun and the planets in your model. With all this, a person could then lay everything out in a big schoolyard, parking lot, or field and create a fairly accurate scale model of the entire Solar system. Finally, you would be able to visualize and conceptualize the proportions of our Solar system more palpably.

Just a ‘heads up’:
Keep in mind that whatever globe or object you select to represent the Sun then becomes the base scale of the entire model. The diameter of your model-Sun represents the diameter of the real Sun in kilometers and so this size scale must be transferred to the toilet paper sheets and each individual planet representation too! It thus becomes the scale for the entire model. This is very important to keep in mind when striving to make the entire thing accurate.

Ok… so here are some specs for you to use if you decide to try this project out some afternoon. The first thing you’ll need are the ‘stats’ (specifications) that astronomers have actually calculated for our Solar system to date.

Here they are (sourced from NASA website):


            Diameter: 1,390,500 km
            Location: it is at the start or center of our Solar system and model.


            Diameter: 4879 km
            Distance from Sun: 57.9 x 10^6 km


            Diameter: 12,104 km
            Distance from Sun: 108.2 x 10^6 km
            Distance from previous planet: 50.3 X 10^6 km


            Diameter: 12,756 km
            Distance from Sun: 149.6 x 10^6 km
            Distance from previous planet: 41.4 x 10^6 km
            Moon Diameter: 3475 km
            Moon distance from Earth: .384 x 10^6 km (avg.)


            Diameter: 6792 km
            Distance from Sun: 227.9 x 10^6 km
            Distance from previous planet: 78.3 X 10^6 km
            Moons: 2


            Diameter: 142,984 km
            Distance from Sun: 778.6 x 10^6 km
            Distance from previous planet: 550.7 X 10^6 km
            Moons: 67


            Diameter: 120,536 km
            Distance from Sun: 1433.5 x 10^6 km
            Distance from previous planet: 654.9 X 10^6 km
            Moons: 62


            Diameter: 51,118 km
            Distance from Sun: 2872.5 x 10^6 km
            Distance from previous planet: 1439 X 10^6 km
            Moons: 27

Neptune :

            Diameter: 49,528 km
            Distance from Sun: 4495.1 x 10^6 km
            Distance from previous planet: 1622.6 X 10^6 km
            Moons: 14


            Diameter: 2370 km
            Distance from Sun: 5906.4 x 10^6 km
            Distance from previous planet: 1411.3 X 10^6 km
            Moons: 5


So let’s go through an abbreviated, short example construction:

Suppose you’ve found a 1 meter wide Sun for your model (a globe of some sort).


Remember that the real Sun is actually 1,390,500 km in diameter.

This model Sun now becomes the scale for your entire model!

The Sun      1,390,500 km in diameter      109
 Earth      =    12,756 km in diameter     =   1  

This calculation shows the Sun is 109 times wider than the Earth.
So if our model Sun is 1 meter wide, our model Earth has to be 1/109th that size
or 9.2 mm (or almost 1 cm in diameter).

This now gives you the info of what you need to look for, for material, to represent your 'model-Earth'. You need to find a marble or similar sphere (oak tree nut perhaps?) that is just under 1 centimeter in diameter. The closer you get to the exact size, the better representation of reality your model is.

(And so it goes for all the rest of the objects representing planets and moons in your model…)

Now let’s deal with distance issues within your model.

Let’s look at the toilet-paper-tissue sections.

If the Sun is actually 1,390,500 km in diameter and the Earth is actually 149.6 x 10^6 km or 149,600,000 km from the Sun, and in our model the Sun is a 1 meter wide representation, and each toilet-paper-tissue-square is 10 centimeters wide, well then… our 'model-9.2-mm-wide-Earth' needs to be positioned at:

 Model Sun           1 meter            10
tissue width      10 actual cm.   =  1


     the real Sun                       1,390,500 km in diameter    10
a tissue square represents  =         139,050 km          =       1

(Side note: You might notice how tiny some of the model planets and moons end up being at this scale i.e. the Moon, Mercury, Pluto, etc. If you find them to be too small to work with, you can always increase the size of the Sun in your model and then be able to proportionally increase the size of all the planets as well. But beware; the distance between planets in your model will then increase substantially as well.)

So one sheet of tissue (10 cm wide) represents 139,050 km.

The distance of the Earth from the Sun is 149,600,000 km.


149,600,000 km      1076
 139,050 km     =       1 

So if you use a 1 meter wide Sun in your model, you’ll need to lay out 1076 squares of toilet paper in a row on the ground and then place your model Earth (a marble? an oak nut?) on that 1076th square to represent its correct size and its proper distance from the model-Sun in proportion to the real thing. These will be 107.6 meters apart from each other in this case!

I think you're set with this info.
Try out the model... I have. It's startling and a bit humbling.


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