Earth is our home planet, which makes it very special for us. It circles around the Sun every 365 days. But Earth is not alone in this aspect: seven other planets and some dwarf planets rotate around the Sun as well. In comparison to the mass of our Sun, that of the planets in our Solar System is very small: if you take 1000 dice, you need 998 to build the Sun and only two to build the planets. From just these two dice, you need 2/3rds for the planet Jupiter and just the remaining 1/3rd for the other planets. Our Earth is so small! All planets are bound to the Sun by gravity. Gravity is THE force in space. Earth also has a moon, and it takes the Moon about a month to rotate around our Earth. When you look into the sky, the Moon and Sun seem to be of the same size. This is because although the Moon is 400 times smaller than the Sun, it is 400 times nearer Earth than the Sun is.
The Sun is our star. It shines its light in every direction in space. We on Earth are very lucky to be at the right distance from the Sun: near enough to have liquid water and warmth and far enough not to be burnt by its radiation. The Sun has been a reliable partner of Earth’s for nearly 4.5 billion years now.
This activity is about the sizes of the Sun and Earth and their distance from one another. But it is not about simply comparing numbers: it is about building a model that will show that the Sun is about 1 million times bigger than the Earth. For this, we will actually fill a Sun sphere with lots of Earth balls!
Before we start, we must take a look at the numbers and do some calculations:
Diameter of the Sun: 1.39 million km
Diameter of the Earth: 12,742 km
Distance from the Sun to Earth: 149.6 million km
We see that
The diameter of the Earth is 109 times less than the diameter of the Sun.
The distance between the Sun and Earth is about 100 times the diameter of the Sun.
How many Earths would fit into the Sun?
This is a bit tricky. For a rough hypothetical estimation, divide the volume of the Sun by the volume of the Earth:
This is about 109³ = 1.3 million
If we want to fit real little balls into a big sphere, we must consider that we cannot squeeze the small balls. In reality, there will be space between the balls!
Let us take a look at our chemistry or math book. There, we can find a method to calculate the highest average density that is possible when small Earth balls are packed as close as possible to each other in a big sphere representing the Sun.
This was determined by Carl Friedrich Gauss. The equation means that only 74.05% of the space in our big solar sphere is actually occupied by the smaller balls. The rest is empty.
This, in turn, means that we can pack
small Earth balls into the Sun sphere.
Scales, distances and materials
Thus, there are several possibilities for model building. But with 1 million little blue Earth balls to consider, we will have to take a look at the possible costs. Even if one Earth ball only costs 0.01 cent, the sum will be (more than) 100€!
A good and cheap possibility is using seeds. Unfortunately, we cannot colour them with fluid Earth blue colour because they would germinate. So if the lack of blue colour is acceptable, use white or the smaller black mustard seeds. They are quite spherical (!) and cheap.
Figure 1: Small black mustard seeds. Credit: Natalie Fischer
Figure 2: Measuring the diameter of a seed. Credit: Natalie Fischer
Black mustard seeds have an average diameter of 1.5 mm, so the diameter of your sphere needs to be 109 · 1.5mm = 16.3 cm . To fill a sphere of diameter 16 cm, you need 2.14 L of black mustard seeds. With a bulk density of 0.89 kg/L, the Sun model will weigh 1.8 kg. This is quite heavy for that small a sphere.
1.8 kg black mustard seeds: 18€
16 cm acrylic sphere: 4€
Please note that acrylic spheres are not available in all sizes! You may have to make a compromise because the sphere available is a bit too big or too small for your chosen Earth ball models.
If you want to colour the small balls so they really resemble little Earth-like balls – and I think this is an important detail – you need to use other materials, e.g. polystyrene beads. They are used to fill bean bags or for the retrofit insulation of un-isolated exterior walls. They are around 2.7–3 mm in diameter, so your sphere needs to be around 30 cm in diameter. For a 30 cm sphere, you will need around 14 L of polystyrene beads. Both are available online.
14 L of polystyrene beads: 2€ (27€/300 L)
30 cm acrylic sphere: 25€.
Acrylic colour (dark blue): 2 €
It is clear that the materials (and their costs) influence the scale of your model. Small wooden balls would of course be perfect, but the model will be too heavy (>32 kg) and too expensive (1000 wooden balls of diameter 5 mm cost 12€, and you need 1 million of them!)
A brief check on the distance between the Sun and Earth (100 times the solar diameter) also shows that we have chosen well: 30 meters is a useful distance, because it shows the huge distance between the two celestial bodies and at the same time it fits well in every schoolyard.
To actually calculate the scale of our model, divide the real diameter by the model diameter:
the scale is 1:4 630 000 000.
That means that 1 cm in our model is 46,000 km in reality. When the students travel through this solar system, one step (80 cm) is about 3.7 million km. That’s pretty fast!
How ‘good’ is your model?
This is a very important question. You can even discuss it with older students. Of course, you will be asked if there are really 1 million or – to be exact – 946,202 Earth balls inside the Sun sphere. The answer is NO. But we are pretty close to this number. ;-)
• Polystyrene balls (or seeds) do not all have the exact same size. Some of them are a bit smaller or bigger because of the production process.
• The acrylic sphere is not available in all sizes. For our model with Earth balls around 3 mm in diameter, the acrylic sphere should be 32.7 cm in diameter. Such a sphere was not available. But because the polystyrene balls were a bit smaller than 3 mm on average, this was acceptable.
• When you fill the sphere and shake it, the little balls settle themselves, and you can fit some more in. You must decide when to stop eventually and declare the model finished.
But the quality of the model does not only depend on the exact number of Earth balls you were able to fit inside the sphere!
Why build this model?
It all starts with the question ‘How much bigger is the Sun compared to Earth?’
Of course, you can collect these values from a textbook or from the Internet and compare them. But these are extremely big numbers, hard to grasp even for adults. So you decide to build a model. As stated above, in most cases, you use two balls, a very big one and a very small one. This alone is already very impressive! But we seek something even more impressive: we really want the students to fill the Sun with Earth balls themselves, and we want them and others to see (nearly) one million Earth balls inside the Sun sphere! We will not build a fake model by gluing Earth balls only in the inside of the sphere to give the impression that the Sun is full of Earth balls! We will really do it!
The painting of the model Sun and Earth balls is part of the model building process. We want the models to look as genuine as possible. Of course, you can use the material without colour, for example, if you feel the painting process takes too long or you do not want younger students to work with colour at all. But the yellow colour makes the sphere more intuitively recognisable by the students as the Sun than a colourless sphere. The same applies to the small Earth balls: a blue tiny ball will look more like Earth than a white one. Without knowing the details, you can guess that the big yellow ball represents the Sun and the tiny blue ones, the Earth.
So this model is built to inspire students! To make them really wonder! To actually make them think about and work with the sizes of the Earth and Sun. Even young students can fill the Sun without knowing about the exact number of balls going in. Before the students fill the sphere, let them put their hands into the box with the million balls and glide their fingers through the ball pool. That’s one way to experience the number 1 million!
Older students can also do the calculations behind the number first and then prove it by putting the calculated number of balls (here, 14 L) inside the sphere.
You see, it is not important to fill exactly 946202 Earth balls inside the Sun sphere.