### The solar system: It's delicious

My darling mother sent me a clipping from Parade magazine in which Marilyn vos Savant of "Ask Marilyn" described the solar system using fruits and vegetables:
If the sun were a pumpkin about a foot wide, Mercury would be a tomato seed 50 feet away; Venus, a pea 75 feet away; Earth, a pea 100 feet away; Mars, a little raisin 175 feet away; Jupiter, an apple 550 feet away; Saturn, a peach 1,025 feet away; Uranus, a plum 2,050 feet away; and Neptune, a plum 3,225 feet away. Pluto stays in the fridge.
Poor Pluto.

[A bowl full of Earths. Photo by Dunemaire.]

Though this heart-healthy analogy of the solar system was terrific at relating the size of the planets and our sun, it didn't do much to help me understand the distance between the planets. Here, my colleague and former PhysicsBuzz contributor Quantum came to the rescue with this solar system calculator.

"I wonder if I could fit the whole solar system onto a tennis court," I thought. I pretended the Sun had the same diameter as a tennis ball - 2.63 inches - and cranked up the calculator. The inner planets (Mercury, Venus, Earth and Mars), as it turned out, would indeed fit in one half of the court if the tennis ball Sun were resting on the baseline.

[The inner planets can all play on the same court.]

Neptune, however, would have to be 10 courts away, assuming they were stacked lengthwise, baselines touching. What's more, Jupiter and Saturn, each pea-sized, would be the only two planets visible. (If the tennis court was green, they would blend in and even Roger Federer would struggle to hit them from 3 courts away.)

As tempting as it is to linger on thoughts of serving a dust mite-sized Earth, let's get back to the food analogies. For Quantum's last birthday, he and some friends made a scale model of the solar system out of desserts.

[My kind of solar system. Photo courtesy of Quantum.]

Beyond focusing on making the planets the right size, they also considered their densities. (The density of an object is its mass divided by its volume.) The gas giants (Jupiter, Saturn, Uranus and Neptune) with their smaller densities, were made of regular cake. The inner rocky planets - the denser bunch - were made of brownies. So too, as you can see, was the asteroid belt. (Yum!)

[The gas giants were made out of spongier cake as they are less dense planets, while the rocky inner planets were made out of denser brownies. It is unconfirmed how the Death Star was made. Photo courtesy of Quantum.]

Though they did include Pluto in the birthday cake solar system, Quantum and friends didn't bake a sun because to keep everything to scale a 10 foot tall cake would have been needed. That's a lot of icing!

[Don't they look so much more delicious now? In this artist's rendering, the planets (and Pluto) are shown with their correct orbital distances relative to the sun in the background (though their sizes are exaggerated) and with correct relative size in the foreground. Photo credit: NASA.]

1. The vegetable/fruit solar system is not scaled correctly (which you can test with that exploratorium website you linked!). If the Sun is a 12 inch pumpkin, then the Earth is only 0.1 inches across, and Jupiter is only 1.2 inches across. Those are a lot smaller than a pea and an apple. It seems like the Sun might need to be about 3 feet across for a pea and apple to be right for Earth and Jupiter. The separations between the planets seem to be ok in the fruit/vegetable model though.

2. @ Steven - Good catch. We could always get a bigger pumpkin (I think you're right about 3 feet), or instead compare the Earth to a single couscous (a cous?) or maybe a Nerd candy. But then we're getting away from the produce isle...

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