A Scale Model

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Critical Thinking Questions

(Think about these carefully before you consult the answers below)

QUESTIONS

1) The planets close to the Sun, including Earth, are rocky planets with high density. The planets farther away, such as Saturn, have low density. Could a low density object, say an Earth-sized ball of Styrofoam tm , orbit as close to the Sun as the Inner Planets? <answer>

2) Can you imagine a scenario in which the all planets orbit a star are essentially the same density, say all high or all low density? <answer>

3) Saturn has a very low overall density, less than that of water. Frequently we hear the statement that Saturn could float on an ocean if we had an ocean large enough. Is this really true? <answer>

4) Try this thought experiment. Take two identical glass jars with lids. Fill one with water and weigh it. Then fill the other jar with just enough pennies so that it exactly matches the weight of the first jar. Now put the lids on both jars. The question is, which jar is more dense? <answer>

ANSWERS

1) There certainly is no reason to forbid such a scenario, as density has nothing specifically to do with the orbital mechanics. (We consider, as Newton did, that the gravitational forces act on a body as if all its mass were concentrated at one point at its center.) While subject to the varying gravitational tugs from other planets, and subject to the minute retarding effects of the interplanetary medium, a low density object should be able to orbit just the same as a high density object as long as the total mass was low compared to that of the Sun. However, as you have learned in chapter 7 of your text, there are specific reasons for the inner or terrestrial planets having high density compared to those farther out.

2) Of course. There is no reason that this could not happen. The density of a planet is dependent on the conditions of its creation, so most any scenario is possible. However, very low density planets close to their stars are unlikely because the energy from the star will drive away the volatile materials that usually lower the planet's overall density. More massive objects, with greater gravitational forces, could maintain more of the low-density volatiles, but at the same time the strong gravity likely will constrict the volume of the object with the result of a higher density. Still, under the right circumstances, it is possible for all the planets in a stellar system to have the same density. It probably isn't likely, but there really is nothing to forbid it.

3) While it is true that an object with the density of Saturn would float on water, Saturn would not for a couple of reasons. First off, you would need an enormous planet with an ocean at least deep enough for Saturn to float in. This in itself is almost inconceivable, and likely would require an object so massive that it could not exist as a planet, but rather would condense into a star itself (or a pre-stellar object known as a brown dwarf). And secondly, Saturn is not a solid object like a Styrofoam tm ball. The outer regions have very low densities, while the inner portions of the planet have densities higher than water. Thus if you could find a ocean large enough, the core of Saturn would sink while the outer layers either would escape into space or dissolve into the ocean. So the idea of Saturn floating on an ocean is helpful in imagining the planet's density -- but the idea is "all wet."

4) OK, it's a trick question. They both have the same density. The mass within the jars is distributed differently (the water v. the pennies), but since both jars are the same size and enclose the same volume, and are the same mass (as evidenced by weight), then they have the same overall density.

 

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