Exploring Comets Part 4
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Density, Porosity and Strength

This article describes three basic properties of Tempel 1: density, porosity and strength; important because they give an insight to where, when and how comets were formed.

Mass

The previous article described the physicist's idea of what mass is. Mass is measure of how much stuff an object contains by describing how it responds to the gravitational pull of another object or how much force must be applied in order to change its speed or its direction of motion.

What's Density?

Let's make your intuitive idea of density precise.

Density is how much mass is packed into an object of a stated volume. For example: imagine two standard size baseballs, one made of lead and the other made of glass. The baseball made of lead would be harder to throw than a baseball of the same size made of glass. That's because the lead baseball has more mass in the same volume than does the glass baseball. We say that the lead ball is denser than the glass ball.

To measure density of an object, we simply divide its mass by its volume. To illustrate, let's consider calculating the density of glass and lead. Here you have to state how you measure mass, for example, in pounds-mass or grams, and how you measure volume, for example, in feet or cubic centimeters.

To put these units into perspective, first note that a centimeter is roughly 4/10 of an inch and a gram is roughly the mass contained in a cube of water that is one centimeter by one centimeter by one centimeter.

If you have a cube of lead that is 3 centimeters on an edge, it has a volume of 3x3x3 = 27 cubic centimeters. If you measured its mass it would be about 230 grams. The density would then be the mass, 230 grams, divided by 27 cubic centimeters or about 8.5 grams per cubic centimeter.

What makes things more interesting is that the density of water is about one gram per cubic centimeter. So a cup of lead has 8.5 times the mass of a cup of water. If they stood side-by-side, Earth would pull on the lead with 8.5 times the force than it would pull on the water. In that case the cup of lead would weigh 8.5 times the cup of water.

Note that it doesn't matter whether the object is liquid, gas or solid.

I have a foam sponge that I wash my car with. Its mass by the kitchen scale is 30grams. It measures 5cm x 12cm x 16cm so its volume is 960 cubic centimeters. Dividing the sponge's mass by its volume we get a density of 0.031 grams per cubic centimeter. Not very dense considering that water is 1 gram per centimeter. More about that sponge in a bit.

Densities in the Solar System

To put densities in the context of the solar system consider the following table.

 Density - grams per cubic centimeter WATER 1.0 PLANETS Mercury, Venus 5.4 & 5.2 Earth 5.5 Mars 3.9 Jupiter, Uranus, Neptune 1.3 - 1.6 Saturn 0.69 SATELLITES Earth 3.3 Mars 1.9 & 2.2 Jupiter Largest four 1.8 to 3.5 Most others 1.3 to 3.5 Amalthea 0.89 Saturn 0.63 to 1.9 Uranus, Neptune, Pluto 1.3 to 2.0 ASTEROIDS About a dozen 1.4 to 3.6

Why we want to know the density of Tempel 1

Density is one of the properties used to identify similarities and differences between solar system objects. Other properties to consider include the direction in which satellites travel around planets and the shape of comet or satellite orbits.

Cases of similarity include those between Pluto and Kuiper Belt Objects, which are small, asteroid size objects recently discovered in the region well beyond Neptune. It is now thought by some that Pluto may be the largest of the Kuiper Belt Objects.

For a case of differences we note that Earth's satellite, the Moon, differs enough from the satellites of Mars to indicate different origins. Some theorists hold that the Moon was produced by a collision between Earth and a Mars-size object. However, the satellites of Mars appear to be captured objects.

Porosity

Little is known about the porosity of other solar system objects in general and about comets in particular.

What is porosity?

We say an object is porous if it has a lot of empty space in it.

Consider again the sponge mentioned above. Let's say that the air in it is just empty space. If I could squash out all the empty space (air) from the sponge, its squashed volume would be a lot less. I approximated that squashed volume by standing on the sponge and squeezing out, approximately, all the air that's in it. Now it measures only 1cm x 12cm x 16cm so its volume is only 192 cubic centimeters.

The empty space is the difference between the squashed and un-squashed volumes or 768 cubic centimeters.

To get a number that measures porosity we simply divide the squashed volume by the un-squashed volume. In the case of the sponge, the porosity is 0.8. If expressed as a percentage, we could say its porosity is 80%, or the sponge is 80% empty space.

Sand has a porosity of about 40%. The porosity of some types of lunar samples ranges from 14% to 24%. For other types, porosity can be as low as 5% or as high as 46%. Porosities of meteorites have been measured and range from zero to 24% but half of the samples measured below 6% and half measured above 6%.

Porosity and Structure

When thinking about porosity you must be careful in knowing what object you're referring to. For example, there is the porosity of Tempel 1 as a whole, its bulk porosity, and the porosity of its ices or its rocky material - its component porosities.

As illustrated above, nearly every object has some empty space in it. Remember the lunar samples? However, an object such as a comet or an asteroid may not have the same porosity everywhere within it. What are some of the interesting structural possibilities that we can imagine?

The bulk porosity of Tempel 1 might be influenced by several kinds of structural features. We can imagine cracks such that each side touches the other with no space between them. A crack like that might be produced by expansion and contraction as the comet heats up when it draws near the sun and cools when it recedes from the sun.

We may also imagine cracks such that the sides of the crack do not touch. In this case the space between the sides might be filled with ice, dust or rocky objects. Bulk porosity may also be affected by the presence of an encrusted surface layer of the comet that has been produced by the heat of the sun, cosmic rays or the atomic particles that are continuously shot out from the sun.

Another phenomenon that can affect Tempel 1's porosity is the presence of holes from which spew forth jets of gas and dust propelled by the gas.

In addition, bulk porosity may be affected by the presence of cometesimals, "baby" comets, drawn together by their own gravity or stuck together as the result of collisions.

Why we want to know the porosity of Tempel 1

Porosity helps determine the rate at which a comet's ice turns into gas. Porous materials, being better heat insulators than solid materials of the same kind, restrict the rate at which the sun's heat is transferred from the comet's surface to its interior thus helping to determine the rate at which gas is produced from solid ice. If a lot of gas is produced there will be a luxurious coma and tail. Also, when gas flows more rapidly, it is able to erode dust more rapidly from the comet's interior.

Porosity affects the size and shape of the craters made by impacting objects such as meteoroids, other comets or Deep Impact's impactor. In extreme cases, if a comet is very porous, its material will compress in front of an impacting object and in doing so will absorb energy that would otherwise be used to excavate a crater.

Strength

Two kinds of strengths are of importance in comet studies: tensile strength and shear strength.

Tensile strength measures a material's ability to resist being torn apart. Suppose you grab the above-mentioned sponge at each end and pull in the horizontal direction. If you are strong enough the sponge will come apart. Another example is tensile strength of a rope. A rope's tensile strength rating is important because it tells you the maximum weight it should be able to support.

In comet studies, tensile strength is of interest because it measures a comet's ability to be torn apart by the gravity of a nearby planet. The tearing action in this case is because the planet's gravitational force on the nearer side of the comet is slightly greater than the force on the farther side of the comet. Comet Shoemaker-Levy 9 was torn into more than 20 pieces before Jupiter's gravity pulled it to the surface of the great planet in 1994.

To understand what shear strength is, again grab that sponge but this time hold your hands so that they touch. Now raise one hand and lower the other. The sponge in one hand rises and the sponge in the other goes down in a shearing action. If you were strong enough, the shear strength of the sponge would be exceeded and the sponge would be torn in two.

A similar thing happens in the cratering process. As the gas in the ejecta rushes out of the crater it rubs against the crater wall. The rubbing force is a shearing force since it is parallel to the wall. But, because the shear strength is exceeded, material is torn from the wall and is swept away as part of the ejecta. It's like a river eroding its bank.

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