Learning Objectives

Upon completion of this lesson, the student will be able to

1. State what the reflectance (albedo) of a planet or moon depends on.

2. Interpret tables containing lists of densities, reflectance, and albedos and related these quantities to identification of planetary materials and planetary compositions.

3. Show an understanding of phase diagrams by stating the phase of any given material based upon a stated temperature and pressure.

Concepts Covered:

• Reflectance

• Density

• Phases of Matter

• Take the Quiz == page down to the bottom of these lecture notes.

Our Sun radiates most of its energy at visible wavelengths, but a significant amount of radiation at infrared wavelengths is also emitted. We have built satellites that take advantage of those parts of the electromagnetic spectrum where the Sun dominates. The planets and moons in our solar system, in general, shine because of the amount of the Sun's light they reflect. So, in order to understand the planets, we must understand the reflective properties of the planets at these wavelengths.

The amount of reflectance from a planet or moon depends on what percentage of the incident radiation is absorbed or transmitted versus how much is reflected off of the body. A ratio of reflected radiation to incoming radiation is often used to describe the reflectance or albedo of a body. A perfect reflector would have a reflectance of 1; a body that reflects very little of the light that hits it would have a reflectance of 0.1 or lower. The albedo of surfaces can also change depending on the angle of the viewer with respect to the Sun (and, as we will see when we discuss remote sensing in more detail, the angle of the surface to the satellite beaming radiation). A mirror-like surface reflects incident visible radiation in almost one direction; fresh snow reflects light in nearly every direction.

Here are some subjective comparisons of reflected energy at infrared (3 to 4 microns, where 1 micron is equal to a millionth of a meter) and visible (400 - 700 nanometers, where 1 nm is equal to a billionth of a meter):

Density

In the context that we are concerned with, what does density mean? What quantities are needed to calculate the density of an object?

How does one calculate the density of a planet? What quantities are needed? It is straight-forward to calculate an approximate volume of a planet or a moon: we know its distance, we can measure its radius, and thus calculate its volume. But, how do we determine the mass of a planet or moon? To do this, we must preview Newton's version of Kepler's Third Law:

where p is the orbital period in seconds, a is the average distance away in meters, M₁ and M₂ are the masses of the two objects in kilograms (M₁ usually being the more massive object), and the gravitational constant, G is:

Solve the following problems by filling in the blank columns:

What if a planet does not have a moon? How do we measure its mass? For example, Mercury and Venus? How do we determine the mass of an asteroid? If we can calculate the mass of the Earth by assuming that the mass of the Moon is negligible by comparison (that is, ignoring it by setting it equal to zero), how do we turn the equation around and get a measure of the mass of the Moon?

OK! We now have a measure of the mass of the body, all we need is the volume:

.

When using the density of a planet or moon as one method to infer its composition, we must take into account many other factors other than just the density of an element, mineral, or rock. For example, the density of the Earth is about 5.5. We could probably mix up some nickel and titanium and get that density, but our publishing these conclusions certainly would provide fodder for planetary scientist humor and our changing disciplines.

There are a number of really great and imaginative web pages with the Periodic Chart of the Elements. Check some of the following pages out for more information:

• www.webelements.com
• Los Alamos National Laboratory
• Pictorial Periodic Table
• Visual Elements Periodic Table (bandwidth intensive: need a direct, on-line connection)

Phases of Matter

Solid

Atoms or molecules are held in place, closely packed together; bonds are tight. A solid has a fixed shape and volume.

Liquid

Atoms or molecules remain together, but move relatively easy. A liquid will assume the shape of its container, but has a fixed volume depending upon the temperature.

Gas

Atoms or molecules move essentially unconstrained. Low density state of matter, having neither fixed volume or shape. A gas will expand to fill the available volume.

Plasma

Molecules are dissociated into component atoms; electrons move freely among positively charged ions. The plasma state pertains to high energy gas, more relevant to astrophysics than planetary sciences.

Phase Diagrams

The following phase diagrams of water and carbon dioxide and the information provided here were adapted from those found at University of Idaho Chemistry Department.

At the left are two phase diagrams for water. On the lower graph we have specified the line for 1 atmosphere, and we can see that the point where this crosses the melting point line is 0 degrees C (273 degrees K), and the point where the 1 atmosphere line crosses the boiling point is 100 degrees C (373 degrees K). Note at the triple point of water, as long as the atmospheric pressure stays low, no matter what the temperature is, water sublimates from a solid to a gas. Remember this for future discussions on the possibility of liquid water on the surface of Mars, where the atmospheric pressure is 0.6% that of Earth's, or roughly 4.56 mm.

The melting curve of ice/water is very special. It has a negative slope due to the fact that when ice melts, the molar volume decreases. Ice actually melts at a lower temperature at higher pressures. (Think of how an ice skater glides along on her skates; the ice momentarily melts due to her weight, and then refreezes when the pressure is released.)

A phase diagram for carbon dioxide illustrates the more common forward slope of the melting point line. Notice that the triple point of carbon dioxide is well above 1 atmosphere. Notice also that at 1 atmosphere carbon dioxide can only be the solid or the gas. Liquid carbon dioxide does not exist at 1 atmosphere. Dry ice (solid carbon dioxide) has a temperature of -78.5 degrees F (-61 degrees C, 212 K) at room pressure, which is why you can get a serious burn (actually frostbite) from holding it in your hands. Although carbon dioxide liquid doesn't exist at normal room pressures, it does exist at slightly elevated pressure.

At left is a qualitative phase diagram for nitrogen. Its triple point occurs at an atmospheric pressure of 0.123 and a temperature of 63.15 K. At lower pressures, nitrogen will sublimate. Remember this point when we discuss Triton, a moon of Neptune, towards the end of the quarter. The normal melting and boiling point for nitrogen (that is, at 1 atmos.) is 63.3 and 77.4 K (-320 degrees F!!) respectively. Liquid nitrogen is cold.

(See also the phase information at Ohio State University for more advanced phase diagrams.)