Physics and Constants Help
Introduction to Physics and Constants
Constants are characteristics of the physical and mathematical world that can be “taken for granted.” They don’t change, at least not within an ordinary human lifetime, unless certain other factors change too.
Math Versus Physics
In pure mathematics, constants are usually presented all by themselves as plain numbers without any units associated. These are called dimensionless constants and include π, the circumference-to-diameter ratio of a circle, and e , the natural logarithm base. In physics, there is almost always a unit equivalent attached to a constant. An example is c , the speed of light in free space, expressed in meters per second.
Table 6-2 is a list of constants you’ll encounter in physics. This is by no means a complete list. Do you not know what most of the constants in this table mean? Are they unfamiliar or even arcane to you? Don’t worry about this now. As you keep on learning physics, you’ll learn about most of them. This table can serve as a reference long after you’re done with this course.
Table 6-2 Some Physical Constants
Here are a few examples of constants from the table and how they relate to the physical universe and the physicist’s modes of thought.
Mass Of The Sun
It should come as no surprise to you that the Sun is a massive object. But just how massive, really, is it? How can we express the mass of the Sun in terms that can be comprehended? Scientific notation is generally used; we come up with the figure 1.989 × 10 30 kg if we go to four significant figures. This is just a little less than 2 nonillion kilograms or 2 octillion metric tons. (This doesn’t help much, does it?)
How big is 2 octillion? It’s represented numerically as a 2 with 27 zeros after it. In scientific notation it’s 2 × 10 27 . We can split this up into 2 × 10 9 × 10 9 × 10 9 . Now imagine a huge box 2,000 kilometers (km) tall by 1,000 km wide by 1,000 km deep. [A thousand kilometers is about 620 miles (mi); 2000 km is about 1240 mi.] Suppose now that you are called on to stack this box neatly full of little cubes measuring 1 millimeter (1 mm) on an edge. These cubes are comparable in size to grains of coarse sand.
You begin stacking these little cubes with the help of tweezers and a magnifying glass. You gaze up at the box towering high above the Earth’s atmosphere and spanning several states or provinces (or even whole countries) over the Earth’s surface. You can imagine it might take you quite a while to finish this job. If you could live long enough to complete the task, you would have stacked up 2 octillion little cubes, which is the number of metric tons in the mass of our Sun. A metric ton is slightly more than an English ton.
The Sun is obviously a massive chunk of matter. But it is small as stars go. There are plenty of stars that are many times larger than our Sun.
Mass Of The Earth
The Earth, too, is massive, but it is a mere speck compared with the Sun. Expressed to four significant figures, the Earth masses 5.974 × 10 24 kg. This works out to approximately 6 hexillion metric tons.
How large a number is 6 hexillion? Let’s use a similar three-dimensional analogy. Suppose that you have a cubical box measuring 2.45 × 10 5 meters, or 245 kilometers, on an edge. This is a cube about 152 mi tall by 152 mi wide by 152 mi deep. Now imagine an endless supply of little cubes measuring 1 centimeter (1 cm) on an edge. This is about the size of a gambling die or a sugar cube. Now suppose that you are given the task of—you guessed it—stacking up all the little cubes in the huge box. When you are finished, you will have placed approximately 6 hexillion little cubes in the box. This is the number of metric tons in the mass of our planet Earth.
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