There are many units of measurement in common use, so, whenever you quote the value of a physical quantity, you should always take care to include the unit as well as the number multiplying that unit. It is no use being told that a distance is 5.
The unit is at least as important as the number. In scientific work there are several internationally agreed conventions for the definition of units and the way in which units should be used and represented when writing down the values of physical quantities. The most widely adopted system of units is known as SI, which stands for Systeme International. This is based on seven carefully defined units that include the metre for length , the second for time and the kilogram for mass.
The other four base units relate to luminous intensity i. The recognised abbreviations for the metre, the second and the kilogram are m, s and kg, respectively. In all cases, units should be written in the singular form, so it should really be 5. In calculations, units should be treated in the same way as numbers, so the result of dividing 6.
The most common derived units are sometimes given their own names and symbols. The angular unit known as a radian is an example, since angular size can be equated to the result of dividing one length a diameter by another length a distance. To do the next activity, you need to know that the Moon's diameter is km. You may wonder how this can be measured from the Earth.
In principle, it is a surprisingly easy measurement to make. First, you have to find the diameter of the Earth, which can be worked out by measuring how much its surface curves. You may be surprised to learn that this measurement was made in about BC by the Greek astronomer Eratosthenes, and that his value was quite close to our modern measurement of km for the equatorial diameter, which is slightly bigger than the polar diameter.
The sizes of the Earth and the Moon can be compared by looking at the Earth's shadow on the Moon's surface during a partial eclipse of the Moon see Figure A careful measurement of this kind reveals that the Earth's diameter is 3. This activity needs to be done when the Moon is clearly visible in the sky. It need not be done at night and, in fact, can be easier in the day or at twilight.
Set up an arrangement with a coin fixed to a rod so that the coin just 'eclipses' the Moon. Figure 22 shows one possible set-up. Observing from one end of the rod, try different coins until you find one that is the right size to eclipse the Moon when fixed somewhere on the rod.
Then adjust the position of the coin until it just blocks your view of the Moon. This is less easy than it sounds, as there will always be some haze visible around the edge of the coin - try to get the best match.
Measure the distance from the coin to the end of the rod where you have placed your eye, and measure the coin's diameter. Record your values like this:. You now have the measurements that will enable you to calculate the angular size of a coin that has the same angular size as the Moon. Use your two measurements on the coin to calculate its angular size in degrees, using the formula introduced earlier, adapted to the current case, i.
Your answer should be about half a degree 0. Any value between 0. This is also your measurement of the angular size of the Moon. So, write down:. I spent a while thinking about the problem and trying to determine "how big an object is at feet" but you can't have something be, for example, 4 inches at a distance of 0 feet because it all mattered how far the 4 inches away was first.. I was curious about this because I wanted to know if a video game was using a different angular size visual size than real life in order to make it harder to use something like a bow and arrow beyond feet.
The former needs some reputation, but the latter can be done once you are stisfied with an answer to one of your questions. You can still switch that check mark if a better answer turns up. They don't have a built-in angular size per se, and the developers might have different ideas of your placement than yourself. But for most games they likely face a compromise: allow users to look around a bit, even though a monitor covers only a rather small fraction of the visual field.
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It follows that twice the distance with the same object would appear half as wide across your vision. That made sense when I first wrote it, but not quite so much when I reread it. Oh well. Think of it this way: If you halve the radius of a circle, you halve its circumference the distance around it. It would only take half as many suns to fill up the circle all the way around the same angle: degrees , so each one would take up double the angle compared to what it would have at the distance you started with.
Think of it this way: the apparent size of the Moon and the Sun in our sky is about the same has to be, or else solar eclipses couldn't happen. Moon is 2, miles in diameter and around , miles away. Sun is , miles in diameter and 93 million miles away, so it's times larger and times further away approximately, but then, the figures I've listed for size and distance are themselves approximate. So, that tells you that the apparent size of the object varies linearly with distance. Think of it this way: if the lineality of the objectitude matches the inversal functiative, then the obtusal archetime rectomates across multidecimal projectinates, thereby reversionating spheritoid diagonicities.
Got it? Look at it this way: if you half the distance to something, its apparent size doubles. In case the other answers were confusing. This is barring refraction, which is a major issue with looking at the sun through our atmosphere, especially at an angle near the horizon.
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