- 1. The intensity of sunlight has been carefully measured for many years by detectors on the ground and on satellites that orbit our Earth. Measurements made by detectors in space are much preferred to those made by detectors on Earth's surface. Why do you think that is? Be specific.

2. To correctly measure the intensity of sunlight at the Earth, a satellite must be positioned the same distance from the Sun as is Earth. Obviously, a satellite circling, say, 200 kilometers above Earth's surface might be as much as 200 kilometers closer to the Sun or 200 kilometers farther from the Sun than is Earth, depending on where the satellite is situated along its orbital path. Given that Earth's average distance from the Sun is about 150 million kilometers, do you think a variation of 200 kilometers matters to a measurement of the Sun's intensity? Support your answer by computing what fraction 200 kilometers is of the Earth-Sun distance.

####### Measuring the Solar Constant

The attached graph shows the measured distribution of solar energy over a wide range of wavelengths. The graph's horizontal axis indicates the wavelength of the energy in units of nanometers . (A nanometer, abbreviated nm, is a billionth of a meter: 10 meter.) Wavelengths visible to the human eye - the optical portion of the spectrum - fall -9 within the range of about 350 nm (violet) to 700 nm (red).

3. On the graph's wavelength axis, draw marks to indicate the range of the optical portion of the Sun's spectrum. If the eventual goal is to compute the Sun's overall luminosity L , why is it necessary to measure the Sun's emission with detectors that are sensitive to both optical and non-optical wavelengths?

The vertical axis of the attached graph is the intensity of the Sun's light expressed in units of watts per square meter per nanometer , abbreviated W/m /nm. There are three components to this rather cumbersome unit: 2

• The number of watts (W) indicates the rate at which energy is emitted, whether for the Sun or for a household light bulb. That is, a 100 watt light bulb will emit more energy each second than a 60 watt bulb, and will therefore appear brighter.

• The Sun's emission shines in all directions. However, let's focus exclusively on the solar wattage shining on a make-believe light sensor whose shape is a square, one meter on a side. That's what the term per square meter refers to in the graph's vertical - axis unit. That is, we're sampling only the sunlight that shines onto a one - square-meter detector and ignoring the rest.

• The third part of the vertical-axis unit, per nanometer (nm) indicates that the numbers along the vertical axis refer to the sunlight intensity measured within very narrow wavelength segments, each just 1 nanometer wide. For example, the Sun gives out less energy at a wavelength of 300 nm (ultraviolet) than at 700 nm (red): about 0.45 W/m /nm compared to 1.4 W/m /nm. 2 2

To determine the solar constant S - the overall intensity of sunlight falling on a 1-meter square at Earth - we must sum up the various amounts received at all of the individual wavelengths. This is easily done using the graph. In fact, the area of the graph underneath the solar intensity curve represents precisely what we are seeking: the solar constant S , in units of watts per square meter (W/m ). To ease the determination of the area underneath the 2 intensity curve, the graph has been divided into small boxes. Counting these boxes is the first step to achieve a value for the area.

4. Count the number of boxes underneath the solar intensity curve in the graph. For boxes that are divided by the curve itself, you might adopt the following procedure: Estimate what fraction of the box lies underneath the curve. If the fraction underneath the curve is less than one-half, omit that box from the count; if the fraction is greater Than one-half, include the box in the count.

5. All we have determined so far is the number of boxes that lie underneath the solar intensity curve. However, the area of each box represents a specific amount of solar energy that can be estimated from the graph's horizontal and vertical axes. (a) What is the width of each box, in nanometers , according to the graph's horizontal axis? (b) What is

PHY 251, page 4