Table of Contents

Sunlight on Earth and Mars

Teacher's Notes

The soil on Mars is incredibly dry and is bathed in the distance by the weakened light of the Sun. Exactly how much sunlight actually reaches the Martian surface? A straight forward activity is presented here, whereby students can determine the intensity of solar radiation on the Martian surface.

For convenience the mathematics has been reduced to a set of simple graphs so that students can focus on the physical concepts involved rather than the mathematical details of this exercise.

This is quite an easy experiment. Excellent results can be obtained in a very short time by simply letting the Sun heat up 500 ml of water in an open pan.

The only mathematical requirement is that students must be able to follow the procedure outlined here and to read simple measurements from the graphs included with this activity.

In this experiment students will make an experimental measurement of the amount of solar energy available on Earth, and then use their experimentally determined value to determine the amount of energy that would be available to astronauts on Mars.

Viking I, Courtesy NASA/JPL

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Things to Emphasize

1. Survival on Mars means utilizing solar energy efficiently. One of the most important pieces of information is the determination of the available solar energy on Mars' surface;

2. All weather events, on all scales, on all the planets are driven by energy
   from the Sun;

3. On Earth all weather events which we experience occur in a layer of the atmosphere called the troposphere;

4. On Earth all agriculture (hence human survival) is dependant upon the weather, which is highly effected by the oceans of the world. On Mars the behaviour of the atmosphere is somewhat simpler because it has no oceans;

5. Without some method of distributing the Sun's energy over the Earth's surface a major fraction of its surface would be uninhabitable. i.e. the equatorial regions would exceed the boiling point of water and the poles would be cold enough the liquefy the atmosphere;

6. A moderate greenhouse effect and atmospheric convection are responsible for making the Earth habitable;

7. Atmospheric convection dominates the weather on Mars;

8. Science investigation involves a multi-step inquiry process: ask an initial question, plan the investigation, record observations and collect data, analyze data to draw a conclusion, and communicate the findings.

Consider the Following

Living on Mars requires that one make extensive use of solar energy since there are no fossil fuels, hydro electric power nor wood (and its related products).

The question then becomes, "How much solar power is available on the surface of Mars?"

The objective of this project is to show students how a simple experiment can make an extremely important scientific measurement; that is, the determination of the Sun's radiant power on the surface of the Earth and on the surface of Mars.

Build an Energy Grabber

Components

The experiment is designed to capture solar energy, and to measure the total amount of energy that the earth receives from the Sun.

An aluminium baking pan (about 30 cm x 30 cm) makes an excellent container. It should be painted flat black on the inside.

Styrofoam pieces can be collected from a variety of sources, especially from vendors of electronic equipment. You may substitute a bed of foam chips in a large box to surround the aluminium pan or an old wool sweater.

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Procedure

1. Add 500 mL of water (which has been allowed to reach the temperature of the outside environment) to the aluminium pan. Record this temperature.

2. Surround the pan with insulating material.

3. Keep the system shaded until the experiment begins.

4. Cover the pan with a thin layer of clear food wrap and fasten it down with tape. Place the container in direct sunlight and record the temperature of the water.

5. Wait exactly 10 minutes and immediately determine the temperature of the water. Record this temperature.

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Solar Angle

During the experiment you will need to determine the overhead angle of the Sun.

A simple method is to stand a thin object, such a pencil, upright on a flat surface. Using a protractor one simply measures the angle that the shadow from the top of the object makes with the flat surface as shown in the figure to the left.

Hint: A piece of string from the top of the object to the tip of the shadow on the flat surface will help in the measurement of the angle.

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Protractor Master

Analysis

1. Calculate the temperature change of the water over the 10-minute
   (600-second) interval.

2. Determine how much energy the water gained using the equation: Energy
   gained = mass (kg) x specific heat x temperature change (see details below).

3. Calculate the energy received per second.

4. Calculate the area of the bottom of the aluminum pan in square metres, (m²) and then calculate the energy that would have been absorbed per m² per second.

After exactly 10 minutes, record the final temperature of the 500 mL water sample, subtract this from the initial temperature to determine the temperature change.

Using Graph 1 to the left, determine the total amount of energy absorbed by the water in joules.

Graph 1

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The energy heating the water has been absorbed over a ten minute interval. Power however is the rate at which energy is absorbed, radiated, or transferred. In other words, power = energy/time (P=E/t) (one watt is equal to one joule per second).

Graph 2 converts the energy absorbed (from graph 1) in ten minutes to absorbed power in watts (W).

Using Graph 2 determine the heating power which corresponds to your observations.

Graph 2

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The observed power is distributed over the surface area of the water. For comparative purposes one must covert this to the amount of power that is absorbed per square metre (m²)

Graph 3 is used to determine the power that would have been received, per square metre, based on the surface area of the water in your experiment.

Graph 3

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To be accurate one must also compensate for the fact that the Sun may not be illuminating the surface of the water from directly overhead, but rather the Sun's radiation is falling at an angle on the water's surface.

As a last step use Graph 4 to calculate your experimental determination of the solar constant at the Earth's surface.

You may assume that the Earth's atmosphere filters out about 25% of the incident solar radiation. From this fact, calculate the absolute value of the solar constant above the Earth's atmosphere.

Graph 4

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Key Ideas

The accurate determination of the solar constant and the ability to monitor changes in the solar constant are viewed to be among the most important measurements in
modern science.

Even slight changes in the solar constant can have a profound affect on the
Earth's climate.

For building computer models of the Earth's energy balance and its affect on weather and climate, a precise value of the solar constant is required if the computer models are
to be accurate.

Topics for Class Discussion

1. What if the solar constant were to decrease? What affect might this have on the Earth's climate?

2. If the solar constant were to decrease, what might one infer about the energy output of the sun.

3. Astronomers have long know that many stars are variable. This means that they vary in their brightness. If there were beings living on planets orbiting around these stars, what would they notice about their "solar constant".

4. Draw a concept map to organize the key ideas for this topic. Start with the Sun and then add and link related concepts, e.g.

   

Solar Power for Space Travellers

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