Power from the Sun

Teacher's Notes

Things to emphasize

All events on Earth, on all scales, living and non-living, are driven by energy from the Sun.
All atmospheric events on Mars are driven by energy from the Sun and the rotational motion of Mars on its axis (Coriolis effect)
To live on Mars one must make effective use of solar energy for food production, machine operation and related dynamic processes such as the extraction of metals and oxygen from the environment (the soil and atmosphere of Mars).

The objective of this activity is to show students how to determine (a) how much energy is available to the astronauts working on the surface of Mars, and (b) to determine the total output power of the Sun.

Consider the Following

Whenever one can sample items on a small portion of a surface (any surface) over which the item being sampled is assumed to be uniform in distribution (over the whole surface) , the total quantity of the items can be calculated, if both the total area of the surface and the area of the sample are known.

For example, if one samples 1m² of a corn field that has a total area of 500m² and finds 6 corn stocks in that 1m² then it is easily calculated that the field contains 500 x 6 = 3000 corn stocks.

This is the basis of a process that is widely used in science to determine quantities that are either too large to count, or too difficult to determine directly.

Activity

The Luminosity of the Sun

Transparency Master	The Calculation Observations taken from space (at the Earth's distance from the Sun) have shown that the Sun illuminates each square metre with 1.3kW of power (also expressed as 1300 joules per second per square metre. This is known as The Solar Constant ). In our imagination we could capture all the Sun's energy if we surrounded the sun with a huge sphere, its radius being equal to the radius of the earth's orbit. Since we chose the radius of the sphere to be equal to the radius of the Earth's orbit, we know that every square metre of it would receive 1.3kW of radiant power.

Transparency Master

The Calculation

Observations taken from space (at the Earth's distance from the Sun) have shown that the Sun illuminates each square metre with 1.3kW of power (also expressed as 1300 joules per second per square metre. This is known as The Solar Constant ).

In our imagination we could capture all the Sun's energy if we surrounded the sun with a huge sphere, its radius being equal to the radius of the earth's orbit.

Since we chose the radius of the sphere to be equal to the radius of the Earth's orbit, we know that every square metre of it would receive 1.3kW of radiant power.

A REALLY big number!

The formula to calculate the surface area of a sphere is given as 4 x pi x r² where pi=approximately 3.14, r = radius of the sphere and r² means r x r.
Using the radius of the Earth's orbit as 150,000,000,000 metres (and the formula above), calculate the surface area of a sphere equal to the radius of the Earth's orbit. (This is a huge number with lots of zeros. Care needs to be taken to multiple r x r first, then multiply the result by 4 x pi. To calculate the total luminosity of the Sun multiply the area of this hypothetical sphere by the solar constant.
Set up a 60W lamp in the classroom. Set up a screen made of Bristol board or cardboard which is 1m x 1m. Set the screen 2m away from the lamp.
1. What would be the surface area of an imaginary sphere 2m in radius centered on the lamp?
2. Assuming the lamp radiates all 60W as light, how much light energy reaches the screen every second?
3. How much light energy would reach the screen every second if the screen were 4m away?
How would one sample items (for purposes of calculating a total quantity) when the individual items are not uniformly distributed over a surface?